The Apprenticeship of a Mathematician

by André Weil

From reviews: "Extremely readable... rare testimony of a period of the history of 20th century mathematics. Includes very interesting recollections on the author's participation in the formation of the Bourbaki Group, tells of his meetings and conversations with leading mathematicians, reflects his views on mathematics. The book describes an extraordinary career of an exceptional man and mathematicians. Strongly recommended to specialists as well as to the general public." --EMS Newsletter (1992)

Genres: Mathematics, Biography, Nonfiction, Memoir, History, Science, India

197 pages, Paperback

First published May 1, 1991

Reviews

[payam Mohammadi · Rating 4 out of 5]

خودزندگینامه نوشتی از آندره ویل ریاضیدان فرانسوی بود. در این کتاب ما با زندگی او و نحوه‌ی ورودش به دنیای ریاضیات آشنا می‌شیم. زندگی‌ای سراسر از اتفاق و سراسر ماجراجویی که از همان اول نمی‌نوشت که این کتاب خودزنگینامه نوشت است ما خیال می‌کردیم داستانی برآمده از ذهن نویسنده هستش؛ آخه چطور میشه آدم تا این حد ماجراجو و تا این حد-گاها- خوش‌شانس که بارها و بارها از دست مرگ فرار می‌کرد. فصل مورد علاقه‌ی من، فصل ۳ بود که درباره‌ی هند نوشته شده بود که واقعا خیلی جالب بود. در این فصل قسمتی بود که نوشته بود وقتی به روستایی از هند می‌رفتند، بومیان خیال می‌کردند که چون این‌ها غربی هستند پس همه‌چی بلد هستند و همه‌چی دارند تا جایی که بیمارانشان رو می‌آوردن پیش اونا تا مداواش کنند. این قسمت منو یاد سفرنامه‌ی کنسول ژاپن در ایران زمان قاجار می‌ندازه که می‌گفت رفته بودیم حوالی-فک کنم-شیراز اهالی اون منطقه به سمت ما هجوم آورده بودند و بیماران‌شون رو به ما نشون می‌دادن تا مداواشون کنیم.
از نکات جالب دیگه‌ی این کتاب جامع‌العلم بودن این بزرگوار بوده که نه تنها در ریاضیات که در فلسفه و شعر هم صاحب نظر بوده و نه تنها فرانسوی که آلمانی، انگلیسی، ایتالیایی، لاتین، کمی سوئدی و کمی پرتغالی هم بلد بوده.
در کل کتاب خوبی بود و واقعا باید همه‌کس این کتاب رو بخونه.

[Saeede Kermani · Rating 4 out of 5]

چه زندگی پر فراز‌ونشیب و چه دوره تحصیلی جذابی، زندگینامه خیلی هیجان انگیزی بود مخصوصن که نویسنده ریاضیدان بوده ولی ترجمه خیلی بد و غیر روونی داشت...
حس مشترک:
« آرزویم این بود که، ریاضیدانی جامع باشم. این آرزو را این طور بیان میکردم که دلم می‌خواست هر موضوع ریاضی را، بیشتر از غیرمتخصص‌ها و کمتر از متخصص‌ها بدانم.»

[Ali Niazi · Rating 4 out of 5]

بخشی از داستان زندگی یک ریاضیدان به نام آندره ویل است و البته بیشتر داستان به اثر جنگ جهانی در زندگی یک ریاضیدان یا بهتر بگم بر علم دارد، زندگی آندره ویل در حین جنگ جهانی و تجسم نحوه زندگی یک ریاضیدان در کشور های مختلف را به تصویر کشیده شده است.

[jeremy wang · Rating 4 out of 5]

I PROMISE THIS IS NOT A MATH BOOK

that aside, this was a very interesting little memoir that positions a mathematician’s apprenticeship as a universal one; weil dances from linguistics to religion to philosophy to art in the span of mere pages, and you get the sense that here writes a man who is passionate about all of them. the span of his intellect is truly remarkable.

there are also plenty of interesting portraits of other people! i learned many little facts about 20th century mathematicians, both great and small, that only andre weil would be able to share (now i get to share these with you, dear mathematically curious reader; message me with questions about lebesgue or picard or jacques feldbau??? or others), and his observations of even non-mathematicians are quite witty.

and here begin my qualms with the book. weil is clearly a thoughtful, liberal person, but he is still immersed in the culture of the time, so his evaluations of people are invariably accompanied by remarks on their “caliber” as intellectuals. and his approach to the many topics he’s interested in is very strange. you can feel some of his sister’s mysticism in him, but it’s paired with an oddly flippant attitude, so that his thoughts are intellectually deep but somewhat irreverent. not sure how i feel about that.

