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What makes mathematicians tick? How do their minds process formulas and concepts that, for most of the rest of the world's population, remain mysterious and beyond comprehension? Is there a connection between mathematical creativity and mental illness?

In The Mind of the Mathematician, internationally famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind. Together they explore the behavior and personality traits that tend to fit the profile of a mathematician. They discuss mathematics and the arts, savants, gender and mathematical ability, and the impact of autism, personality disorders, and mood disorders.

These topics, together with a succinct analysis of some of the great mathematical personalities of the past three centuries, combine to form an eclectic and fascinating blend of story and scientific inquiry.

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This vividly illustrated history of the International Congress of Mathematicians a meeting of mathematicians from around the world held roughly every four years acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century. Because the congress is an international meeting, looking at its history allows us a glimpse into the effect of wars and strained relations between nations on the scientific community. ... Read more

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This revised and greatly expanded second edition of the Russian text Tales of Mathematicians and Physicists contains a wealth of new information about the lives and accomplishments of more than a dozen scientists throughout five centuries of history: from the first steps in algebra up to new achievements in geometry in connection with physics. The heroes of the book are renowned figures from early eras, such as Cardano, Galileo, Huygens, Leibniz, Pascal, Euler, Lagrange, and Laplace, as well some scientists of last century: Klein, Poincaré, and Ramanujan.

A unique mixture of mathematics, physics, and history, this volume provides biographical glimpses of scientists and their contributions in the context of the social and political background of their times. The author examines many original sources, from the scientists’ research papers to their personal documents and letters to friends and family; furthermore, detailed mathematical arguments and diagrams are supplied to help explain some of the most significant discoveries in calculus, celestial mechanics, number theory, and mathematical physics. What emerges are intriguing, multifaceted studies of a number of remarkable intellectuals and their scientific legacy.

Written by a distinguished mathematician and accessible to readers at all levels, this book is a wonderful resource for both students and teachers and a welcome introduction to the history of science.

Customer Reviews (1)

A glimpse into the biographies of some great minds!
Simon Gindikin did an excellent job in this new edition of his book. I got acquainted with his research not too long ago when reading an essay on Penrose's Twistor theory in the "Mathematical Intelligencer" by Springer dating from early 80's.
Eventually I found out the first edition of his book, which was already quite delightful.
The book, besides being filled with witty historical facts, contains also a few interesting problems to improve one's mathematical culture.
I'm particulary kind of the chapter on Huygens and his mechanical works,Poincare's ideas on non-euclidean geometry and finally and the above mentioned article on twistor theory(which could be included on a course on analytical/projective geometry, example).
As my usual cliche, "Two thumbs up!".
... Read more

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G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.Amazon.com Review
A Mathematician's Apology is a profoundly sad book, thememoir of a man who has reached the end of his ambition, who can nolonger effectively practice the art that has consumed him since he wasa boy. But at the same time, it is a joyful celebration of thesubject--and a stern lecture to those who would sully it bydilettantism or attempts to make it merely useful. "Themathematician's patterns," G.H. Hardy declares, "like the painter's orthe poet's, must be beautiful; the ideas, like the colours orthe words, must fit together in a harmonious way. Beauty is the firsttest: there is no permanent place in the world for uglymathematics."

Hardy was, in his own words, "for a short time the fifth best pure mathematician in the world" and knew full well that "no mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." In a long biographical foreword to Apology, C.P. Snow (now best known for The Two Cultures) offers invaluable background and a context for his friend's occasionally brusque tone: "His life remained the life of a brilliant young man until he was old; so did his spirit: his games, his interests, kept the lightness of a young don's. And, like many men who keep a young man's interests into their sixties, his last years were the darker for it." Reading Snow's recollections of Hardy's Cambridge University years only makes Apology more poignant. Hardy was popular, a terrific conversationalist, and a notoriously good cricket player.

When summer came, it was taken for granted that we should meet at the cricket ground.... He used to walk round the cinderpath with a long, loping, clumping-footed stride (he was a slight spare man, physically active even in his late fifties, still playing real tennis), head down, hair, tie, sweaters, papers all flowing, a figure that caught everyone's eyes. "There goes a Greek poet, I'll be bound," once said some cheerful farmer as Hardy passed the score-board.

G.H. Hardy's elegant 1940 memoir has provided generations of mathematicians with pithy quotes and examples for their office walls, and plenty of inspiration to either be great or find something else to do. He is a worthy mentor, a man who understood deeply and profoundly the rewards and losses of true devotion. --Therese Littleton ... Read more

Customer Reviews (31)

A Non-Mathematician's Apology
It is a melancholy experience for one to find himself reading about mathematicians and not mathematics. It is a sad experience to travel down memory lane and note that any interest one had in mathematics during the school and college days were for grades and grades only. It is, perhaps, even sadder to realize that the aesthetic aspect of it was never really and truly detected; still more to realize that that abstractness, though acceptable in mild doses, was considered as some sort of weirdness. The case for my mathematical life, then, or for that of any one else who has been a non-mathematician in the same sense which I have been one, is this: that, though the chance to make a contribution is lost, there, perhaps, exists still the opportunity to stroll through it and enjoy the walk.

