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Wednesday, December 04, 2019

The Art of Conjecturing: On Karen Olsson’s “The Weil Conjectures” | Science & Technology - lareviewofbooks

Michael J. Barany, teaches history of science at the University of Edinburgh and writes on the history and culture of modern mathematics reviews Karen Olsson’s “The Weil Conjectures,” a hybrid elegy and memoir about the power of conjecturing — in math, life, and writing. 
Photo: Michael J. Barany

THE INTELLECTUALLY TOWERING French mathematician André Weil, whose life spanned most of the 20th century, spent the latter half of his career as a professor at the imposing Institute for Advanced Study (IAS) in Princeton, New Jersey. If you visited his faculty profile page on the IAS website any time before June 2017, you would have seen only one honor listed: “Member Poldavian Acad of Sci and Lett.”

Don’t bother looking up Poldavia on a map or its academy in a directory of learned societies. The country is fictional. It was invented by a right-wing journalist in 1929 to provoke and mock political opponents whose sympathies extended to Eastern Europeans devastated by the Great War. Poldavia’s academy came about in the next decade, when a renegade collective of French mathematicians launched a project to rewrite the foundations of modern mathematics. At Weil’s suggestion, they adopted a collective pseudonym, Nicolas Bourbaki, and endowed him with a backstory as a Poldavian refugee.

Weil contributed prolifically to both Bourbaki’s mathematics and his lore, in 1948 going so far as to complete an application in Bourbaki’s name to join the American Mathematical Society. At some unknown point, Poldavia and other Bourbaki fictions (like the portmanteau city of Nancago from Bourbaki’s early post–World War II homes of Nancy, France, and Chicago, Illinois) migrated from Bourbaki’s curriculum vitae to Weil’s. In town for my PhD graduation, I paid a visit to the IAS archives and came across a Weil CV that included Poldavia and Nancago. I shared the find with an archivist, who was not so charmed by the farce. Shortly thereafter, Poldavia disappeared from Weil’s web profile.

Poldavia appears only fleetingly in Karen Olsson’s genre-defying The Weil Conjectures. But the entangled motifs and motives Poldavia represents — mathematics, fiction, speculation, brilliance, biography, hardship, mockery, intimidation, solidarity, generosity, and moral and theoretical imagination — run throughout the book, making it one of the most insightful meditations on modern mathematics I have ever read. With startling originality, Olsson confronts the problem of knowing mathematics from the outside. In the process, she vividly portrays the human dimensions of mathematical creativity...

The book introduces them as alarmingly precocious children, conversing in ancient Greek and competitively reciting verse, and, more whimsically, swearing off knee socks. Part One follows their lives through adolescence to the outbreak of World War II: Simone propounds inscrutable philosophies and quixotically pursues a moral program of radical empathy in coal mines and factories and on the front lines of the Spanish Civil War, while André emerges as a formidable mathematician, learns Sanskrit, decamps to India, returns to France, and begins conspiring under the sign of Bourbaki. Parts Two, Three, and Four take the story through André’s imprisonment for failing to report for duty during the war, and then his flight to the United States; Simone’s dogged attempts to comprehend her brother’s mathematics and her own wartime moral and philosophical obsessions; André’s eponymous conjectures that used daring analogies to “span the gap between the continuous (space) and the discrete (whole numbers)”; and Simone’s death in 1943, partly from limiting her diet to what she imagined were the wartime rations of children in France. Part Five considers Simone’s legacy and then moves the main arc of the story to Japan, where André would become associated with another conjecture developed by Yutaka Taniyama and Goro Shimura. He returned there near the end of his life to accept the Kyoto Prize.
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Recommended Reading
The Weil Conjectures:
On Math and the Pursuit of the Unknown

Source: lareviewofbooks