I would like to have help in producing examples of mathematicians that, in some sense I'll explain below,turned their career into failure. I am mainly interested in examples from XIX and XXth century.

I'd like to hear of mathematicians that:

  • started their career in a very promising manner and then turned to pseudosciences, or devoted all their energies to "lost causes".
  • lost years and years in trying to prove statements that turned out to be wrong and/or for which there were not suitablly developed techniques.
  • lost their life in trying to support theories that turned out to be of little use/ of limited interest/ not well granted.
    • developed complete theories that rapidly went "out of fashion" and did never become fashionable again.
    • missed by little big opportunities of great results.
    • were very famous during their lifetime and are completely forgotten nowadays.

I am of course thinking of reasonably well-known mathematicians, not of an obscure Molvanian guy that got lost in his studies.

I list just one example which falls into some of this categories:

Luigi Fantappié that became quite famous in the 30ies for his theory of analytic functionals. This theory was somewhat halted, since it needed a more abstract approach that was possible only after sheaf theory was developed in the 50ies. He then developed an alternative "final relativity theory" that was completely ignored by physicist (missing the opportunity to anticipate of some years the theory of Lie algebra deformations). He also devoted enormous amount of time to the so-called theory of sintropy which turned out being a bizarre mixture of pseudoscience, theological considerations, doubtful philosophical statements.

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    Shinichi Mochizuki, perhaps. – sand1 Aug 4 at 12:43
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    It’s a bit delicate because you are essentially asking for put-downs of people with achievements — and who is in a position to do that? Even some of the greatest could be said to have “wasted time” — Newton with alchemy, Hamilton with quaternions, Klein with politics, Einstein with unification, Nash with the Riemann hypothesis, etc., but standards for criticism are mercifully more generous in science than in movies or gastronomy. – Francois Ziegler Aug 4 at 18:27
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    Yes I know it's delicate. That's why I've tried to put down a list of criteria that sounded to me as objective as possible, and an example. Still hope to get some name out of this.. (as for Mochizuki - I haven't said it explicitely but I'd rather avoid living mathematicians...) – Nicola Ciccoli Aug 6 at 12:15
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    I suppose it would be snarky to say "All string theorists" – Carl Witthoft Aug 6 at 13:37

Alexander Abian may fit the bill here.

His most notable contribution to mathematics was proving consistency and independence of four of the Zermelo-Fraenkel axioms. source: Wolfram Mathworld.

They are : Extensionality, Replacement, Power set, and "Sum-set" (i.e., Union). See, for example, Abian and LaMacchia's Original Paper.

So far, so good. However, Abian spent the last 10 years of his life promoting his "Moonless Earth" theory.

From the wikipedia article:

Abian gained a degree of international notoriety for his claim that blowing up the Moon would solve virtually every problem of human existence. He made this claim in 1991 in a campus newspaper. Stating that a Moonless Earth wouldn't wobble, eliminating both the seasons and its associated events like heat waves, snowstorms and hurricanes. Refutations were given toward that idea by NASA saying that part of the exploded Moon would come back as a meteorite impacting the Earth and causing sufficient damage to extinguish all life, while restoring the seasons in the process.

Abian said that "Those critics who say 'Dismiss Abian's ideas' are very close to those who dismissed Galileo." This claim and others, made in thousands of Usenet posts during the last portion of his life, gained Abian mention (not entirely favorable) and even interviews in such diverse publications as Omni, People, Weekly World News, and The Wall Street Journal.

One possibility is Ted Kaczynski, the Unabomber. He has been described as a mathematical prodigy and Allen Sheilds, his doctoral adviser, told once the Kaczynski was the best doctoral student he ever directed.

  • I had in mind people with stronger recognized accomplishment in math. – Nicola Ciccoli Aug 4 at 11:49

Lucjan Emil Böttcher (1872–1937) might fit the bill. He got his PhD in Leipzig in 1898 under Sophus Lie and lectured at Lwow Polytechnics from 1901 until his retrement in 1935. His publications, staring with his PhD thesis, are full of ideas anticipating holomorphic dynamics (developed about 20 years later by Pierre Fatou and Gaston Julia), and his theorem on local behavior of a holomorphic function around its superattracting fixed point is well known (and referred to as Böttcher's theorem). It is amazing how much he accomplished without the notion of a normal family, introduced by Paul Montel, which gave solid foundations to holomorphic dynamics in one variable and accelerated its development. However, Böttcher's goal was to put iteration of holomorphic maps into the framework of Lie groups, which was a hopeless task. Besides, his writings were lacking in rigor, which is probably why his applications to extend his lecturing licence from Lwow Polytechnics to Lwow University met with failure (he tried 4 times). There were mathematicians at Lwow University familiar with complex variables and special functions (mainly Jozef Puzyna, a student of Weierstrass and an author of the first monograph in Polish on analytic functions, incorporating also elements of set theory and group theory), but they did not appreciate Böottcher's work. Böttcher continued teaching and popularizing activities (e.g., making Russell's paradox familiar to Lwow scholarly community), but did not publish any mathematical research after 1914. Around that time he became actively involved with spiritism and later published 2 brochures, on turning tables and on afterlife (this interest might have been influenced by his attending Wilhelm Wundt's lectures in Leipzig, possibly also by his earlier contact with Julian Ochorowicz, an inventor, publicist and spiritist, and Wundt's student). Judging from Lwow's newspapers, at the moment of his death he was more recognized as a “spiritual” activist than as a mathematician.

Two examples come to my mind but they are not to be taken too seriously.

Our set theory professor in his lectures introduced Bertrand Russell jokingly by saying that he had started off as a mathematician, then became a philosopher, then became a peace activist. The implication was that this was clearly a downhill career.

My other example is Oded Schramm. He was a probability theorist, the inventor of Schramm–Loewner evolutions (SLE). His `failure' was that he died too early in a mountaineering accident (at the age of 46). I mean, he could have avoided it by not going into the mountains. I hope I didn't offend anybody's sensitivities. (But then one could list Évariste Galois as well, and possibly others.)

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    Schramm is not an example because he was not advocating any crackpot theories and he is not in any sense forgotten today. Likewise others who die at a young age are not good examples merely for dying early. – KCd Aug 8 at 9:36

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