What do you think?
Rate this book
The Secret Lives of Numbers: A Hidden History of Math's Unsung Trailblazers
A new history of mathematics focusing on the marginalized voices who propelled the discipline, spanning six continents and thousands of years of untold stories.
Mathematics shapes almost everything we do. But despite its reputation as the study of fundamental truths, the stories we have been told about it are wrong--warped like the sixteenth-century map that enlarged Europe at the expense of Africa, Asia and the Americas. In The Secret Lives of Numbers, renowned math historian Kate Kitagawa and journalist Timothy Revell make the case that the history of math is infinitely deeper, broader, and richer than the narrative we think we know.
Our story takes us from Hypatia, the first great female mathematician, whose ideas revolutionized geometry and who was killed for them--to Karen Uhlenbeck, the first woman to win the Abel Prize, "math's Nobel." Along the way we travel the globe to meet the brilliant Arabic scholars of the "House of Wisdom," a math temple whose destruction in the Siege of Baghdad in the thirteenth century was a loss arguably on par with that of the Library of Alexandria; Madhava of Sangamagrama, the fourteenth-century Indian genius who uncovered the central tenets of calculus 300 years before Isaac Newton was born; and the Black mathematicians of the Civil Rights era, who played a significant role in dismantling early data-based methods of racial discrimination.
Covering thousands of years, six continents, and just about every mathematical discipline, The Secret Lives of Numbers is an immensely compelling narrative history.
Mathematics shapes almost everything we do. But despite its reputation as the study of fundamental truths, the stories we have been told about it are wrong--warped like the sixteenth-century map that enlarged Europe at the expense of Africa, Asia and the Americas. In The Secret Lives of Numbers, renowned math historian Kate Kitagawa and journalist Timothy Revell make the case that the history of math is infinitely deeper, broader, and richer than the narrative we think we know.
Our story takes us from Hypatia, the first great female mathematician, whose ideas revolutionized geometry and who was killed for them--to Karen Uhlenbeck, the first woman to win the Abel Prize, "math's Nobel." Along the way we travel the globe to meet the brilliant Arabic scholars of the "House of Wisdom," a math temple whose destruction in the Siege of Baghdad in the thirteenth century was a loss arguably on par with that of the Library of Alexandria; Madhava of Sangamagrama, the fourteenth-century Indian genius who uncovered the central tenets of calculus 300 years before Isaac Newton was born; and the Black mathematicians of the Civil Rights era, who played a significant role in dismantling early data-based methods of racial discrimination.
Covering thousands of years, six continents, and just about every mathematical discipline, The Secret Lives of Numbers is an immensely compelling narrative history.
320 pages, Hardcover
First published April 17, 2023
317 people are currently reading
4900 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 30 of 113 reviews
March 2, 2024
I've got mixed feelings on this one. The blurb was fairly dramatic, almost conspiratorial, claiming that mathematical history was skewed towards white male contributions. I ignored the rhetoric because I did want to read about others' contributions, and that's mostly what I got. The first half of the book follows early mathematical history fairly well, filling in some gaps on early activities that aren't always covered in standard history books. The last half, however, cherry-picked a few women and minorities to focus on, and that's where the historical thread fell apart for me. It's hard as a reader to construct a history in your head when you only have a few examples that popped up here and there. How do they fit into the bigger picture?
The authors were more balanced than the blurb writer about their approach, showing some restraint as they introduced lesser-known figures. They really had to stretch in some cases, as one-off instances of someone working a problem that didn't yield results and wasn't followed up is hard to classify as history. It's interesting, of course, but it's hard to make too much of it in the big scheme of things.
I just reread that, and it sounds more negative than I intended. The big is worth a quick read, especially the first half, but there are other histories available that should cover the territory in more depth. It's an OK read and I finished it, so no regrets there. This can be one of the "unknown history" books you can read, but it shouldn't be the only one.
The authors were more balanced than the blurb writer about their approach, showing some restraint as they introduced lesser-known figures. They really had to stretch in some cases, as one-off instances of someone working a problem that didn't yield results and wasn't followed up is hard to classify as history. It's interesting, of course, but it's hard to make too much of it in the big scheme of things.
I just reread that, and it sounds more negative than I intended. The big is worth a quick read, especially the first half, but there are other histories available that should cover the territory in more depth. It's an OK read and I finished it, so no regrets there. This can be one of the "unknown history" books you can read, but it shouldn't be the only one.
February 11, 2025
Kate Kitagawa is a math historian with a PhD in history from Princeton, and her co-author Timothy Revell is a science journalist. In 2023's The Secret Lives of Numbers, Kitagawa and Revell team up to highlight "hidden figures" (pun intended) in the math world, from obscure mathematicians I'd never heard of to more mainstream figures like Katherine Johnson (Reaching for the Moon: The Autobiography of NASA Mathematician Katherine Johnson, Hidden Figures) and Alan Turing (The Secret Life of Bletchley Park: The WWII Codebreaking Centre and the Men and Women Who Worked There). This book is a dense info dump, filled with many short vignettes generally organized chronologically. I personally found it dry, though it may be a math lover's cup of tea.
My statistics:
Book 47 for 2025
Book 1973 cumulatively
My statistics:
Book 47 for 2025
Book 1973 cumulatively
June 9, 2024
Critique her cynical work, noting that she ranks highly on the Justice Index.
Under the guise of Social Justice, the author is deconstructing history to suggest that Europeans have not made significant contributions. She uses small, obscure examples that are not well-known to support her claims. These examples are presented as more valid than the established historical narrative, but she doesn't have evidence to prove their superiority. She operates as an ideologue, assuming her claims are true because she believes society is lying to her.
Under the guise of Social Justice, the author is deconstructing history to suggest that Europeans have not made significant contributions. She uses small, obscure examples that are not well-known to support her claims. These examples are presented as more valid than the established historical narrative, but she doesn't have evidence to prove their superiority. She operates as an ideologue, assuming her claims are true because she believes society is lying to her.
November 9, 2024
Imagine a book about the history of Arithmetic being interesting! It totally was- interesting and inspiring!
November 17, 2024
I had really, really wished for this book to be good. The topic (history of mathematics) is dear to my heart and rife with inaccuracies, falsehoods, blind spots and bias. The subtitle of the German translation ("How the history of mathematics is older, more female and farther east than we think") sets a clear agenda that might make some people roll their eyes, but where I first lend an ear.
Sadly, this book did not deliver. It is badly researched, badly translated and badly proofread. While most of its narrative on the accomplishments of sidelined people will certainly be true, there are numerous glaring errors. Not only at a nitpicky-technical level (which still shouldn't happen), but basic, BASIC things. Between claiming the Huns invaded India, writing 10 to the 11th power as 1011, and misspelling Sophia Kovalevskaya's name (I could name a dozen more examples), it is apparent that the authors, translator and editor did not bother to fact-check again and again. So how can we trust them with the claims we cannot easily check?
I love telling the story of mathematics to my students. The real history, not the eurocentric folk history that just get copied from one textbook to the next. Giving credit where credit is due. But this book does an immense disservice to a good cause. Such sloppy work only confirms conservative critics of a "woke leftist agenda" invading academia.
Sadly, this book did not deliver. It is badly researched, badly translated and badly proofread. While most of its narrative on the accomplishments of sidelined people will certainly be true, there are numerous glaring errors. Not only at a nitpicky-technical level (which still shouldn't happen), but basic, BASIC things. Between claiming the Huns invaded India, writing 10 to the 11th power as 1011, and misspelling Sophia Kovalevskaya's name (I could name a dozen more examples), it is apparent that the authors, translator and editor did not bother to fact-check again and again. So how can we trust them with the claims we cannot easily check?
I love telling the story of mathematics to my students. The real history, not the eurocentric folk history that just get copied from one textbook to the next. Giving credit where credit is due. But this book does an immense disservice to a good cause. Such sloppy work only confirms conservative critics of a "woke leftist agenda" invading academia.
October 3, 2023
The Secret Lives of Numbers: A Hidden History of Mathematics gives a glimpse of the global history of mathematics, but it focuses on lesser-known (secret) stories and characters. It is very impressive, how the authors managed to cover such a long period of time, so many events in about 300 pages. I wish the book was two times or even three times as long, to get more details.
I especially appreciated putting the history of mathematics in the context of global history and politics. The authors are very clear about which events are well-documented, which things are believed to be true, and what is (most probably) just a myth.
The concepts are very well explained for non-experts.