A Mathematician's Apology

G.H. Hardy (1877-1947) is a famous mathematician and this book is famous, perhaps because he is its author, but the question of whether the book is especially remarkable and worthy of praise is separate from the fact of its being famous. Hardy loved mathematics, and he loved it for itself, not for what it offered to the physical world of a man's life. Useful mathematics, in his view, lacks the aesthetic and moral purity of mathematics that has no worldly use. Spin out the implications of this and add in that the quality of person's life (the ongoing value of his life as he lives it) is determined by the aesthetic and moral value of what he creates and you get Hardy's view of himself and others. The value of his life lay, he believed, in his mathematically creative past. Once Hardy lost his mathematical creativity, he felt himself to be of no ancillary value. His life, as a thing of ongoing value, was finished. From that point on, his life was "trivial".

Add one star to make four if C.P. Snow's introduction is taken into account.

INTERESTINGBUT DATED
Thetitle" A mathematiciansapolgy" occurs so often in bibliographysthat when I saw a copy of this famous bookI decided that I should read it as I have always had a particular love for mathematics.Not being a mathematicecian myself but having read many similar expositions of mathemematics and being a user of much mathematics I was keen to see what all the fuss was about.
I must say I was rather disapointed.This is a short book .The introduction by the Writer /Phyicist CP Snow being almost as long as the book.
Hardy comes accross as a the sort of Englishman that has long since been extinct.A prewarboffin type ,living in his own little world.A genius , true, but a rather sad one.
The book is permeated with Hardy's sadness that he has lost his mathematical prowess.True mathematics is a young mans game .But isn't this true of most of life? At least be thankfuul that once you had a gift.Be happy that now other young men will carry on the tradition.
Hardy's predictionthat his mathematics was of no practiccal use shows how wrong he was.Even as he wrote in the 40'snumber theory was being used in code breaking, Relativity theory has implications in nuclear energy and Quantum theory has helped to change the world in semiconductor physics.
Of couse maths is not donefor purly practical purposes .But neirther is any study of Science or nature.Man yearns to understand.That is a very human quality.
There is no in deep discussion of why mathematics works.
In short we get a picture of a rather shallow man.The passing of 70 years have done little to enhance his reputation.
Compare this book to that of the MathematicianJacobBronofski.A man a multiple intersstswho loved his fellow mankind.His writings are still as fresh as there were when they were writen 60 years ago

A Well- Titled Classic
This is a sad thoughtful book, slightly off-base due to recent developments, but still full ofsad and wonderful truths about mathematics and mathematicians.

What is mathematical beauty?
In the most famous phrase of the book, Hardy proclaims that "Beauty is the first test: there is no permanent place in this world for ugly mathematics." Quite so, but wherein does mathematical beauty consist? Here is Hardy's answer:

"What 'purely aesthetic' qualities can we distinguish in such theorems as Euclid's [on the infinity of primes] or Pythagoras's [on the irrationality of the square root of two]? ... In both theorems (and in the theorems, of course, I include the proofs) there is a very high degree of [1] unexpectedness, combined with [2] inevitability and [3] economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions. There are no complications of detail; one line of attack is enough in each case; and this is true too of the proofs of many much more difficult theorems, the full appreciation of which demands quite a high degree of technical proficiency. We do not want many 'variations' in the proof of a mathematical theorem: 'enumeration of cases', indeed, is one of the duller forms of mathematical argument." "The beauty of a mathematical theorem depends a great deal on its [4] seriousness ... The 'seriousness' of a mathematical theorem lies ... in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas."

I say: these four conditions are neither individually necessary nor jointly sufficient. In support of which I offer the following considerations.

Unexpectedness. Counterexample to the necessity of this criterion: Bernoulli's theorems on the logarithmic spiral. Bernoulli discovered numerous remarkable properties of this spiral: that it is "equal to its caustics by reflection and refraction, to its evolute, and to numerous other derived or conjugate curves" (Le Lionnais). Surely the unexpectedness would have worn off as his study went on. But there is no indication that Bernoulli's appreciation for the theorems diminished with it. On the contrary he wrote that "This marvelous spiral gives me such overwhelming pleasure that I can scarcely satisfy my desire to contemplate it" (ibid.).

