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The idea of this soft question raised by a little girl when I was talking for children in a children's cancer clinic about the heaven of mathematics and its beauties during a friendly mathematical game. As a professional mathematician and a MathOverflowist I think it is more appropriate for MathOverflow forum but I am not sure that they can understand the importance of such questions for those who have no hope to see tomorrow's sunshine.

Who is our hero? Which one of the professional mathematicians is really a hero? Those who wrote more than $1000$ papers? Those who proved the most complicated conjectures of the century? Those who took a Ph.D below $18$ years old? Those who have the IQ $200$? Those who won a Nobel or Fields medal?...

Do you think they deserve the "hero" badge just because they have great mathematical talents and works? I don't think so!

Let's look at the question by a different point of view. What is the specialty of a hero? Being powerful and inaccessible? Maybe such people are special but a hero's actions and character should be accessible for all members of the society. He/she should be an ideal to follow not an idol to hallow. Becoming a famous great mathematician is inaccessible for many people because it depends on some instinctive parameters like IQ but trying to be a great mathematician is accessible for all of us. Who are our heroes? Those who do their best. We can follow them and learn many things from their endless effort. Now it is time to bring the idea of the main question.

Life is hard but it is harder for those who are suffering from an incurable disease. Even the simplest daily works are big challenges for them and they need an indefatigable effort to do any usual act. They try to solve these unsolvable problems every day but some of them try to go further and further and become great professionals in one of the realms of knowledge. Our heroes are among them. There are many famous and unknown cases of such heroes. For example writers and physicists have their own heroes in this sense, Helen Keller and Stephen Hawking. Now my question is about mathematicians:

Question: Do you know anybody with a serious incurable disease who became a professional mathematician or a professional mathematician who keeps working after a serious incurable illness? Do you know a hero?

Remark: In order to avoid opinion based answers, please stay in the defined frame of the question and add some references for any mathematician who you think has the given conditions.

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Arturo is my hero! –  The Chaz 2.0 Nov 14 '13 at 22:51
Not really what you're looking for, but the user Saaqib Mahmuud impresses me. –  Git Gud Nov 14 '13 at 22:55
Euler was blind towards the end of his life and that didn't seem to slow him down. Does that count? Perhaps John Nash (who is still among us) can be counted given his well-documented schizophrenia? –  Daniel Rust Nov 14 '13 at 23:31
Alan Turing broke the crypto system of Nazi Germany and was driven into suicide in the end. –  azimut Nov 14 '13 at 23:34
According to the math.SE guidelines on subjective questions, I think this constitutes a constructive subjective question, as it "invites sharing experiences over opinions" and "insists that opinion be backed up with facts and references" (perhaps the latter is not explicitly required, but that can be edited in). I don't think it should have been put on hold. –  Tim Ratigan Nov 15 '13 at 0:22

9 Answers 9

I do think the likes of Euler, Fermat, Gauss, Euclid, Newton, Erdős, and many others who revolutionized the study of mathematics deserve the title of hero, but that doesn't seem to be what you're after.

I think Galois is a hero by your standards, as he created his own field of mathematics before he was 20, when he fatefully died in a duel over a girl who had been cheating on his opponent with Galois. The night before he died, he wrote down all of his major discoveries so they wouldn't be lost to history in the event of his untimely death. His work, famously, ultimately led to the proof of the lack of existence of a solution by radicals to polynomials of degree greater than or equal to 5, as well as a proof that trisection of an angle with a ruler and compass is impossible.

Kepler has some sort of a sob story, but he was more known for his contributions to astrophysics than to mathematics.

Ramanujan was born poor in India. Without available literature, he discovered many modern mathematical results in number theory without being taught it. He died young, and ended up making massive contributions to number theory, graph theory, and analysis.

Meanwhile, both Gödel and Pythagoras starved themselves to death, so maybe that counts for something?

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You know the legend about Galois has been a bit exaggerated. For instance he had already written all his works. Ramanuian on the other hand had been invited to Cambridge by Hardy. Which seems quite a good opportunity. No doubt they were geniuses and not particularly on the lucky side though. –  lcv Nov 15 '13 at 9:18
I've read the 1837 paper on the impossibility of the trisection, and there's no mention of Galois' work. The modern proof also makes no use of Galois theory, so I think it's false that that particular theorem ever used Galois' results. –  Jack M Nov 15 '13 at 9:39
@lcv I know Ramanujan went to Cambridge, it's just that the more impressive part of his story is in India. And while Galois may have written some of his works, he did in fact spend the night writing down as much as he could in letters to colleagues so that his studies would not be lost, and that's not an exaggeration. –  Tim Ratigan Nov 18 '13 at 21:55
@JackM At least one of the proofs of the impossibility of trisection relies on the fact that a ruler and compass construction, given a segment of unit length, can construct the rationals and can construct an extension of the form $F(a+b\sqrt n)$ where $a,b,n\in F$ and $F$ is whatever field has already been constructed. However, trisection would require a general solution to the cubic equation, which is impossible without the use of cube roots. This proof definitely makes use of Galois theory. –  Tim Ratigan Nov 18 '13 at 21:56
@Tim.Ratigan It uses field theory, not Galois theory. Even if you use the term "Galois" to refer to field theory, the original statement was that Galois' own work led to this result. –  Jack M Nov 18 '13 at 23:27

Ok, lets make my comment an answer: Alan Turing broke the crypto system of Nazi Germany. Because of his homosexuality, the thank of the British government was to drive him into suicide in the end.