I especially appreciated putting the history of mathematics in the context of global history and politics. The authors are very clear about which events are well-documented, which things are believed to be true, and what is (most probably) just a myth.
The concepts are very well explained for non-experts.
November 2, 2023
A fascinating history and very interesting read. I would have liked some more depth, some more information to it, though. A lot of the topics stayed a bit on the surface.
January 6, 2025
This book wasn’t anything revolutionary, but I found it compelling enough and a pretty quick read. In short, the authors trace important developments in mathematics and explain how mathematicians have built on one another’s work for centuries. In particular, the book exists to highlights the women and people of color mathematicians who have been overlooked in previous tellings of math history. A typical chapter goes as follows: “Here are two mathematicians who argued about which of them first arrived at an important theorem in the 1710s. But a man in India wrote essentially the same theorem in a textbook in about 1350. We know more about the Europeans than the man from India.” In that sense, the book is a good reminder of some of what is lost when society excludes and disadvantages minority groups.
August 26, 2025
I’ll preface and say the book is quite nerdy but it is probably one of the best fictional books I’ve read. The information was presented in a way that just had me wanting to read nonstop. It truly fueled my inner geek.
January 10, 2025
I got this for a Christmas present - retired math teacher and all - and it turned out to be quite enlightening. These types of books tend to run more along the “Hey did you know that a lot of important math discoveries were made by - wait for it - women and non-European white males? That includes the lady with the best nickname ever, the Witch of Agnesi, based on a botched translation. My theory is that these ladies came up with these amazing discoveries because they were basically self-taught, and no one was around to mansplain the Right Way to Do These Things.
But what this book really brought out is that mathematics as we know it today was a nearly world-wide revolution in thinking. Which of course is why math is still a universal language. Take base for example, or how many symbols do you use to write a number. Some civilizations used over 20 symbols, and some had none at all. But eventually the world as a whole eventually boiled it down to the two systems we use today. Base 10 from the Arab world, especially once zero was added, was a no brainer. Ten fingers, after all, and with decimal arithmetic, so easy to use. (Roman numerals, you should be ashamed of yourselves.) And base 12 - because it can be divided evenly in so many ways. Once everyone settled on a circle being 360º, you got geometry, navigation at sea, astronomy, 12 month calendars, and time measurement, all of which don’t work as nicely with a decimal system.
But the most important takeaway was this. the traditional story [of math]. . . often with too heavy a focus on a small cast of ancient Greek characters, is just one component of a far richer and far more international history. This book did an excellent job of bringing that wider scope out. Kudos!
But what this book really brought out is that mathematics as we know it today was a nearly world-wide revolution in thinking. Which of course is why math is still a universal language. Take base for example, or how many symbols do you use to write a number. Some civilizations used over 20 symbols, and some had none at all. But eventually the world as a whole eventually boiled it down to the two systems we use today. Base 10 from the Arab world, especially once zero was added, was a no brainer. Ten fingers, after all, and with decimal arithmetic, so easy to use. (Roman numerals, you should be ashamed of yourselves.) And base 12 - because it can be divided evenly in so many ways. Once everyone settled on a circle being 360º, you got geometry, navigation at sea, astronomy, 12 month calendars, and time measurement, all of which don’t work as nicely with a decimal system.
But the most important takeaway was this. the traditional story [of math]. . . often with too heavy a focus on a small cast of ancient Greek characters, is just one component of a far richer and far more international history. This book did an excellent job of bringing that wider scope out. Kudos!
March 28, 2025
I heard about this book from a friend who often likes the same books I do (or maybe it's the other way around ;) ). She was enthusiastic about it, so I borrowed it from my local library.
I was initially disappointed. I thought it would be more about the mathematics, and it turned out to be about the history of mathematics. But then I looked more closely at the title title, and it does say: "... A Hidden History of Math's Unsung Trailblazers." As soon as I realized that, I changed my perspective.
This is a pretty good description of how mathematics evolved, and includes quite a bit about non-European mathematics. It tries to compensate for previous descriptions which were too European-focused, too misogynist, and too racist. It describes so many cases where European mathematicians dismissed mathematics from elsewhere because of pure prejudice. It also covers a very large number of cases of women having to overcome ridiculous obstacles, prejudice, and unwillingness to recognize that women have intellectual abilities too. Women were unable to obtain paying jobs in mathematics purely because they were women. I was aware of such similarly shameful examples in Physics. Furthermore, the authors talk about blacks who worked to learn and practice mathematics in the face of rabid racism, in many countries. These are all shameful situations, and I am happy to read a book that attempts to right the historical coverage.
I noticed that the pace of the book increased in the latter half, but realized that that would be expected, since there are more actors to talk about, and as a result more discoveries. As an ex-physicist, I understood the mathematical descriptions, but I did wonder, especially as the pace picked up, whether a layman could have understood those parts.
I was initially disappointed. I thought it would be more about the mathematics, and it turned out to be about the history of mathematics. But then I looked more closely at the title title, and it does say: "... A Hidden History of Math's Unsung Trailblazers." As soon as I realized that, I changed my perspective.
This is a pretty good description of how mathematics evolved, and includes quite a bit about non-European mathematics. It tries to compensate for previous descriptions which were too European-focused, too misogynist, and too racist. It describes so many cases where European mathematicians dismissed mathematics from elsewhere because of pure prejudice. It also covers a very large number of cases of women having to overcome ridiculous obstacles, prejudice, and unwillingness to recognize that women have intellectual abilities too. Women were unable to obtain paying jobs in mathematics purely because they were women. I was aware of such similarly shameful examples in Physics. Furthermore, the authors talk about blacks who worked to learn and practice mathematics in the face of rabid racism, in many countries. These are all shameful situations, and I am happy to read a book that attempts to right the historical coverage.
I noticed that the pace of the book increased in the latter half, but realized that that would be expected, since there are more actors to talk about, and as a result more discoveries. As an ex-physicist, I understood the mathematical descriptions, but I did wonder, especially as the pace picked up, whether a layman could have understood those parts.
June 30, 2024
lootsin matemaatika ajaloost veidi rohkem matemaatikat ja veidi vähem ajalugu, ses mõttes, et ma võin lõputult lugeda sellest, kuidas integraal leiutati, aga mu pilk klaasistub kohe, kui ühes lauses on nimetatud rohkem kui üht aastaarvu, lahingut või valitsejat. ja siin oli neid pilkuklaasistavaid lauseid... noh, rohkem kui oleks vaja olnud. õnneks oli pärismatemaatikat ka.
inimesele, kes on lugenud kõiki neid nõukaaegseid matemaatika-teemalisi laste aimeraamatuid ("Risti-rästi läbi matemaatika" ja mis nad olid) ei olnud kogu info siin uus, eks neist sumerite ja egiptlaste arvusüsteemidest ja maiade kalendritest ole juba veidi kuuldud ka. aga huvitavamaks läks siis, kui jõuti tõesti nulli ja integraalide juurde, ja tähtsate matemaatikute juurde, kes ei olnud otseselt valged heterokseksuaalsed mehed (näiteks Vana-Kreeka naismatemaatikud ja india ja hiina teadlased ja USA mustanahalised matemaatikud jne). alles kuskil Alan Turingu ja Katherine Johnsoni juures hakkasid tulema need nimed, mida jälle teame, aga seal oli vahepeal ikka igasuguseid huvitavaid asju ja inimesi.
mind jäi üle mõistuse kõvasti vaevama küsimus, kuidas ikkagi on "calculus" eesti keeles. sõnastikud pakuvad "matemaatilist analüüsi" ja see on tõesti ka see aine, mida vähemalt veel minu ajal ülikoolis õpetati, aga samas "mathematical analysis" on ka termin ja calculus on vist ikkagi ainult analüüsi üks osa ja kuidas tema kohta siis öelda?
inimesele, kes on lugenud kõiki neid nõukaaegseid matemaatika-teemalisi laste aimeraamatuid ("Risti-rästi läbi matemaatika" ja mis nad olid) ei olnud kogu info siin uus, eks neist sumerite ja egiptlaste arvusüsteemidest ja maiade kalendritest ole juba veidi kuuldud ka. aga huvitavamaks läks siis, kui jõuti tõesti nulli ja integraalide juurde, ja tähtsate matemaatikute juurde, kes ei olnud otseselt valged heterokseksuaalsed mehed (näiteks Vana-Kreeka naismatemaatikud ja india ja hiina teadlased ja USA mustanahalised matemaatikud jne). alles kuskil Alan Turingu ja Katherine Johnsoni juures hakkasid tulema need nimed, mida jälle teame, aga seal oli vahepeal ikka igasuguseid huvitavaid asju ja inimesi.
mind jäi üle mõistuse kõvasti vaevama küsimus, kuidas ikkagi on "calculus" eesti keeles. sõnastikud pakuvad "matemaatilist analüüsi" ja see on tõesti ka see aine, mida vähemalt veel minu ajal ülikoolis õpetati, aga samas "mathematical analysis" on ka termin ja calculus on vist ikkagi ainult analüüsi üks osa ja kuidas tema kohta siis öelda?