Inevitability. There are many senses in which there can be ``no escape from the conclusion'' in a proof. A specification is needed for meaningful discussion. It seems to me that the only way to narrow down Hardy's intention is to take his phrase regarding "one line of attack" as his explication of inevitability. This is still very vague, but I think it is precise enough to admit counterexamples. A counterexample, then, would have to be a proof which we admire not for charging at the Achilles heel of the enemy, but rather for winning the battle by masterful deployment of forces and exquisite interplay between cavalry and infantry. I believe there is mathematical beauty of this type, for example Galois theory, and in particular its proof of the insolubility of the quintic. Another example is the theory of Riemann surfaces, which any general enjoys deploying with a deft touch, but which is nevertheless unlikely to win a battle all by itself. These are examples of a more general phenomena: the application of ideas from one field to a seemingly unrelated one (in our cases: group theory in algebra, and topology in complex analysis). Such interconnections are a considerable source of aesthetic pleasure. But this can hardly be said to be due to their enabling a single line of attack to replace a plurality of such lines. On the contrary, such interconnections often, as in our examples, function as simpler and more elegant alternatives to some aspect of a previously perceived "brute force" line of attack. (In fact, such connections are often discovered in precisely this manner; again this is the case in our examples.)

Economy. This, I take it, is what Hardy defines when he writes that "the weapons used seem so childishly simple when compared with the far-reaching results." A counterexample, then, would consist in beautiful use of advanced weapons to prove simple results. But surely there can be no doubt that advanced theories can yield beautiful spin-off proofs of rather basic results. For example, there are a number of beautiful solutions of the ancient isoperimetric problem based on modern theories such as complex analysis, vector analysis, etc. (for which, see my article in the Am. Math. Monthly).

Seriousness. As we see above, seriousness amounts to connectivity. Now, a theorem with no connectivity with the rest of mathematics is not likely to count as mathematics at all. However, it seems to me that there are enough beautiful theorems whose seriousness is so unexceptional (e.g., Bernoulli's theorems on the logarithmic spiral, the theorem that there are five regular polyhedra) that a criterion weak enough to include them would be too weak to have any teeth. Another source of examples of beautiful theorems with very limited connectivity is classical number theory, of which Euler wrote that "I must confess that I derive nearly as much pleasure from investigations of this kind as from the deepest speculations of higher mathematics".

All criteria at once. The theorem on integration by parts (which is surely not beautiful) scores highly on all four counts, thus proving that they are not jointly sufficient. ... Read more

Product Description
The life of Vito Volterra, one of the finest scientists and mathematicians Italy ever produced, spans the period from the unification of the Italian peninsula in 1860 to the onset of the Second World War--an era of unparalleled progress and unprecedented turmoil in the history of Europe. Born into an Italian Jewish family in the year of the liberation of Italy's Jewish ghettos, Volterra was barely in his twenties when he made his name as a mathematician and took his place as a leading light in Italy's modern scientific renaissance. By his early forties, he was a world-renowned mathematician, a sought-after figure in European intellectual and social circles, the undisputed head of Italy's mathematics and physics school--and still living with his mother, who decided the time was ripe to arrange his marriage. When Italy entered World War I in 1915, the fifty-five-year-old Volterra served with distinction and verve as a lieutenant and did not put on civilian clothes again until the Armistice of 1918. By 1925, he was president of the world's oldest scientific society, the Accademia dei Lincei, the founder and president of Italy's National Research Council, a mentor to the brilliant and restless Enrico Fermi, and "Mr. Italian Science" to the rest of the world. But none of this was enough to keep the government of Benito Mussolini from stripping him of all his honors and affiliations in 1931, when he was one of only twelve professors in the entire country to refuse to sign an oath of loyalty to the Fascist regime. This book, based in part on unpublished personal letters and interviews, traces the extraordinary life and times of one of Europe's foremost scientists and mathematicians, from his teenage struggles to avoid the stifling life of a "respectable" bank clerk in Florence, to his seminal mathematical work--which today influences fields as diverse as economics, physics, and ecology--and from his spirited support of Italy's scientific and democratic institutions during ... Read more

Customer Reviews (5)

Volterra di vivero.
I have just reluctantly completed my second reading of "The Volterra Chronicles".The first time I was pleased to follow the scientific information and see the historical framework revealed.This second time, I read purely for enjoyment and the amazing feeling of being in that time/place while still observing it through a present day lens. Judith R. Goodstein has accomplished an awesome feat of authorship. Thesensibilities of today, and her focusing of our hindsight, inform our view of the personal and professional choices of Volterra.At the same time the reader is made aware of his, and his accomplished countrymen, interaction with the real constraints of their society. The strength of his intellect and, most vividly, his character emerge indelibly.Truly - Volterra lives.