Other very good examples are already mentioned: Évariste Galois who was killed in an organized duel at the age of 20. John Nash and Kurt Gödel are (respectively were) brilliant mathematicians, despite of (or because of?) serious mental disorders. And of course Paul Erdős, who only lived for mathematics, was quite a emotional person and wasn't interested in material prosperity at all.

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Solomon Lefschetz was badly injured and lost both hands in an accident in his early twenties, after which he switched to a brilliant career in mathematics.

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The Lefschetz fixed point theorem is one of my favorites, and I was amazed to learn that he actually lived most of his life with wooden hands! –  Dylan Yott Nov 15 '13 at 18:10
A nice example for my question. Thanks. –  Saint Georg Nov 15 '13 at 18:27

I don't think Jean Leray had any serious disease. Still, I think his work made as a prisoner during World War II is quite remarquable:

World War II began in 1939 and Leray served as an army officer. He was captured in 1940 and sent to a prisoner of war camp in Austria where he remained until the end of the war in 1945. While at the camp Leray and some of his fellow captives organised a "université en captivité" and Leray became its rector. Not wishing the Germans to know that he was an expert in hydrodynamics, since he feared that if they found out he would be forced to undertake war work for them, Leray claimed to be a topologist. He worked only on topological problems for the years he was held captive in the camp.

Although he had undertaken some topological work it was not easy for Leray to work on the topic without reading topological literature. He was able to obtain some papers through Hopf who was at this time in Zurich but much of Leray's work was done independently of the developments which had taken place in the subject. After his release in 1945 Leray published a three part work Algebraic topology taught in captivity.

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Riemann was a very sickly person, but i don't think of anything in particular; though his mark despite this would be one of a hero in any case. John Nash is schizophrenic, Kurt Gödel was paranoid, Euler went blind, and that's all I know of.

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Weierstrass apparently had very serious illness (I'm not exactly sure what) for a long time starting at a young age (around 35), and still managed to publish some impressive results.

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I think Emmy Noether classifies. After Nazi party legislation had her expelled from the University of Göttingen... well, she just kept on teaching. From wikipedia:

When Adolf Hitler became the German Reichskanzler in January 1933, Nazi activity around the country increased dramatically. At the University of Göttingen the German Student Association led the attack on the "un-German spirit" attributed to Jews and was aided by a privatdozent named Werner Weber, a former student of Emmy Noether. Antisemitic attitudes created a climate hostile to Jewish professors. One young protester reportedly demanded: "Aryan students want Aryan mathematics and not Jewish mathematics."[70]

One of the first actions of Hitler's administration was the Law for the Restoration of the Professional Civil Service which removed Jews and politically suspect government employees (including university professors) from their jobs unless they had "demonstrated their loyalty to Germany" by serving in World War I. In April 1933 Noether received a notice from the Prussian Ministry for Sciences, Art, and Public Education which read: "On the basis of paragraph 3 of the Civil Service Code of 7 April 1933, I hereby withdraw from you the right to teach at the University of Göttingen."[71][72] Several of Noether's colleagues, including Max Born and Richard Courant, also had their positions revoked.[71][72] Noether accepted the decision calmly, providing support for others during this difficult time. Hermann Weyl later wrote that "Emmy Noether—her courage, her frankness, her unconcern about her own fate, her conciliatory spirit—was in the midst of all the hatred and meanness, despair and sorrow surrounding us, a moral solace."[70] Typically, Noether remained focused on mathematics, gathering students in her apartment to discuss class field theory. When one of her students appeared in the uniform of the Nazi paramilitary organization Sturmabteilung (SA), she showed no sign of agitation and, reportedly, even laughed about it later.[71][72]

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Many choices. What about Perelman? Or Grothendieck? Erdős also had very strong ethical principles.

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P. Erdős appears to be a pretty extreme case of a mathematician continuing to work "after a serious incurable illness." His latest paper was published in 2008, some twelve years after he died! (Well, okay, it's in a collection of papers from a workshop held in 2006, but that's still a good ten years AD!) –  Arthur Fischer Nov 15 '13 at 8:59
Euler can beat that. But Erdos was a truly good person. –  André Nicolas Nov 15 '13 at 9:06
To my understanding, Grothendieck was a deeply flawed man despite his undeniable brilliance. While I can (and do) certainly idolize him for the mathematics he produced I would hesitate to call him a hero. –  Mike Miller Nov 15 '13 at 12:20
@Mike Was? Or are you following Erdős and pronouncing Grothendieck 'dead' since he no longer produces mathematics? –  user43208 Nov 16 '13 at 12:18
@Mike "deeply flawed"? Wow. What are you referring to? –  Did Nov 23 '13 at 16:33

Lev Pontryagin is my favorite.

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Terrific! Pontryagin was notorious for his antisemitism. And blind. Truly awful man. And blind. –  André Nicolas Nov 15 '13 at 8:57

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