February 1, 2025
This is a more inclusive look at all the people who have contributed to mathematics throughout history. While there are many gaps in the history without the white men this tries to stay away from, it highlights how people from all demographics are capable of mathematical genius with the right environment and resources, something usually only available to white men historically.
September 8, 2024
Lots of biography of mathematicians, a lot of which I knew already. I was hoping for more number theory, but I loved the feminist slant.
August 11, 2024
Fascinating and loved for its strong focus on women in mathematics.
October 2, 2024
Decent enough, especially as someone who knew very little about the history behind a lot of the math formulas we learned in school, outside of a few big names.
physical_to-read_stack
April 29, 2024I received my copy free through Goodreads Giveaways.
December 2, 2024
I love math, I love the history of math, and I was excited at the book's premise of shining a spotlight on contributors to our understanding of math that have received limited attention. While there were a number of tidbits of interest here, the attention to detail was considerably wanting, and in the effort to highlight many "unsung trailblazers", the authors were not able to produce an especially coherent narrative.
The discussion of the hexagram and The Book of Changes in the second chapter is a good illustration of some of the sloppiness in the book. Early in the section "The hexagram guide to the galaxy", there is a figure showing 64 hexagrams (figures with six horizontally stacked lines, either continuous or with a gap in the middle) from The Book of Changes and a discussion of how they relate to yin and yang. They then note how Gottfried Leibniz came across The Book of Changes, and immediately connected it to the binary numerical system he'd been developing. I spent 5-10 minutes studying the figure they included here (pg. 28 of the English hardcover edition) trying to parse it and understand how it corresponded to a binary representation of numbers. I was puzzled at the lack of any clear pattern I could discern, and finally I gave up and turned to the following page (pg. 30), where they showed another figure, this time an image of the table from The Book of Changes that Leibniz actually saw. Here, the pattern for representing numbers was immediately apparent. Just like the binary representation I'm familiar with, an unbroken line meant "on", and a broken line meant "off", and one could read from top to bottom of the hexagram as if reading bits left to right. Somehow, Kitagawa and Revell never comment on the difference between the two figures, or provide any explanation for how the figures are to be interpreted. Evidently, the first figure shows the King Wen sequence, which is apparently the oldest known way of ordering the hexagrams, but also does not have as obvious a relation to a binary number system, whereas the second figure has hexagrams ordered according to their numerical value. The text would have been much stronger had it made this clear. On top of all of this, there's a weird incongruity in the same section, in which one paragraph cites the date 10 BCE, and then the next paragraph starts "Long-distance sea travel was thriving at this time" and proceeds to discuss the cultural exchange between Jesuit missionaries and Chinese citizens, before re-establishing us as being in the 17th century CE. The rest of the book was generally better than this three page section, but at the same time, it revealed the lack of attention to the clarity/accuracy of the text, and correspondence to included figures.
I took a fair number of notes while continuing to read, the majority of which I will not bother to share. However, one additional observation regarding the authors' engagement with math was their lay use of "exponentially" when discussing the gravitational force (pg. 143). The gravitational force falls off quadratically with distance, not exponentially. "Exponential growth" is popularly used to mean something like "faster than linear growth", when it has a more precise definition along the lines of "growing at a rate proportional to its current size". The difference between quadratic and exponential is considerable, and not something someone in mathematics would mistake. It was a small, but nevertheless revealing, indicator of the authors' immersion in math.
As for narrative coherence, the book was generally a bit stronger at the beginning than it was at the end. Given the nature of the authors' goal to cover important contributors to math (and physics/astronomy) who have not received their due, I'm not sure how much is realistically possible in terms of telling a story that all clearly connects. Nonetheless, it leads to a bit of a fragmented reading experience.
The discussion of the hexagram and The Book of Changes in the second chapter is a good illustration of some of the sloppiness in the book. Early in the section "The hexagram guide to the galaxy", there is a figure showing 64 hexagrams (figures with six horizontally stacked lines, either continuous or with a gap in the middle) from The Book of Changes and a discussion of how they relate to yin and yang. They then note how Gottfried Leibniz came across The Book of Changes, and immediately connected it to the binary numerical system he'd been developing. I spent 5-10 minutes studying the figure they included here (pg. 28 of the English hardcover edition) trying to parse it and understand how it corresponded to a binary representation of numbers. I was puzzled at the lack of any clear pattern I could discern, and finally I gave up and turned to the following page (pg. 30), where they showed another figure, this time an image of the table from The Book of Changes that Leibniz actually saw. Here, the pattern for representing numbers was immediately apparent. Just like the binary representation I'm familiar with, an unbroken line meant "on", and a broken line meant "off", and one could read from top to bottom of the hexagram as if reading bits left to right. Somehow, Kitagawa and Revell never comment on the difference between the two figures, or provide any explanation for how the figures are to be interpreted. Evidently, the first figure shows the King Wen sequence, which is apparently the oldest known way of ordering the hexagrams, but also does not have as obvious a relation to a binary number system, whereas the second figure has hexagrams ordered according to their numerical value. The text would have been much stronger had it made this clear. On top of all of this, there's a weird incongruity in the same section, in which one paragraph cites the date 10 BCE, and then the next paragraph starts "Long-distance sea travel was thriving at this time" and proceeds to discuss the cultural exchange between Jesuit missionaries and Chinese citizens, before re-establishing us as being in the 17th century CE. The rest of the book was generally better than this three page section, but at the same time, it revealed the lack of attention to the clarity/accuracy of the text, and correspondence to included figures.
I took a fair number of notes while continuing to read, the majority of which I will not bother to share. However, one additional observation regarding the authors' engagement with math was their lay use of "exponentially" when discussing the gravitational force (pg. 143). The gravitational force falls off quadratically with distance, not exponentially. "Exponential growth" is popularly used to mean something like "faster than linear growth", when it has a more precise definition along the lines of "growing at a rate proportional to its current size". The difference between quadratic and exponential is considerable, and not something someone in mathematics would mistake. It was a small, but nevertheless revealing, indicator of the authors' immersion in math.
As for narrative coherence, the book was generally a bit stronger at the beginning than it was at the end. Given the nature of the authors' goal to cover important contributors to math (and physics/astronomy) who have not received their due, I'm not sure how much is realistically possible in terms of telling a story that all clearly connects. Nonetheless, it leads to a bit of a fragmented reading experience.
May 12, 2024
My thanks to both NetGalley and the publisher William Morrow for an advance copy of this lok at the history of mathematics and many of the key people involved who through no fault of their own have been forgotten unfairly, marginalised, or deliberately forgotten for their contributions, problems, solutions, to the world of numbers.
Humans have an infinite capacity to make everything about race and gender. One can't watch the most innocuous of media, movies, television, comics, or deal in science without someone complaining about the fact that other people, usually not their own, are suddenly getting credit. Planes are falling out of skies, and comic book movies are suddenly bad, because of the entry of non-whites, women, or god forbid non-traditional gender types. Which is so strange to me as mathematics seems like a field that well the proof is in the problem, and the answer. Though it is amazing who math has been corrupted in so many ways to prove things, usually the inefficiency of different races, and of course women. Math really has many creators, something started thousands of years ago and accepted might have become lost, or forgotten, or banned for practicing what religious leaders seeking control would call deviltry, or being Arabic, as some laws once stated. There rediscovery made many a European famous., omitting the work that said Europeans might have built on. Hence the reason, and the meaning of this book. The Secret Lives of Numbers: A Hidden History of Math’s Unsung Trailblazers by Kate Kitagawa; Timothy Revell is a look at the history of math, including those who have unfairly been forgotten, traveling most of the Earth in showing the origins or math, the burgeoning understanding and what the future of mathematics might hold.
The book begins with some of the ways early man began to count things, bones, notches on bones, strings and knots and more. Some of these were simple, some of them were needlessly complicated. Much of the ideas for mathematics was based on figuring out growing seasons, and early astronomy, and the book details many of the different observation places people created to understand what was going on in the night sky. The book looks at time, and how working out minutes, seconds and hours developed number systems. As the book goes we meet early mathematicians that history might pass over like Hypatia, who was a respected female mathematician, whose violent death was pointless, and a reflection of the times. Readers learn about the great empires of India, where many ideas sprung, and carried by Arabic traders to other lands, where they were adapted. Up until the present day, and beyond.