Life of a great mathematician
Vito Volterra, one of the finest scientists and mathematicians Italy ever produced, is best known for his theory of functionals, which led to his later contributions in integral and integro-differential equations; for his interest in solid state physics, astronomy and mathematical biology, whose importance he was among the first to stress. In Goodstein's words "Volterra's life exemplifies the post-unification rise of Italian mathematics, its prominence in the first quarter of the twentieth century, and its precipitous decline under Mussolini... The meteoric rise and tragic fall of Volterra and his circle thus constitutes a lens through which we may examine in intimate detail the fortunes of Italian science in an epic scientific age".
Born in Ancona, into a rather poor Jewish family in the year of the liberation of Italy's Jewish ghettos, Volterra showed very early promise in mathematics. He attended the University of Pisa, where he graduated in physics and where he became professor of rational mechanics in 1883. Ten years later he moved to Turin and in 1900 to Rome, where he taught mathematical physics at the University "La Sapienza". Volterra, an enthusiastic patriot, in 1905 was elected a senator of the Kingdom of Italy on grounds of high scientific standing. In his 1907 talk for the inauguration of the first congress of the Italian Society for the Progress of the Sciences, Volterra proudly drew a comparison between his era and the Renaissance: "In that time of the wonderful restoration of intellectual life, Italy became the very center of universal scientific thought. Today, I venture to wish that the destiny reserved for us not be a lesser one, as the pure and authentic Italian soul rises and takes shape, reviving our thought and restoring to us our ancient country". During World War I, already well into his 50s, he joined the Italian Army and worked on the development of airships. His hopes for Italian science were soon to be betrayed. When Benito Mussolini took power, Volterra joined the opposition to Fascism, and in 1931 he was one of the twelve university professors (over more than a thousand) who refused to take a mandatory oath of loyalty. He was compelled to resign his university post and membership of scientific academies in Italy (he belonged to quite a number of them all over the world), and, during the following years, he lived largely abroad.
This very elegant book, based in part on unpublished private letters and documents, interviews, and personal contacts of the author with members of the scientist's family during her frequent stays in Italy, tells the quite unique life of an extraordinary person in a country and in an age characterized by dramatic events. Judith Goodstein traces a full-size portrait of the man, both in his private and public life. All around him, she draws a vivid picture of the very strong and somewhat suffocating ties within the Volterra family; of the very high quality of the gifted group of mathematicians who interacted with Volterra; of the intriguing happenings in the Italian academic community; of the dramatic conditions of intellectuals in a country that was gradually sinking from a freshly built democracy into a coarse Fascist regime. There are also flavorful glimpses on the scientific communities abroad, in Europe as well as and in North and South America. When in the USA, Volterra lectured in French, though admitting "that at the present time the most indispensable language seems to be English".
It would be hard to provide highlights of the story, so many are the facts, the ideas, the emotions, the surprises the reader will meet along this beautifully depicted historical journey. The book will be of interest not only to scientists, but also to historians and to other learned people: it can be read like a novel, where attention paid to meaningful details and little known episodes conveys a realistic picture of the life of Italians in those years - and of the Jewish community in particular - better than many academic historical essays would.
Bravo Goodstein: elegance, style, thorough insight... the reader will feel that she herself was a witness on the scene.

Andrea Frova
(Professor of Physics, Università "La Sapienza", Roma)
and Mariapiera Marenzana
(Professor of History and Italian Literature)

A Master Mathematician
Amust-read foryour specialreading list this summer is The Volterra Chronicles by Judith Goodstein. This book gives a very well-written and detailedaccount of a renowned Jewish Italian mathematician, Vito Volterra, and his rise to fame during a very turbulentperiod inItalian history (1860-1940). For thosenot familiar with Vito Volterra and his scientific and mathematicalwork, Dr. Goodstein offers bothan exciting and captivating biographyof a great and noble mathematician.

Good Read
This book was very enjoyable to read. I recommend it to anyone who would like to learn more about the academic life in Italy during these very interesting times. The portrait of the customs of an Italian Jewish family, to which Volterra belonged, is particularly well drawn.

The Rise and Fall of Italian Mathematics & Science 1960-1940
The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860-1940

Vito Volterra, one of the great Italian scientists and mathematicians, lived during tumultuous times spanning the years of the Italian unification to the outbreak of the Second World War.He was born into a middle class Jewish family His early years were spent in the Jewish ghetto of Ancona under the eyes of his protective mother who tried to discourage him from a career in mathematics.At twenty-three he became a tenured professor at Pisa and by 1900 he was appointed professor at the University of Rome.

Goodstein has constructed a detailed record of Volterra's personal life by gaining access to the Volterra family's letters and photographs.She provides rich insights into the Italian scientific and mathematical achievements and vividly records the Italian academic world and the response to the national political scene.

This biography is a powerful tribute to a man who dominated the field of mathematics. He developed the areas of integral and differential equations, worked in the field of elastic media and then branched into the area of theoretical ecology and began to apply his mathematical expertise to biological systems.

The ascendancy of Fascism brought the golden age of science and mathematics in Italy to an end.It is interesting that there was a disproportionately large number of Jews within Italian science and mathematics.Mussolini's regime was actively anti-Semitic and barred Jewish scientists and mathematicians from holding university posts and membership in scientific organizations.