[Matthew · Rating 4 out of 5]

Andre Weil was Simone Weil's brother, whose life during the war was equally interesting. Who else has proven great theorems while in a French prison?

[Rafaela · Rating 4 out of 5]

During my long, ongoing obsession with mathematicians and physicists, I've read quite a few things (mostly negative) about André Weil, whose famous sister, Simone, I knew nothing about. So I decided to check out his autobiography, which left me pleasantly surprised.

Weil knows how to write and paint a colorful picture of the places he has been, and he has smart (and sometimes quite funny) insights about different cultures and people. I love his irreverence, his intellectual curiosity and his sense of humor, which permeate the narrative. India has never caught my interest, but André made it sound so rich and alive. It's very beautifully written and informative! I wish it had been longer.

On the not-so-positive parts:

- The self-censorship. Given his famous arrogance, I wasn't expecting him to be open and vulnerable about some parts of his life he may not have been proud of. But it's quite odd how his wife just suddenly appears in his life, without him mentioning that she was married to another remember of Bourbaki when they got together. He also spent a few paragraphs using the Bhagavad Gita to explain/justify his decision to avoid the draft, which irked me and felt not so honest to me.

- I wish he had included his experiences in the US too. He said in an interview that he decided against it, because nothing interesting happened since he got a job in Chicago, but I disagree and wish he had had a more positive view of the second part of his life 😕 And being Brazilian, I definitely wanted more details about his years in São Paulo.

I missed reading about the less glamorous side of his life: his marriage and kids, his relationship with his parents after Simone's death (which he talks little about), his views (mostly negative, afaik) about the US and his colleagues in Chicago and Princeton, the future generations of Bourbaki members, Bourbaki's legacy, his frustrated desire to return to France, what made Japan and the Kyoto Medal so special to him, etc. I didn't feel like I got the full(er) picture I wanted, but it was worth the read.

(There isn't as much math as I thought there'd be, which I appreciate. I don't know much about it, so I prefer to read about his personal life and relationships. However, some people might be disappointed, especially because of the title)

Anyway, I loved his autobiography, but now I wish we also had a bio about André Weil written by a third party. He travelled a lot, served time in prison (where he made one of his best works lol), experienced different cultures, knew several languages (including Sanskrit), was very erudite, had a very interesting famous sister who died too young, possessed a famously difficult personality, engaged in the good old academic bullying, made controversial choices (wrt the draft, the Taniyama-Shimura-Weil conjecture, etc.)... In some ways, he reminds me a lot of Oppenheimer and I could read a 700-page long book about him as well.

I also can't wait to read his daughter's book "At Home with André and Simone Weil" someday, even if it's not the proper biography we need. Sylvie Weil is a good writer too, although of a different kind.

[Fredrik · Rating 5 out of 5]

Fantastisk bok! Weil skriver om sin oppvekst og sitt utrolig spennende liv før han fikk etablert seg som matematiker i Chicago. Han vokste opp i Frankrike før andre verdenskrig, studerte i Italia og Tyskland, og bodde to år i India (og besøkte mange av de samme stedene jeg var selv for noen år siden), flyttet tilbake til Frankrike, besøkte Finland omtrent da krigen startet, og ble arrestert der, mistenkt for å være russisk spion. Han klarte å komme seg til Sverige, hvor han via Bergen ble fraktet til England, og se etter lang venting kom tilbake til Frankrike, hvor han satt tre måneder i fengsel (hans mest produktive måneder) for ikke å møte opp til militærtjeneste. Han ble dømt til 5 år i fengsel, men slapp unna mot å delta i krigen som soldat. Da Frankrike tapte mot Tyskland klarte han å komme seg vekk som soldat, og etter mye og men klarte han å flykte til USA (nevnte jeg at han var jøde?), hvor han underviste noen år, før han fikk en stilling i Sao Paulo i Brasil, der han underviste til 1947, før han fikk en stilling i Chicago. Han er mannen bak Weil-formodningene, og grunnleggeren av Bourbaki (og også symbolet Ø for den tomme mengde).