When I was in school, I really wasn't good in math, as I had no real interest in it, nor a good understanding. Once I was in college, and suddenly had a budget, and had to but my own groceries, that I became interested in math, figuring out sales prices, with coupons, and percentages in my head like a young Karen Uhlenbeck, the first woman to win the Abel prize, and featured in the book. I began to read books on math, fascinated by the history of Zero, also covered in the book, and how numbers could tell us so much about the world. This is the fist book that I can say I understood everything, well some I had to read a few pages over. The authors are very good at conveying information, and even better conveying the history that was changed by certain forms of math. Time, the invention of zero, even algorithms, all have effects on us today, and by reading and even better understanding where and to whom we can thank for their work, is a really great thing.
History fans and math fans will really enjoy this. I was surprised how much I learned, and how many facts I could toss at people while I read this. I really enjoyed the style of the writing, and hope to read more books by these two authors.
Humans have an infinite capacity to make everything about race and gender. One can't watch the most innocuous of media, movies, television, comics, or deal in science without someone complaining about the fact that other people, usually not their own, are suddenly getting credit. Planes are falling out of skies, and comic book movies are suddenly bad, because of the entry of non-whites, women, or god forbid non-traditional gender types. Which is so strange to me as mathematics seems like a field that well the proof is in the problem, and the answer. Though it is amazing who math has been corrupted in so many ways to prove things, usually the inefficiency of different races, and of course women. Math really has many creators, something started thousands of years ago and accepted might have become lost, or forgotten, or banned for practicing what religious leaders seeking control would call deviltry, or being Arabic, as some laws once stated. There rediscovery made many a European famous., omitting the work that said Europeans might have built on. Hence the reason, and the meaning of this book. The Secret Lives of Numbers: A Hidden History of Math’s Unsung Trailblazers by Kate Kitagawa; Timothy Revell is a look at the history of math, including those who have unfairly been forgotten, traveling most of the Earth in showing the origins or math, the burgeoning understanding and what the future of mathematics might hold.
The book begins with some of the ways early man began to count things, bones, notches on bones, strings and knots and more. Some of these were simple, some of them were needlessly complicated. Much of the ideas for mathematics was based on figuring out growing seasons, and early astronomy, and the book details many of the different observation places people created to understand what was going on in the night sky. The book looks at time, and how working out minutes, seconds and hours developed number systems. As the book goes we meet early mathematicians that history might pass over like Hypatia, who was a respected female mathematician, whose violent death was pointless, and a reflection of the times. Readers learn about the great empires of India, where many ideas sprung, and carried by Arabic traders to other lands, where they were adapted. Up until the present day, and beyond.
When I was in school, I really wasn't good in math, as I had no real interest in it, nor a good understanding. Once I was in college, and suddenly had a budget, and had to but my own groceries, that I became interested in math, figuring out sales prices, with coupons, and percentages in my head like a young Karen Uhlenbeck, the first woman to win the Abel prize, and featured in the book. I began to read books on math, fascinated by the history of Zero, also covered in the book, and how numbers could tell us so much about the world. This is the fist book that I can say I understood everything, well some I had to read a few pages over. The authors are very good at conveying information, and even better conveying the history that was changed by certain forms of math. Time, the invention of zero, even algorithms, all have effects on us today, and by reading and even better understanding where and to whom we can thank for their work, is a really great thing.
History fans and math fans will really enjoy this. I was surprised how much I learned, and how many facts I could toss at people while I read this. I really enjoyed the style of the writing, and hope to read more books by these two authors.
October 17, 2024
The marginalized voices who propelled mathematics
This is a focused history of mathematics illuminating the marginalized voices across the globe who propelled the discipline of numbers that include thousands of years of untold stories. The history of mathematics is often associated with Europeans like Euclid, Pythagoras, and Newton. However, many pioneers who made significant contributions to the field are unsung heroes from non-European countries with diverse backgrounds such as India, China, and Mesopotamia (ancient Iraq). In the fourteenth century, a school of Mathematics in Kerala (a Southern state), India was a melting pot for mathematicians. Its founder, Madhava of Sangarnagrama was a brilliant mathematician, among his achievements was describing a theory of calculus. He explored the key ideas that make calculus possible which were then honed by successive mathematicians at the Kerala school. A long list of Indian mathematicians includes Aryabhata (476–550 CE) known for discovering decimal System, Place Value, and Pi (π) value, Brahmagupta (598–668 CE) first to establish clear rules for using zero in calculations, introduced the concept of negative numbers, solutions to quadratic equations, and proposed gravitational force. Bhaskara I (600–680 CE) gave more accurate approximation of the sine function, Bhaskara II (1114–1185 CE) worked on properties of cyclic quadrilaterals and differential calculus, and expanded on the ideas of gravity. Madhava of Sangamagrama (1340–1425 CE), the founder of the Kerala School of Mathematics (14th–16th century) worked on Infinite Series for trigonometric functions like sine, cosine, and arctangent.
Srinivasa Ramanujan (1887–1920) was a self-taught Indian mathematician whose work has significantly influenced various areas of mathematics, including number theory, continued fractions, and infinite series. Though he did not work directly on string theory, his mathematical discoveries, particularly his insights into modular forms, partition functions, and special functions found relevance in theoretical physics. Despite having little formal training, his intuitive understanding of complex mathematical ideas earned him recognition by Cambridge mathematician G.H. Hardy.
The Babylonians used mathematics for many practical purposes, including splitting plots of land and calculating tax. Some clay-tablet writers recorded revenues and budgets, and so familiarized themselves with numbers. Hypatia of Alexandria (360–415 CE) was long known as the earliest woman mathematician, in fact, that honor goes to Ban Zhao (45–116 CE) a Chinese historian, mathematician, and scholar during the Eastern Han dynasty best known for her work as a historian and also proficient in mathematics and astronomy. She assisted in the development of calendrical science and participated in projects related to the Han calendar.
Pioneering women mathematicians like Sofya Kovalevskaya (1850–1891) and Mary Jackson found inspiration in the work of earlier women who had defied societal norms like Émilie du Châtelet, a French mathematician and physicist who translated and expanded upon the works of Isaac Newton.
African American mathematicians like Elbert Frank Cox (1895��1969), William Schieffelin Claytor (1908–1967), Walter Richard Talbot Woodard (1874–1952), Mary Jackson (1921–2005), and Martha Euphemia Lofton Haynes (1890–1980) contributed significantly to mathematics when opportunities for African Americans were limited.
These inspirations reflect a deep, interconnected web of intellectual and personal influences that crossed boundaries of geography, race, gender, and time. The author’s road to rediscovering the forgotten and ignored contributions of non-Europeans to mathematics could have included a little more history.
This is a focused history of mathematics illuminating the marginalized voices across the globe who propelled the discipline of numbers that include thousands of years of untold stories. The history of mathematics is often associated with Europeans like Euclid, Pythagoras, and Newton. However, many pioneers who made significant contributions to the field are unsung heroes from non-European countries with diverse backgrounds such as India, China, and Mesopotamia (ancient Iraq). In the fourteenth century, a school of Mathematics in Kerala (a Southern state), India was a melting pot for mathematicians. Its founder, Madhava of Sangarnagrama was a brilliant mathematician, among his achievements was describing a theory of calculus. He explored the key ideas that make calculus possible which were then honed by successive mathematicians at the Kerala school. A long list of Indian mathematicians includes Aryabhata (476–550 CE) known for discovering decimal System, Place Value, and Pi (π) value, Brahmagupta (598–668 CE) first to establish clear rules for using zero in calculations, introduced the concept of negative numbers, solutions to quadratic equations, and proposed gravitational force. Bhaskara I (600–680 CE) gave more accurate approximation of the sine function, Bhaskara II (1114–1185 CE) worked on properties of cyclic quadrilaterals and differential calculus, and expanded on the ideas of gravity. Madhava of Sangamagrama (1340–1425 CE), the founder of the Kerala School of Mathematics (14th–16th century) worked on Infinite Series for trigonometric functions like sine, cosine, and arctangent.