In 1931 Vito Volterra was one of only twelve Italian university professors who refused to sign the oath of allegiance to the Fascist government required by all members of the faculty, which resulted in his expulsion from the scientific community. Volterra's life parallels the rise and decline of Italian mathematics and science and provides us with a lens to examine the fortunes of Italian science during this time period. ... Read more

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FROM THE REVIEWS: ... Read more

Customer Reviews (3)

I love this book
I know very little about math, and I say that only to make it clear that I don't have thetools that some people have to explain why I loved reading this book, and why I will read it again, or give it as a gift. But I am a reader, and I couldn't put this book down, and I usually feel that way only about novels. So as a reader I will say that this is a beautiful book. It's almost perfect, in a way. (In the same way that I would say Laurie Colwin's book, Happy All The Time, is the perfect modern American novel.) And that's because it's so hard to put down.

The book is rubbish
Do not buy it. You are wasting you time and money.

Maths limitations, undecidability and randomness: a story
These interviews of G. Chaitin provide a good picture of what science is about: just another human activity. It shows how subjectivity is a part of what people call science...The book provides a historical perspective of the work by Hilbert, Godel, Turing,...on maths and its limitations. Mostly computer scientists and mathematicians will be interested in reading this book since it goes all about Godel and Turing's achievements on the limits of formalisms, undecidability and the limits of mathematics in general...without forgetting the work of G. Chaitin in algorithmic information theory and randomness in mathematics that continues the work of these great men. ... Read more

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Women Becoming Mathematicians looks at the lives and careers of thirty-six of the approximately two hundred women who earned Ph.D.s in mathematics from American institutions from 1940 to 1959. During this period, American mathematical research enjoyed an unprecedented expansion, fueled by the technological successes of World War II and the postwar boom in federal funding for education in the basic sciences. Yet women's share of doctorates earned in mathematics in the United States reached an all-time low. This book explores the complex interplay between the personal and professional lives of those women who embarked on mathematical careers during this period, with a view to understanding how changes in American society during the 1950s, 1960s, and 1970s affected their career development and identities as mathematicians.The book is based on extensive interviews with thirty-six women mathematicians of the postwar generation, as well as primary and secondary historical and sociological research. Taking a life-course approach, the book examines the development of mathematical identity across the life span, from childhood through adulthood and into retirement. It focuses on the process by which women who are actively involved in the mathematical community come to "know themselves" as mathematicians. The women's stories are instructive precisely because they do not conform to a set pattern; compelled to improvise, the women mathematicians of the 1940s and 1950s followed diverse paths in their struggle to construct a professional identity in postwar America. ... Read more

Customer Reviews (2)

No limit to women's success in math
The reason I ordered this book was because my mother's cousin, Kenneth Wolfson, is mentioned in it several times.His support of his female students is well known and remembered by all who knew him.The book itself encourages me to pursue my own degree in mathematics.I owe my future career to my cousin and all of the women in this book.Thank you for being strong and proving to the academic world that women have a place in mathematics.

a good book
I first saw this book in the UT Math Library. I sat down and didn't stop reading it for 45 minutes (too bad I had class). It's really interesting and a quick read. ... Read more

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Customer Reviews (2)

Eye-opening
This is an important work and makes clear yet more aspects of the impact of the Holocaust on the course of modern history.It may be a bit hard to follow for people to whom the names of prominent 20th Century mathematicians are not well-known, but it shows how the Nazis changed the course of scientific history by scattering and murdering so many in one important discipline.

Interesting but pedantic
When the author begins by saying "We need to define what a mathematician is", you know you are in for a slog. The book consists of case studies, which are quite varied. No clear gestalt emerges from the individual situations or even if one is possible. ... Read more

Product Description
This book provides an essential resource for teachers, and for parents keen to try practical maths tasks with their children at home. The book contains illustrated biographies of ten influential mathematicians, plus clear explanations of their theories and ideas. Photocopiable activities focus on problem solving and investigation, while differentiated activities support and extend groups within the class. A key vocabulary is available for use during maths lessons, plus a list of resources required to carry out tasks. There are links to the aims of the NNS for KS2, although the book can also be used effectively at KS3. Cross-curricular links, include the history of ancient civilisations, science, philosophy and astronomy. ... Read more

Customer Reviews (1)

A very good reference book, but not a reading book or textbook
This book is everything the Booklist review states: excellent selection of individuals, a number of appendicies that provide valuable cross-tabulation information, and the most thorough time-line of mathematics I have seen (35 pages).It is a respectable reference book for students and the general public with reading skills of grade 9 or higher.The mathematics content is accessible to persons with intermediate algebra or higher.

The unfortunate drawback of this book is that the biographies are in alphabetical order.The publishing company missed a valuable opportunity: if instead published in order of mathematical developments (semi-chronological) with some bridging material, the book could be both an "armchair" reading book for the general public and a textbook for courses in liberal arts mathematics, mathematics history, etc.Given the excellent cross-tabulations in the appendices, an electronic edition would also be highly valuable.

A minor issue with the book is that the biographies have been slightly sanitized so as to be palatable with high school libraries in the U.S.At the same time, the authors struck a balance by being very forthcoming about the lives and fates of persons.For example, the entry on Pythagorous is excellent for a high-school reference book.

