Bertrand Russell wrote that: “Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” I agree. Math is, however, a human thing, all tangled up with the nature of human personality and the history of our civilizations. Well-written biographies of great mathematicians put that “stern perfection” in a proper human context.
I wrote
Unknown Quantity: A Real and Imaginary History of Algebra
Elegantly written, skillfully ornamented with personal reminiscences and anecdotes (some very funny), this is all that a biography should be. The subject, David Hilbert (1862-1943) was a mathematician of the first rank in the decades around 1900. He was also a champion of talent wherever it might be found. When, in 1915, the Senate of Göttingen University would not grant formal lecturer rank to Emmy Noether because of her sex, Hilbert protested that, “We are a Senate, not a bath-house.” He then announced lectures in his own name, but had Noether deliver them.
When my daughter acquired a pet hamster in 2005 I named him Hilbert. On his death the following year I posted an obituary poem, In Hilbertiam, which can still be read on the internet.
"It presents a sensitive portrait of a great human being. It describes accurately and intelligibly on a nontechnical level the world of mathematical ideas in which Hilbert created his masterpieces. And it illuminates the background of German social history against which the drama of Hilberts life was played. Beyond this, it is a poem in praise of mathematics." -SCIENCE
When I was asked to review this book, my first instinct was to decline. Newton (1642-1727) was a towering genius but a dull fellow, with no interest in other human beings. He often published anonymously for fear that, he explained: "Public esteem, were I able to acquire and maintain it … would perhaps increase my acquaintance, the thing which I chiefly study to decline." How can a biographer make such a person interesting?
The author dodges very nimbly around this problem, giving us an account, not so much of the man as of his reputation and influence. Perhaps this means that her book is not a true biography, but it is done with such skill and wit, I include it anyway.
Isaac Newton has become an intellectual avatar for our modern age, the man who, as even children know, was inspired to codify nature's laws by watching an apple fall from a tree. Yet Newton devoted much of his energy to deciphering the mysteries of alchemy, theology, and ancient chronology. How did a man who was at first obscure to all but a few esoteric natural philosophers and Cambridge scholars, was preoccupied with investigations of millennial prophecies, and spent decades as Master of the London Mint become famous as the world's first great scientist? Patricia Fara demonstrates that Newton's reputation, surprisingly…
Gödel (1906-1978) is, like Newton, an unpromising subject for biography. He was antisocial and mentally unstable. His obsessive fear of being poisoned led eventually to him starving himself to death.
Rebecca Goldstein is a professor of philosophy with a deep interest in logic and the foundations of mathematical truth – the applecart that Gödel overturned in 1931 with his tremendous paper on the incompleteness of axiomatic systems. She is also an experienced novelist. This combination makes her just the right person to construct a gripping story out of Gödel’s weirdness and world-shaking importance.
Probing the life and work of Kurt Goedel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning-and brought him to the edge of madness.
This is a work of historical fiction by a master storyteller. I have been acquainted with Charles Kingsley (1819-1875) since being given The Water-Babies and Westward Ho! to read in childhood. Here he takes as his subject Hypatia of Alexandria (370-415), daughter of the mathematician and philosopher Theon. She was played by Rachel Weisz in the 2009 movie Agora.
Hypatia’s own contributions to mathematics are unclear. “All Hypatia's work is lost except for its titles and some references to it,” says her biographical entry in the MacTutor online history of math; but since she does have a MacTutor entry, I claim her as a mathematician.
Queen Victoria liked Hypatia so much she appointed Charles Kingsley personal tutor to her son, the future King Edward VII.
Hypatia, or New Foes with an Old Face is an 1853 novel by the English writer Charles Kingsley. It is a fictionalised account of the life of the philosopher Hypatia, and tells the story of a young monk called Philammon who travels to Alexandria, where he becomes mixed up in the political and religious battles of the day. Although intended as Christian apologia, the novel has a deliberate anti-Catholic tone, and it also reflects Kingsley's other prejudices about race and religion, many of which were typical to the 19th century. For many years the book was considered one of Kingsley's…
First published in 1937, this is a classic in its field: still, so far as I know, the most comprehensive one-volume collection of math biographies. Bell’s 42 subjects range from Zeno of Elea (fifth century B.C.) to Georg Cantor (1845-1918) and include all eight Bernoullis. Nor is the book as exclusionary as its title suggests: Sofia Kovalevskaya shares a chapter with Karl Weierstrass.
I read the book in my teens and retain that early affection. However, I love this book the way we love family members: with differences of opinion and occasional irritations (some of which I aired in Unknown Quantity). Bell is sometimes wrong -- e.g. about Galois -- and often opinionated. Still, he shapes the history of math in a way I have found true and useful overall.
Writing Unknown Quantity was something of a challenge to myself, by myself. At the very end of the book I note that while math today at the highest levels is remarkably unified, there are still distinct styles of mathematical thinking. It was always the algebraic style that gave me the most trouble. Hoping to correct this, I took a deep dive into the history of algebra.
I am not sure that the effort made me a better algebraist; but I do think that coming to algebra from sort of the outside – I mean, from inside math and as a lifelong lover of math, but from outside the most purely algebraic style of thinking – I am well-equipped to see the history of the subject in true perspective.
When I was writing this book, several of my friends jokingly called it the Nazi baby book, with one insisting it would make a great title. Nazi Babies – admittedly, that is a catchy title, but that’s not exactly what my book is about. SS babies would be slightly more on topic, but it would be more accurate to say that I wrote a book about SS men as husbands and fathers.
From 1931 to 1945, leaders of the SS, a paramilitary group under the Nazi party, sought to transform their organization into a racially-elite family community that would serve…
From 1931 to 1945, leaders of the SS, a paramilitary group under the Nazi party, sought to transform their organization into a racially-elite family community that would serve as the Third Reich's new aristocracy. They utilized the science of eugenics to convince SS men to marry suitable wives and have many children.
Marriage and Fatherhood in the Nazi SS by Amy Carney is the first work to significantly assess the role of SS men as husbands and fathers during the Third Reich. The family community, and the place of men in this community, started with one simple order issued by…