Srinivasa Ramanujan (1887–1920) was a self-taught Indian mathematician whose work has significantly influenced various areas of mathematics, including number theory, continued fractions, and infinite series. Though he did not work directly on string theory, his mathematical discoveries, particularly his insights into modular forms, partition functions, and special functions found relevance in theoretical physics. Despite having little formal training, his intuitive understanding of complex mathematical ideas earned him recognition by Cambridge mathematician G.H. Hardy.
The Babylonians used mathematics for many practical purposes, including splitting plots of land and calculating tax. Some clay-tablet writers recorded revenues and budgets, and so familiarized themselves with numbers. Hypatia of Alexandria (360–415 CE) was long known as the earliest woman mathematician, in fact, that honor goes to Ban Zhao (45–116 CE) a Chinese historian, mathematician, and scholar during the Eastern Han dynasty best known for her work as a historian and also proficient in mathematics and astronomy. She assisted in the development of calendrical science and participated in projects related to the Han calendar.
Pioneering women mathematicians like Sofya Kovalevskaya (1850–1891) and Mary Jackson found inspiration in the work of earlier women who had defied societal norms like Émilie du Châtelet, a French mathematician and physicist who translated and expanded upon the works of Isaac Newton.
African American mathematicians like Elbert Frank Cox (1895��1969), William Schieffelin Claytor (1908–1967), Walter Richard Talbot Woodard (1874–1952), Mary Jackson (1921–2005), and Martha Euphemia Lofton Haynes (1890–1980) contributed significantly to mathematics when opportunities for African Americans were limited.
These inspirations reflect a deep, interconnected web of intellectual and personal influences that crossed boundaries of geography, race, gender, and time. The author’s road to rediscovering the forgotten and ignored contributions of non-Europeans to mathematics could have included a little more history.
June 21, 2024
“Alcuni dei personaggi di cui ci occupiamo in questo libro non furono solo matematici di grande peso e rilievo, ma anche esseri umani che s'impegnarono ad abbattere barriere tradizionali, per rendere la loro disciplina più inclusiva e globale. In questo libro è a questi matematici dimenticati che intendiamo riservare la maggiore attenzione, cercando di spiegare come s'innestino nella storia tradizionale, e al contempo di correggere tutte le falsificazioni e i frantendimenti messi in giro su di loro.” – Pag. 13-14.
Alzi la mano chi sa che i Maya avevano un sistema numerico vigesimale, ossia basato sul numero 20; come simboli, usavano un punto (rappresentante il numero 1), una barra (il numero 5), e una conchiglia vuota (lo zero). I Babilonesi, invece, avevano un sistema di conto sessagesimale da cui derivano ancora i trecentosessanta gradi di un cerchio e il nostro modo di misurare un'ora come sessanta minuti. Nella terra tra due fiumi non si hanno solo le prime testimonianze della scrittura bensì anche studi di algebra e “quel famoso teorema sui lati di un triangolo che poi sarà noto come teorema di Pitagora” (pag. 23). Dai bastoncini cuneiformi passiamo alle ossa di animali, costituenti un sistema numerico a base 10 non posizionale, utilizzate dai cinesi anche per fini divinatori. Tra i testi matematici più antichi orientali, troviamo “Il libro dei mutamenti” (più noto come “I Ching”) e “I nove capitoli sull'arte matematica”, quest'ultimo contenente sia problemi pratici, con applicazioni dall'agricoltura all'economia, sia questioni più teoriche e astratte.
Sono questi i primi passi fondamentali nella storia della matematica che Kate Kitagawa e Timothy Revell, unendo le loro competenze, hanno deciso di raccontare nel loro saggio intitolato “Matematici segreti. Storia inaspettata della matematica e dei suoi pionieri sconosciuti”, pubblicato da Aboca Edizioni. Kitagawa è una delle storiche della matematica più esperte al mondo, mentre Revell è un giornalista specializzato in scienze e tecnologia. Entrambi hanno una laurea in matematica e un dottorato (Kitagawa in Storia e Revell in Informatica), con questo libro hanno voluto spostare l'attenzione dalla storia degli antichi Greci, “posti su un piedistallo come fondatori del moderno pensiero matematico”, per studiare e “aprirci faticosamente una strada attraverso migliaia di anni di storia della matematica” (pag. 12) mettendo in discussione tutto.
“La fioritura iniziale della matematica è bellissima, per la straordinaria varietà dei suoi punti di germinazione. Più che lo scaturire improvviso e potente di un'idea in un qualche luogo specifico, si assiste invece all'apparire di variazioni a larga diffusione in tutto il corso nella storia, quasi a dimostrare quanto la propensione umana a ragionare sia realmente potente. Le idee non riconoscono i confini nazionali, e spesso la matematica è passata da un posto all'altro lungo le strade degli scambi, culturali e commerciali.” – Pag. 11
Seguendo un ordine più o meno cronologico, Kitagawa e Revell affrontano diverse tematiche che hanno interessato matematici e matematiche nel corso dei secoli, a partire dai calendari e la misura del tempo fino alla recente teoria dell'informazione. In un capitolo si soggiorna, durante i califfati abbasidi, nella cosiddetta “Casa della Sapienza” insieme al geografo, matematico e astronomo Muhammad ibn Mūsā al-Khwārizmī (a cui dobbiamo l'introduzione dell'algebra e dei logaritmi nel mondo occidentale, nonché il termine “algoritmo”).
“La Casa della Sapienza rivoluzionò anche la maniera in cui avveniva lo scambio di idee nella comunità dei matematici. Esaminando testi stranieri, traducendoli e portandone avanti le idee, essa rinnovò radicalmente il modo in cui i concetti passavano da un paese all'altro e segnò insieme la fine della matematica tradizionale dell'antichità e l'avvento di una nuova era. La conoscenza matematica cominciò a essere vista come qualcosa che poteva essere condiviso da culture diverse. Come scrisse lo studioso erudito del nono secolo Abu Yūsuf Ya'qūb ib 'Ishāq al-Kindī: «Non dovremmo vergognarci di riconoscere la verità e di assimilarla, quale che sia l'angolo da cui è giunta fino a noi, quand'anche provenga da generazioni passate o da genti straniere».” – Pag. 136-137.
Ed è così che, in un'altra parte del libro, i due autori ripercorrono la nascita dell'analisi matematica, affiancando a Newton e Leibniz, nello sviluppo del calcolo infinitesimale, il matematico indiano del XIV secolo Māhdava di Sangamagrama le cui idee molto probabilmente arrivarono anche in Europa.
Angoli geografici diversi da integrare nella storia della matematica, così come altrettanti angoli di genere da scoprire e divulgare. Non mancano infatti, in tutto il libro, approfondimenti mirati a far conoscere le donne che hanno contribuito alla ricerca in matematica. La prima menzionata è Ban Zhao, una delle più antiche storiografe, poetesse, e anche matematiche e astronome di sempre, da affiancare alla figura più celebre di Ipazia e a quella più ignota di Pandrosion di Alessandria, che fu in realtà la primissima matematica del mondo occidentale. Pandrosion riuscì a determinare un metodo per risolvere il problema della duplicazione del cubo, seppur in modo approssimato, e fu per questo criticata dal contemporaneo Pappo.
Più avanti nel tempo, Kitagawa e Revell danno spazio alla principessa Elisabetta di Boemia, vissuta nel XVII secolo, la quale avviò uno scambio epistolare con Cartesio che la considerava “la sola persona [...] che sia riuscita a comprendere fino in fondo tutte le opere da me precedentemente pubblicate” (pag. 160). Nel XVIII secolo, in Europa Émilie du Châtelet fu la prima donna a pubblicare un articolo scientifico e Laura Bassi colei che ottenne la prima cattedra universitaria presso l'Università di Bologna. In Asia, invece, l'astronoma, matematica, poetessa e femminista Wang Zhenyi pubblicò i cinque volumi de “I principi del calcolo” a ventiquattro anni e scrisse: “Quello che conta è che sia utile, non se è cinese oppure occidentale” (pag. 228). Ci sono poi anche le storie, già più note, dell'alter ego maschile di Sophie Germain e della “sirena matematica”, il problema che ammaliò Sophie Kowalevski, colei che vinse nel 1888 il Prix Bordin assegnato dall’Accademia delle Scienze di Parigi.