This book can be found in public libraries throughout the U.S. and at many high-school and college libraries as well.

Other books to consider:

Victor Katz has published A History of Mathematics: An Introduction (2nd Edition) which is suitable for an upper-division mathematics-major course in math history.Highly recommended to teachers and students researching the development of mathematics.

Tobias Dantzig's Number: The Language of Science which would be better subtitled "the vocabulary of measurement", is accessible to any successful college sophomore.It gives a somewhat chronological account of the human development of number concepts.Highly recommended to anyone interested in number concepts.
... Read more

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Ioan James introduces and profiles sixty mathematicians from the era when mathematics was freed from its classical origins to develop into its modern form. The subjects, all born between 1700 and 1910, come from a wide range of countries, and all made important contributions to mathematics, through their ideas, their teaching, and their influence. James emphasizes their varied life stories, not the details of their mathematical achievements. The book is organized chronologically into ten chapters, each of which contains biographical sketches of six mathematicians. The men and women James has chosen to portray are representative of the history of mathematics, such that their stories, when read in sequence, convey in human terms something of the way in which mathematics developed.Ioan James is a professor at the Mathematical Institute, University of Oxford.He is the author of Topological Topics (Cambridge, 1983), Fibrewise Topology (Cambridge, 1989), Introduction to Uniform Spaces (Cambridge, 1990), Topological and Uniform Spaces (Springer-Verlag New York, 1999), and co-author with Michael C. Crabb of Fibrewise Homotopy Theory (Springer-Verlag New York, 1998). James is the former editor of the London Mathematical Society Lecture Note Series and volume editor of numerous books. He is the organizer of the Oxford Series of Topology symposia and other conferences, and co-chairman of the Task Force for Mathematical Sciences of Campaign for Oxford. ... Read more

Customer Reviews (5)

it's just ok
I read this book a few months ago. I thought it got kind of stale by the end, they way the author presents the information is fine, but I think that after a while the biographies start to run together. The mathematicians start to fall in similar types, like the mathematician who was famous and didn't have many problems who overshadowed a brilliant mathematician who fell into obscurity. You do learn a lot of information about the mathematicians themselves, but I think that the book could have been better with less mathematicians, or more important famous ones (extend the time frame).

Good book
This book is a collection of short biographies of notable mathematicians from Euler to von Neumann.It does a good job of explaining both a mathematicians background and the significance of their contributions to mathematics.Great to read through or as a reference to have on the shelf.

Very good historical account of lives
The only reason that this book doesn't get 5 stars is because of the fact that not enough emphasis is placed on the achievements of the mathematicians in terms of their mathematics.

However, this does not take away from the fact that is is exteremely well researched, laid out and presented. We get a meaningful insight into how these geniuses (genii?) lived and that fact that they were quite ordinary people with the same levels of hardship (and in some cases even more) as the rest of us. Perhaps an improvement could be made on further mathematicians, both past and present.

Still recommended reading.

Learn how mathematicians interacted with each other
When reading about the great ones of mathematics, I always enjoy short biographies rather than long ones. If the biographer is required to fill a large section of a book, then they tend to cover more detail than I really care for. While I do enjoy some details about the personal life of a mathematician, anything more than just a few morsels tends to detract from their accomplishments in mathematics.
James strikes the perfect balance in describing the lives of these great historical figures. Each biographical sketch is less than ten pages and he covers their life from birth to death. One valuable thing that he does is give their complete names, which is often omitted from biographies. In fact, despite all of my reading about the people of mathematics, there were some whose full names I had not known until I read this book.
The emphasis is on the lives of the people, and the general concepts of the mathematics that they created, rather than the specifics. No formulas are used in the explanations. Personal and professional interactions are a large part of the life of nearly all mathematicians, and from these biographies, we learn many of the specifics of how contemporaries reacted to each other. As is always the case, the full range of human foibles are displayed as the lives of the mathematicians unfold.
The lives of these sixty mathematicians are described in chronological order according to their birth years. Given that they all began their mathematically productive lives at different ages, this leads to some degree of overlap in both directions. Nevertheless, it is possible to easily trace the development of the major mathematical ideas as they are nurtured from early germs to towering oaks.
Mathematicians are people who find themselves in a social and political environment that they must cope with and sometimes just survive in. In this book, you will learn about sixty of them who made a major contribution, sometimes starting from a point of privilege, and other times only after great struggle. It is well worth reading for pleasure and can also be used as a resource for a course in mathematical history.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.