[Mike · Rating 4 out of 5]

Interesting book to read. Growing up Weil attended many lectures by famous mathematicians such as Picard and Lebesgue (Pg 40) The best math seminars were at the house of Jacques Hadamard (Pg 38 - 39). These seminars were exactly like the Physicist's Lev Landau. You can read about Landau's seminar in "Landau’s Theoretical Minimum, Landau’s Seminar, ITEP in the Beginning of the 1950’s" by BORIS L. IOFFE. What a time to be alive, one could freely and easily travel Europe. As a student, Weil would often find himself in the homes of prominent mathematicians across Europe, such as Ostrowski in Göttingen (Pg 55). Max Dent had the manuscript of Siegel's "Transcendental numbers". A book I've heard of before reading this one and plan to read soon. Weil was allowed to read the manuscript, but only at Dent's home and he couldn't share his notes with anyone (Pg 53). I just find this kind of funny. While at Cambridge, Weil told Mordell he wrote his thesis based on his paper "On the rational solutions of the indeterminate equation of the third and fourth degree", but Mordell showed no curiosity in it (Pg 94). As WW II broke out, Weil was in Finland. He was accused of being a Russian spy and was nearly executed for it. While in prison he would do some of his best writing (Pg 146) something we hear from many historical figures who spent time locked up. You won't find much talk about his mathematical work in this book. I am a big fan of Andre Weil and I plan to read many of his books and papers in the future.

[Laura · Rating 2 out of 5]

Non sono riuscita a terminarlo. Ero molto curiosa di leggere questa autobiografia perché Weil è stato un matematico di grande spessore, ma è stata una lettura davvero spiacevole! Tranne i primi capitoli in cui era descritta la sua vita universitaria, dal capitolo sul viaggio in India in poi è stata una tortura. Non so a chi possa interessare visto che io che studio Matematica l'ho trovato a dir poco tedioso!

[Octoberbear · Rating 4 out of 5]

Fun book, narrating most events (before Weil's time in Brazil) that you can find on the wikipedia page of André Weil from a first-person perspective. André and Simone's fascination with Hindu religions and Sanskrit poetry can be found in great detail here. Unbeknownst to me before, he is also an avid world traveler; you see Weil's flexible, philosophical, and a fun-loving mind from these stories.

[Gage Hoefer · Rating 3 out of 5]

3.5

I'm a sucker for most autobiographies of mathematicians, especially if I have had to study their work before. A very interesting nomadic life Weil used to lead.

[Raghu · Rating 4 out of 5]

Weil, a colossal figure in 20th c. mathematics (Weil conjectures, founding Bourbaki) but probably less well know that his sister Simone the mystic, has led a very interesting, itinerant life. His memoir recalls some remarkable events that he was incidentally present for, such as the London Blitz, Weimar's embrace of Hitler, Gandhi-Viceroy negotiations in Delhi, etc. He met some remarkable public figures (not counting famous mathematicians) such as Tagore, Nehru, Rajagopalachari, Zakir Hussain (a friend), Kriplani, C. V. Raman (& K. S. Krishnan for his side of the Nobel Prize story), Trotsky (via his sister). All along, Weil has amazingly incisive, even prophetic, remarks on world and local events (not sure how much of that is from the post-hoc recounting of events).

The chapter on his stay in India (1930-32 as lecturer at the Aligarh Muslim University) are enough to recommend the book. His understanding and even-handed description of the revolutionary events as well as mundane social and academic life of 1930's India are rich enough to evoke comparisons to other famous travelogues by Faxien or Ibn Battuta! Plus, he hired and mentored some mathematicians who went on to become influential academics (T. Vijayaraghavan, D. D. Kosambi, Sarvadaman Chowla).

Much like Robert Oppenheimer (it was probably in the air in the late 1920's), Weil was also deeply influenced by the Bhagvad Gita (and well-read in the Sanskrit classics) and similarly seems to have applied it's principles to various life-changing decisions, such as his pacifist stance in the midst of World War II, leading him to spend years in jail. Several near-escapes, described in ironic/bemused tones, such as his wife's cross-border escape from Vichy France, eventually bring him to the US. All mathematics is mentioned in an incidental fashion conveying a sense that the lived life is the mathematician's apprenticeship.