Così come non ha genere, la scienza e la ricerca non hanno colore o etnia. Gli ultimi capitoli del libro sono dedicati alle vite di altri “matematici segreti”, persone appartenenti a minoranze che, nonostante le discriminazioni subite, sono riuscite a contribuire in tanti modi e con impatti differenti. Per esempio, Elbert Frank Cox fu la prima persona nera al mondo a conseguire un dottorato in matematica nel 1924 con una tesi sulle soluzioni di un tipo di equazione legata ai numeri di Bernoulli. In seguito docente presso la Howard University di Washington, “la maggior parte del tempo lo spese nel formare una generazione di matematici” (pag. 286) e grazie a lui fu istituito il primo programma di dottorato in matematica in uno degli Historically Black Colleges and Universities. Come Cox, anche Euphemia Haynes, la prima donna afroamericana a conseguire un dottorato in matematica nel 1943, si concentrò “sull'insegnamento e sul miglioramento delle condizioni della propria comunità e sul suo diritto a pari opportunità educative” (pag 290). E poi David Blackwell, le “calcolatrici di Harvard”, o Srinivasa Ramanujan... Sono solo altri tre dei tantissimi nomi ricordati e recuperati da Kitagawa e Revell che, in diversi ambiti, si sono passati il testimone con altri ricercatori e ricercatrici, perché la matematica, come scrivono i due autori, “è una staffetta” (pag. 343).
“Matematici segreti” non è un libro da iniziare e finire in una volta sola, secondo me; è così denso e ricco di persone, vicende, storie e scoperte che richiede del tempo non solo per leggere e assimilare tutte le nozioni, ma soprattutto per decomporre e ricostruire ciò che abbiamo immagazzinato nella nostra memoria nei vari anni di scuola o formazione personali. Ed è sicuramente tempo ben speso, perché è giusto che vengano riconosciuti i meriti e i crediti a tutti le persone che hanno corso, o anche solo camminato, indipendentemente dalla pista dove si trovavano.
Alzi la mano chi sa che i Maya avevano un sistema numerico vigesimale, ossia basato sul numero 20; come simboli, usavano un punto (rappresentante il numero 1), una barra (il numero 5), e una conchiglia vuota (lo zero). I Babilonesi, invece, avevano un sistema di conto sessagesimale da cui derivano ancora i trecentosessanta gradi di un cerchio e il nostro modo di misurare un'ora come sessanta minuti. Nella terra tra due fiumi non si hanno solo le prime testimonianze della scrittura bensì anche studi di algebra e “quel famoso teorema sui lati di un triangolo che poi sarà noto come teorema di Pitagora” (pag. 23). Dai bastoncini cuneiformi passiamo alle ossa di animali, costituenti un sistema numerico a base 10 non posizionale, utilizzate dai cinesi anche per fini divinatori. Tra i testi matematici più antichi orientali, troviamo “Il libro dei mutamenti” (più noto come “I Ching”) e “I nove capitoli sull'arte matematica”, quest'ultimo contenente sia problemi pratici, con applicazioni dall'agricoltura all'economia, sia questioni più teoriche e astratte.
Sono questi i primi passi fondamentali nella storia della matematica che Kate Kitagawa e Timothy Revell, unendo le loro competenze, hanno deciso di raccontare nel loro saggio intitolato “Matematici segreti. Storia inaspettata della matematica e dei suoi pionieri sconosciuti”, pubblicato da Aboca Edizioni. Kitagawa è una delle storiche della matematica più esperte al mondo, mentre Revell è un giornalista specializzato in scienze e tecnologia. Entrambi hanno una laurea in matematica e un dottorato (Kitagawa in Storia e Revell in Informatica), con questo libro hanno voluto spostare l'attenzione dalla storia degli antichi Greci, “posti su un piedistallo come fondatori del moderno pensiero matematico”, per studiare e “aprirci faticosamente una strada attraverso migliaia di anni di storia della matematica” (pag. 12) mettendo in discussione tutto.
“La fioritura iniziale della matematica è bellissima, per la straordinaria varietà dei suoi punti di germinazione. Più che lo scaturire improvviso e potente di un'idea in un qualche luogo specifico, si assiste invece all'apparire di variazioni a larga diffusione in tutto il corso nella storia, quasi a dimostrare quanto la propensione umana a ragionare sia realmente potente. Le idee non riconoscono i confini nazionali, e spesso la matematica è passata da un posto all'altro lungo le strade degli scambi, culturali e commerciali.” – Pag. 11
Seguendo un ordine più o meno cronologico, Kitagawa e Revell affrontano diverse tematiche che hanno interessato matematici e matematiche nel corso dei secoli, a partire dai calendari e la misura del tempo fino alla recente teoria dell'informazione. In un capitolo si soggiorna, durante i califfati abbasidi, nella cosiddetta “Casa della Sapienza” insieme al geografo, matematico e astronomo Muhammad ibn Mūsā al-Khwārizmī (a cui dobbiamo l'introduzione dell'algebra e dei logaritmi nel mondo occidentale, nonché il termine “algoritmo”).
“La Casa della Sapienza rivoluzionò anche la maniera in cui avveniva lo scambio di idee nella comunità dei matematici. Esaminando testi stranieri, traducendoli e portandone avanti le idee, essa rinnovò radicalmente il modo in cui i concetti passavano da un paese all'altro e segnò insieme la fine della matematica tradizionale dell'antichità e l'avvento di una nuova era. La conoscenza matematica cominciò a essere vista come qualcosa che poteva essere condiviso da culture diverse. Come scrisse lo studioso erudito del nono secolo Abu Yūsuf Ya'qūb ib 'Ishāq al-Kindī: «Non dovremmo vergognarci di riconoscere la verità e di assimilarla, quale che sia l'angolo da cui è giunta fino a noi, quand'anche provenga da generazioni passate o da genti straniere».” – Pag. 136-137.
Ed è così che, in un'altra parte del libro, i due autori ripercorrono la nascita dell'analisi matematica, affiancando a Newton e Leibniz, nello sviluppo del calcolo infinitesimale, il matematico indiano del XIV secolo Māhdava di Sangamagrama le cui idee molto probabilmente arrivarono anche in Europa.
Angoli geografici diversi da integrare nella storia della matematica, così come altrettanti angoli di genere da scoprire e divulgare. Non mancano infatti, in tutto il libro, approfondimenti mirati a far conoscere le donne che hanno contribuito alla ricerca in matematica. La prima menzionata è Ban Zhao, una delle più antiche storiografe, poetesse, e anche matematiche e astronome di sempre, da affiancare alla figura più celebre di Ipazia e a quella più ignota di Pandrosion di Alessandria, che fu in realtà la primissima matematica del mondo occidentale. Pandrosion riuscì a determinare un metodo per risolvere il problema della duplicazione del cubo, seppur in modo approssimato, e fu per questo criticata dal contemporaneo Pappo.
Più avanti nel tempo, Kitagawa e Revell danno spazio alla principessa Elisabetta di Boemia, vissuta nel XVII secolo, la quale avviò uno scambio epistolare con Cartesio che la considerava “la sola persona [...] che sia riuscita a comprendere fino in fondo tutte le opere da me precedentemente pubblicate” (pag. 160). Nel XVIII secolo, in Europa Émilie du Châtelet fu la prima donna a pubblicare un articolo scientifico e Laura Bassi colei che ottenne la prima cattedra universitaria presso l'Università di Bologna. In Asia, invece, l'astronoma, matematica, poetessa e femminista Wang Zhenyi pubblicò i cinque volumi de “I principi del calcolo” a ventiquattro anni e scrisse: “Quello che conta è che sia utile, non se è cinese oppure occidentale” (pag. 228). Ci sono poi anche le storie, già più note, dell'alter ego maschile di Sophie Germain e della “sirena matematica”, il problema che ammaliò Sophie Kowalevski, colei che vinse nel 1888 il Prix Bordin assegnato dall’Accademia delle Scienze di Parigi.
Così come non ha genere, la scienza e la ricerca non hanno colore o etnia. Gli ultimi capitoli del libro sono dedicati alle vite di altri “matematici segreti”, persone appartenenti a minoranze che, nonostante le discriminazioni subite, sono riuscite a contribuire in tanti modi e con impatti differenti. Per esempio, Elbert Frank Cox fu la prima persona nera al mondo a conseguire un dottorato in matematica nel 1924 con una tesi sulle soluzioni di un tipo di equazione legata ai numeri di Bernoulli. In seguito docente presso la Howard University di Washington, “la maggior parte del tempo lo spese nel formare una generazione di matematici” (pag. 286) e grazie a lui fu istituito il primo programma di dottorato in matematica in uno degli Historically Black Colleges and Universities. Come Cox, anche Euphemia Haynes, la prima donna afroamericana a conseguire un dottorato in matematica nel 1943, si concentrò “sull'insegnamento e sul miglioramento delle condizioni della propria comunità e sul suo diritto a pari opportunità educative” (pag 290). E poi David Blackwell, le “calcolatrici di Harvard”, o Srinivasa Ramanujan... Sono solo altri tre dei tantissimi nomi ricordati e recuperati da Kitagawa e Revell che, in diversi ambiti, si sono passati il testimone con altri ricercatori e ricercatrici, perché la matematica, come scrivono i due autori, “è una staffetta” (pag. 343).