Captivating!
Don't miss these captivating tales of the life and the times of mathematicians starting from the period of Tsar Peter the Great of Russia, and right up to recent times, at least up to and including the Cold War. Even if you aren't in math, I think you are likely to be caught up in the drama of the various lives, times, and events. The writing is fast paced and engaging, much like that of Constance Reid's books: "Hilbert", or "Courant"... Over the tumultous historical periods, it has been said that mathematicians have been more likely than others to have been uprooted in the upheavals of history, perhaps because they are concerned with theories and ideas that are more universal. But their lives are still much affected by the times and the events of history: The French Revolution(Galois, Poisson, Fourier...), the Napolionic Wars(Cauchy, Abel...), the period of Bismarck and Nationalism in Europe(Weierstrass, Cantor, Lie...), the Russian Revolution(Alexander, Kolmogorov...), the two World Wars, and the crisis period between WWI and WWII(Banach, Hadamard, Courant, Hilbert...), and the Cold War(von Neumann, Wiener...). The pictures on the cover give you a sample of the profiles in the book: G. Polya, K. Weierstrass, A. N. Kolmogorov, N. Wiener, S. Kovalevskaya, and S.-D. Poisson. Even if you won't get to meet them in person (I was a guest at George Polya's ninetieth birthday!), this book is the next best thing. ... Read more

Product Description
This book contains a collection of tales about mathematicians and the mathematical, derived from the author's experience. It shares with the reader the nature of the mathematical enterprise, and gives a glimpse of mathematical culture. The book brings legendary names to life, and shares little known stories about names we have heard all our lives. The book is written in a brisk and engaging manner and it also includes a number of attractive photographs and illustrations. ... Read more

Customer Reviews (3)

"Mathematical Apocrypha" is Full of Interesting and Humorous Anecdotes
In my reading of Steven Krantz's "Mathematical Apocrypha", I encounter numerous anecdotes that endorse the view that not only do mathematicians tend to be eccentric, but they are often very funny -- sometimes intentionally so, and sometimes not.
As something of an amateur mathematician-mathematical hobbyist, I find Krantz's book a very good read -- well worth buying. My guess is that many non-mathematicians could also find in the book many stories about mathematicians and their numerous quirks that could provide for humorous storytelling and joking.
As an enthusiaist of mathematical ideas and those who generate them, I find "Mathematical Apocrypha" to be the best source of mathematical anecdotes I've yet been blessed with encountering.

Rather colourless
I thought this book would be about the non-mathematical lives of famous mathematicians, and I was not proven wrong. The problem is that it is a compilation of one-paragraph anecdotes of many matehmaticians' lives, which makes for good coffee table reading and not bedtime reading. There is very little substance to any of the lifestyles of any of the characters.

The accounts themselves relate to the famous and not-so-famous, but many of them are questionable as to whether they actually deserve to be in this book as they are may times simple accounts of a person's daily life - chronicling the events that happen to many of us on a daily basis.

I summary the stories are too brief and there are other (better) factual books on the real lives and histories behind mathematics and mathematicians.

Stories about mathematicians as storytellers
Quite against the opinion of many, mathematicians are people too. They have quirks, foibles and eccentricities that are only slightly different in kind from those possessed by the remainder of the population. If you doubt that statement, read this book and be convinced. The author has collected together a set of the most interesting short stories about people, independent of the fact that they do math. It is funny, insightful and can be read by anyone. After I started it, I found it very difficult to put down, and I highly recommend it to everyone, whether they can balance an equation or not.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more

Product Description
This is the true story of a little girl, Caryn Navy, who, after she became blind at age 10, began to find mathematics fascinating. An independent girl, she learned to travel the subways of New York by herself, trained with a seeing-eye dog, went to college in another state, and earned a Ph.D. in mathematics and computer science. Caryn married an electrical engineer and together they started their own successful computer company. ... Read more

Customer Reviews (1)

Excellent biography for visually impaired students to read!
I work with visually impaired students & this book is the best way to show that anyone with a visual impairment can be successful.I purchased it so I can braille it.Thank you! ... Read more

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This book offers a unique perspective on ways in which mathematicians: perceive their students' learning; teach; reflect on their teaching practice. Elena Nardi achieves this by employing two fictional, yet entirely data-grounded, characters to create a conversation on these important issues. The construction of these characters is based on large bodies of data including intense focused group interviews with mathematicians and extensive analyses of students' written work, collected and analyzed over a substantial period.

Customer Reviews (1)

A collection of explanations and inspirations
Mathematicians may be extraordinary thinkers, but they occasionally have something inspirational or profound to say as well, and many of those sayings have been collected in this book. It is clear that the author considers this a labor of love, as the amount of research that had to be done to put this book together must have been very substantial. The quotes are organized into categories such as "the creative process in mathematics", "mathematics and the arts", "about mathematicians", "anecdotes and humor" and "mathematics education." This makes it much easier to find a quote where the point coincides with the one you want to make.
If there was ever a mathematics book designed for browsing, it is this one. Find a copy and spend some time looking through it. It is an effort well spent. ... Read more

Product Description
Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field, remains an important tool for exploring the increasingly complex problem of mental life.

The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought. ... Read more

Customer Reviews (3)

The Psychology of Invention in the Mathematical Field
Not only is this book fascinating, it's the only one of it's kind. The book has also proved very useful to me in life. As a graduate student I used Poincaré's implicit `advice' (described in the book) in the following way. In electrodynamics we had a long problem sheet to hand in every two weeks. I started by writing down answers to all problems that I knew. Then, I thought about the next-easiest problem each day walking twice to and from the University (about 1 1/2 hours altogether). When the answer came I wrote it down and iterated the process. Before the end of two weeks most of the problems (from Jackson) had been solved. Poincari's advice is very good about giving the unconscious a chance to work. Phooey and double phooey on the silly, uncreative skinner-box types and other behaviorists who don't recognize the unconscious as the source of creativity!

The Psychology of Math
The Mathematician's Mind is a study on how research mathematicians go about the business of advancing their field.Jacques Hadamard, a prominent mathematician, wrote this psychology text over 50 years ago, after having done his best work 50 years prior. Although in some ways dated, both in content and in writing style, the book provides an interesting examination of the role of the conscious and subconscious in solving a problem, particularly the process of incubation and (seemingly) sudden inspiration. He brings up the roles intuition and logic play in the way various mathematicians go about their business.Hadamard also examines the influence of aesthetics in not just choosing a problem, but in solving it. He studies the choice of research direction, with the interesting comment that Hadamard himself avoided areas of research where there was already a great deal of activity.

The book is short enough that if the subject interests you, it is worth your time.

The text is also published under the title "The Psychology of Invention in the Mathematical Field."

A study of the mental workings of some great mathematicians
This is a short study of how creative thought works.Hadamard, a world-class mathematician best known for his proof of the prime number theorem in 1896, wrote this in the 40's, basing it on correspondence with many of the great living mathematicians of his time.The actual questions he posed are preserved in an appendix.

Most of his respondents were mathematicians (and he limited his correspondence to the best minds in the field), but he did get information from several other fields, and cites data about physicists (a letter from Einstein forms another appendix), chemists, physiologists, metaphysicians, and so on.What he is trying to examine is a slippery subject, perhaps best explained by a quote.Here is a discussion of Sidgwick, an economist: "His reasonings on economic questions were almost always accompanied by images, and the images were often curiously arbitrary and sometimes almost undecipherably symbolic.For example, it took him a long time to discover that an odd symbolic image which accompanied the word 'value' was a faint, partial image of a man putting something on a scale."

Hadamard gives his own mental images that accompany his following through the steps of Euclid's famous proof of the infinitude of primes.I won't reproduce that here for space reasons, but the contrast with Sidgwick's--and with other reports of mental activity--is fascinating.Many other examples are given, from Mozart to Polya to Galton to Poincare. Hadamard makes it clear that language and thought are not the same thing, contrary to a commonly expressed view among linguists.He cites Max Muller's comments equating thought and language, and acknowledges that for Muller it may be so, but convincingly demonstrates, by quoting numerous other mathematicians, that it is not true for everyone.The further conclusion, that the process of creative thought, while following similar patterns in similar discipline, can vary dramatically, is as far as Hadamard can go with the data he has.

One other note: this book was originally titled "The Psychology of Invention in the Mathematical Field" and is available under that title from Amazon, published by Dover Books.It's not immediately clear from the Amazon page that this is so.The Dover edition is substantially cheaper.

A fascinating and informative book. ... Read more

Product Description
"We gave this story to a very competent, and very pretty gal artist. We said, ""Read this carefully, dream on it, and come up with an illustration."" A week later, she returned with the finished drawing. ""The hero,"" she said. We did a double take. ""Hey! That''s not the hero."" She looked us straight in the eye. ""Can you prove it"" She had us. We couldn''t, and she left hurriedly to go home and cook dinner for her family. And what were they having Frog legs--what else" ... Read more

Product Description
Compilation of fifty biographies of mathematicians from throughout history and approximately thirty-five articles describing math concepts and principles. ... Read more

Customer Reviews (1)

nice collection, but there's a mistake in the math
I saw this at my library and thought seriously about buying it for my kids.I even learned a few new things - I never knew Lewis Carroll was a mathematician!But I found an math error in the entry on fractions, specifically the part about equivalent fractions.It says

"4/6 becomes 2/3 when divided by 2...
16/36 [divided by] 2 = 8/18,
8/18 [divided by] 2 = 4/9".

Although I understand his intent, the presentation is incorrect.You cannot divide a number by 2 and end up with an equivalent number, unless that number is zero.The multiplicative identity holds that the ONLY number we can multiply or divide by, and end up with an equivalent number, is 1.I believe he meant to say:

"4/6 becomes 2/3 when the numerator and denominator are both divided by 2..."
This is the same as multiplying by (1/2)/(1/2).Because the numerator and denominator are the same, it is equivalent to 1, but it is written in a form that allows you to divide the numerator and denominator of 4/6 by the same amount, which leads to the equivalent 2/3.

I'm curious if this was ever corrected in an updated publishing of the book.

A simpler approach to this problem would be to factor the numerator and denominator, then cancel the common factors.This approach also uses the multiplicative identity, when the same amount is canceled from both the numerator and denominator. ... Read more