“Matematici segreti” non è un libro da iniziare e finire in una volta sola, secondo me; è così denso e ricco di persone, vicende, storie e scoperte che richiede del tempo non solo per leggere e assimilare tutte le nozioni, ma soprattutto per decomporre e ricostruire ciò che abbiamo immagazzinato nella nostra memoria nei vari anni di scuola o formazione personali. Ed è sicuramente tempo ben speso, perché è giusto che vengano riconosciuti i meriti e i crediti a tutti le persone che hanno corso, o anche solo camminato, indipendentemente dalla pista dove si trovavano.
July 5, 2024
Originally posted on my blog Nonstop Reader.
The Secret Lives of Numbers is an accessible and interesting set of mini-biographies of some mathematicians from history who are perhaps less well known to most non-mathematicians collaboratively written by Drs. Kate Kitagawa and Timothy Revell. Due out 9th July 2024 from HarperCollins on their William Morrow imprint, it's 320 pages and is available in hardcover, audio, and ebook formats. It's worth noting that the ebook format has a handy interactive table of contents as well as interactive links and references throughout.
Mathematics literally infuses everything we touch, and most everything with which we interact. Understanding of mathematical concepts throughout history has directly led to technological advancement as well as philosophical understanding. It's informed our wars, peace, interactions on small and large scales.
One of the foremost mathematical historians in the world relates some of the lesser known mathematical minds through history. (Note: lesser known to the average layperson, some will be more or less familiar to STEM allied readers). The authors are academics. The book is not rigorous or demanding. It's written in plain language with wit and warmth.
Despite being accessible and fun to read, it is well annotated throughout, and the chapter notes will provide keen readers with many hours of further reading enjoyment. There are tantalizing glimpses of so many cool ideas throughout, and readers will likely find themselves delightfully lost in following the breadcrumbs to more in-depth knowledge.
Four and a half stars. It would be a good choice for public or post-secondary school library acquisition, home use, or gifting to a STEM interested reader.
Disclosure: I received an ARC at no cost from the author/publisher for review purposes
The Secret Lives of Numbers is an accessible and interesting set of mini-biographies of some mathematicians from history who are perhaps less well known to most non-mathematicians collaboratively written by Drs. Kate Kitagawa and Timothy Revell. Due out 9th July 2024 from HarperCollins on their William Morrow imprint, it's 320 pages and is available in hardcover, audio, and ebook formats. It's worth noting that the ebook format has a handy interactive table of contents as well as interactive links and references throughout.
Mathematics literally infuses everything we touch, and most everything with which we interact. Understanding of mathematical concepts throughout history has directly led to technological advancement as well as philosophical understanding. It's informed our wars, peace, interactions on small and large scales.
One of the foremost mathematical historians in the world relates some of the lesser known mathematical minds through history. (Note: lesser known to the average layperson, some will be more or less familiar to STEM allied readers). The authors are academics. The book is not rigorous or demanding. It's written in plain language with wit and warmth.
Despite being accessible and fun to read, it is well annotated throughout, and the chapter notes will provide keen readers with many hours of further reading enjoyment. There are tantalizing glimpses of so many cool ideas throughout, and readers will likely find themselves delightfully lost in following the breadcrumbs to more in-depth knowledge.
Four and a half stars. It would be a good choice for public or post-secondary school library acquisition, home use, or gifting to a STEM interested reader.
Disclosure: I received an ARC at no cost from the author/publisher for review purposes
January 27, 2025
I am a PhD student in mathematics, that is the context I come to this from. I also study PDE and am familiar with Noether and Kowalevski, who I agree deserve higher regard in the history of mathematics.
That being said, this book is bad on so many levels:
1. It is poorly written. The book could have been edited down to 1/4 of the size and communicated the same amount of information. There are heaps of paragraphs which communicate ZERO information. The authors are not good at communicating mathematical concepts either.
2. There are many factual errors, and the authors do not provide references or citations. Thus there are many sections where it feels like the authors are making stuff up because...
3. ...this book is a piece of political writing not history. The authors go out of their way to diminish the contributions of European mathematicians and elevate the (extremely minor) contributions of "minority" mathematicians. For example, they insinuate the Indian Kerala school discovered calculus and that Newton and Leibniz would not have arrived at their theories had it not been for Kerala, but after much drivel they finally admit that "The idea that a school in India could have passed the baton to Newton and Leibniz is an exciting possibility". An EXCITING POSSIBILITY! This is a book billed as history, but presents wildly speculative theories disguised as fact (with no citations remember!), not because these things are true, but because they are "exciting possibilities".
I think that there is ample room for a well-researched, well-cited, history of mathematics with the stated goal of bringing to light the stories that were glossed over by traditional histories of mathematics. But this book is not that!
That being said, this book is bad on so many levels:
1. It is poorly written. The book could have been edited down to 1/4 of the size and communicated the same amount of information. There are heaps of paragraphs which communicate ZERO information. The authors are not good at communicating mathematical concepts either.
2. There are many factual errors, and the authors do not provide references or citations. Thus there are many sections where it feels like the authors are making stuff up because...
3. ...this book is a piece of political writing not history. The authors go out of their way to diminish the contributions of European mathematicians and elevate the (extremely minor) contributions of "minority" mathematicians. For example, they insinuate the Indian Kerala school discovered calculus and that Newton and Leibniz would not have arrived at their theories had it not been for Kerala, but after much drivel they finally admit that "The idea that a school in India could have passed the baton to Newton and Leibniz is an exciting possibility". An EXCITING POSSIBILITY! This is a book billed as history, but presents wildly speculative theories disguised as fact (with no citations remember!), not because these things are true, but because they are "exciting possibilities".
I think that there is ample room for a well-researched, well-cited, history of mathematics with the stated goal of bringing to light the stories that were glossed over by traditional histories of mathematics. But this book is not that!
June 9, 2024
The Secret Lives Of Numbers by Kate Kitagawa and Tim Revell is a book about the history of the invention of Mathh and different attributes of math. From the first use of absolute zero to the invention of algebra decimals and so so much more if that sounds boring to you it is only because I am doing the book a great injustice this book was so good it talks about the first women in mathematics the first segments of humanity to do math the different people who invented similar techniques as well as the actual numbers we used to count. For example I had no idea algebra and the numerals we use all came from Baghdad I learned about a bone that was dated 20,000 years old that shows measurements by 60s there was even a woman in the ming dynasty who was the Right hand lady for the empress and taught her and the higher up concubines how to do math something women were not taught not only in China but around the world. Not to mention the names you will hear that will be familiar and household names throughout history. This book is not long but long enough to cover almost every class of math there is from astronomy to calculus algebra and on and on so good so interesting I am not a fan of math nor was I great at it but I do love history and couldn’t pass this book up and I’m so glad I didn’t it was so truly interesting. I want to thank William Morrow for my free arc copy via NetGalley. Please forgive any mistakes as I am blind and dictate my review.
July 26, 2024
"Mathematics has been filled with fascinating characters for millenia" - so true!! I have only known one or two and they are truly different. It stands to reason these characters would be found in every clime and every time. Like Terry Bisson's bears who discover fire, these interesting people come up with the bases for the technology we all use. The glimmer we get of an oral mathematical system in west Africa should alert us to the fact that we only know what someone wrote down on a medium that could survive the years. Not every culture wrote things down, but we can never therefore conclude that they had no complex math. I liked the different reasons for people to become interested in math. Some had real world needs, like predicting monsoons and eclipses. Some just enjoyed figuring things out. And the book is a joy to read - fun and filled with trivia for those of us who need trivia. It's interesting for example to know that pi only needs to be calculated to 14 decimal places in order to control rockets launching into space. I like that a "She Figures" report exists, as well as the "Erdos number". My most favorite thing personally is to learn that the famous al-Khwarizmi and other mathematicians of his era did not have modern notation to use (like equals signs), and had to write everything out in words. That is something I'd like to read in Arabic - it looks like the Library of Congress has some of its pages.
September 3, 2024
This book is at once both fascinating and frustrating.
The cross-cultural history of mathematics is the fascinating part. It gets away from a Euro-centric and male-centric development of mathematical ideas and processes. As the authors write (170),
"[Mathematics] is an ever-evolving body of knowledge affected by culture, location and time," a point they demonstrate repeatedly and well. The inclusion of women mathematicians like Hypatia, Mary Cartwright and Dona Strauss provides an historical correction, akin to what the film "Hidden Figures" did for the NASA space program.
The frustrating part comes from the authors' discussion of math itself, as in Chapter 15, "Number Crunching." I got an A in college calculus, but their use of calculus equations loses me. Discussions of things like Apollonius' problem, Diophantus' notation, and "Problems still to solve" left me adrift. When they write something like, "...as we discussed in chapter 8," with no further explanation, I don't know what they mean and am not going to go back and re-read chapter 8.
In their conclusion, the authors note that math started with "scratches on bones and clay" and leads us into "a world awash in data" that requires a mathematics to store, sort, analyze and make sense of. They just need to realize that when it comes to math, their readers may be fascinated by the history they provide but are still in the "scratches on bones and clay" stage when it comes to understanding the math itself.
The cross-cultural history of mathematics is the fascinating part. It gets away from a Euro-centric and male-centric development of mathematical ideas and processes. As the authors write (170),
"[Mathematics] is an ever-evolving body of knowledge affected by culture, location and time," a point they demonstrate repeatedly and well. The inclusion of women mathematicians like Hypatia, Mary Cartwright and Dona Strauss provides an historical correction, akin to what the film "Hidden Figures" did for the NASA space program.
The frustrating part comes from the authors' discussion of math itself, as in Chapter 15, "Number Crunching." I got an A in college calculus, but their use of calculus equations loses me. Discussions of things like Apollonius' problem, Diophantus' notation, and "Problems still to solve" left me adrift. When they write something like, "...as we discussed in chapter 8," with no further explanation, I don't know what they mean and am not going to go back and re-read chapter 8.
In their conclusion, the authors note that math started with "scratches on bones and clay" and leads us into "a world awash in data" that requires a mathematics to store, sort, analyze and make sense of. They just need to realize that when it comes to math, their readers may be fascinated by the history they provide but are still in the "scratches on bones and clay" stage when it comes to understanding the math itself.
October 12, 2024
Generally I must say the book read really nice, the stories about the people in history of mathematics are interesting, but I was probably expecting something little different: this is more about the mathematicians/physics/astronomers in history and less about the ideas ... The goal seems to be to put bigger emphasis on achievements of women and minorities in mathematics - which is probably fine because we know just the big names and there were many others. But sometimes I had a feeling it's too forced. Anyway, the stories were interesting and it was mostly a pleasure to read them, sometimes I felt that some facts about their lifes could be left out because they were not important. What was disturbing more was that many of the illustration and images were like "randomly" selected and many times I didn't understand the real reason why do I need to see the particular image or even that there was something contradicticting on the image vs in the text. Unfortunately there were some errors (at least in the Slovak translation) which disturbed me even more (how can you trust a mathematical book containing errors?) - I hope it just happened in the translation... As I said I think the book was more focused on the stories of people rather than the ideas and I think many readers don't notice those errors as they don't spend too much time with understanding some of the ideas explained there because sometimes it's quite confusing and it could be definitely be explained better.
February 16, 2024
I received an ARC of this book from Netgalley and the publisher in exchange for my honest review.
This book is about the historical people, events, civilizations, and cultures giving rise to mathematical systems, mathematical discoveries, uses for mathematics. There are some examples of numbers or numerical methods of solving problems, but that’s not the book’s focus.
A discussion of the pre-historic use of numbers and ways of marking them is discussed, and the various numerical systems used by ancient civilizations, through the common era, even into the recent past and present, and how those differ. Much of the difference has to do with culture, worldview, and mythology or religion. In several instances, the leaders of a predominant religion made decrees against mathematics since it didn’t fit with the belief of those leaders.
Although mathematics is universal, it’s astounding the amount of racism, sexism, classism, and economic-status has held promising mathematicians back. There are women, blacks, former-slave, and poor people who’ve overcome these obstacles and became great mathematicians. There are still disparities in the number of women who get PhDs in statistics or mathematics vs their male counterparts, although in most fields of study it’s close to even.
This book is about the historical people, events, civilizations, and cultures giving rise to mathematical systems, mathematical discoveries, uses for mathematics. There are some examples of numbers or numerical methods of solving problems, but that’s not the book’s focus.
A discussion of the pre-historic use of numbers and ways of marking them is discussed, and the various numerical systems used by ancient civilizations, through the common era, even into the recent past and present, and how those differ. Much of the difference has to do with culture, worldview, and mythology or religion. In several instances, the leaders of a predominant religion made decrees against mathematics since it didn’t fit with the belief of those leaders.
Although mathematics is universal, it’s astounding the amount of racism, sexism, classism, and economic-status has held promising mathematicians back. There are women, blacks, former-slave, and poor people who’ve overcome these obstacles and became great mathematicians. There are still disparities in the number of women who get PhDs in statistics or mathematics vs their male counterparts, although in most fields of study it’s close to even.
August 26, 2024
This is a really interesting and even fun read of the well known and far-less-well known corners of mathematical history. For example - Leibniz or Newton for the first to develop calculus? How about maybe Madhava, an Indian mathematician 300 years prior?
This isn't only a book for math majors. While there are certainly a lot of equations, the authors tell the fascinating and sometimes sad stories of the many who were not white males from the "Western Civilization" canon who nonetheless contributed mightily to the advancement of the subject. It's wonderful to see them getting their due in this book.
If you're not into math, read it for that part of story and for insight into how much has gotten overlooked and suppressed by prejudice. Also, for how counting first developed, and the ingenious methods used in early history to count (and add). These aspects are of general interest, in my opinion.
If you are into math, read it for the above as well as for the specifics of how the amazing discoveries came about.
And finally, if you're the publisher, be alerted that (if you already haven't been), in the first edition, the Pascal's Triangle on the right side of page 76 has three typos. Identifying them is left as an exercise for the reader.
This isn't only a book for math majors. While there are certainly a lot of equations, the authors tell the fascinating and sometimes sad stories of the many who were not white males from the "Western Civilization" canon who nonetheless contributed mightily to the advancement of the subject. It's wonderful to see them getting their due in this book.
If you're not into math, read it for that part of story and for insight into how much has gotten overlooked and suppressed by prejudice. Also, for how counting first developed, and the ingenious methods used in early history to count (and add). These aspects are of general interest, in my opinion.
If you are into math, read it for the above as well as for the specifics of how the amazing discoveries came about.
And finally, if you're the publisher, be alerted that (if you already haven't been), in the first edition, the Pascal's Triangle on the right side of page 76 has three typos. Identifying them is left as an exercise for the reader.
September 13, 2024
This is like a reprise on Rebecca Stott's "Darwin's Ghosts" in the sense that Rebecca presents a series of lucid portraits of characters (and their environment) that have had the general idea of evolution, and Kate presents portraits of a number of characters who have made very significant contributions to mathematics. Rebecca has a very memorable description of Basra, and Al-Jahiz, who wrote the "Book of Animals" as well as much else, while Kate has (as one example) the Abbasid dynasty (750-1258) and the great Al-Khwarisme (780-850), writer of the "Compendious Book on Calculation by Completion and Balancing".
The House of Wisdom (Library of Baghdad) included a society of scientists and academics, a translation department, and a library that preserved the knowledge acquired by the Abbasids over the centuries. Research and study of alchemy, which was later used to form the structure of modern chemistry, was also conducted there. Oh that we could have leaders so interested in science now!
At the House of Wisdom, in Baghdad, scholars pored over Indian books on mathematics. These works used a set of ten symbols to represent numbers-not letters of the alphabet, as in Baghdad and Rome. In the early 800s, mathematician Muhammad ibn Musa al-Khwarizmi wrote a book on how to do math using the Indian system.
The House of Wisdom (Library of Baghdad) included a society of scientists and academics, a translation department, and a library that preserved the knowledge acquired by the Abbasids over the centuries. Research and study of alchemy, which was later used to form the structure of modern chemistry, was also conducted there. Oh that we could have leaders so interested in science now!
At the House of Wisdom, in Baghdad, scholars pored over Indian books on mathematics. These works used a set of ten symbols to represent numbers-not letters of the alphabet, as in Baghdad and Rome. In the early 800s, mathematician Muhammad ibn Musa al-Khwarizmi wrote a book on how to do math using the Indian system.
Displaying 1 - 30 of 113 reviews