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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.

No living mathematicians please.

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    $\begingroup$ Shinichi Mochizuki, perhaps. $\endgroup$
    – sand1
    Aug 4 '18 at 12:43
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    $\begingroup$ 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. $\endgroup$ Aug 4 '18 at 18:27
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    $\begingroup$ 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...) $\endgroup$ Aug 6 '18 at 12:15
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    $\begingroup$ I suppose it would be snarky to say "All string theorists" $\endgroup$ Aug 6 '18 at 13:37
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    $\begingroup$ I don't know if Joshua King qualifies, but his story has a certain charm, almost like something out of Aubrey's Brief Lives. $\endgroup$ Sep 28 '20 at 17:00
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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.

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  • $\begingroup$ Abian also considered a "theory" that the Big Bang should be replaced by a Big Suck, and that there was a "mass-time equivalence". $\endgroup$ Oct 3 '20 at 5:30
  • $\begingroup$ His most notable contribution to mathematics was proving consistency and independence of four of the Zermelo-Fraenkel axioms. --- This is surely not his most notable contribution, and the web page you cited does not claim this. I don't have time now (need to shower and leave immediately), but as I'm somewhat familiar with his work, Ph.D. dissertations written under him (one by a former colleague of mine), and books, I'm sure I could come up with several more significant contributions. In fact, the example you gave wasn't even a new result and Abian states this in the paper. $\endgroup$ Jul 15 at 14:42
  • $\begingroup$ FYI, I mentioned the Abian/LaMacchia paper in this 26 December 1999 sci.math post, which I suspect is where Eric Weisstein learned about it (or in one of my subsequent mentions of it in sci.math), as it was pretty much unknown at the time. Also, in this 20 September 2000 sci.math post I gave some then mostly internet-unknown info about Abian, some of which might still be of interest (e.g. text of a story about Abian in PEOPLE magazine, 24 June 1991, p. 84). $\endgroup$ Jul 15 at 20:20
  • $\begingroup$ @DaveLRenfro It's just my naivety here. I didn't intend to diminish Abian's stature as a mathematician. At the time, it was all that I knew about his career. Thanks for providing further background. I'll have a read of the sci.math posts. It was also not my intention to poke fun at him. I see this episode as a glorious outburst of eccentricity on Abian's part. I'd love to have known him. $\endgroup$
    – nwr
    Jul 15 at 21:14
  • $\begingroup$ Your description of Abian's somewhat individual approach (not tending to follow the literature) in the sci.math posts does paint a charming picture of a man who loved his subject. $\endgroup$
    – nwr
    Jul 15 at 21:27
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One possibility is Ted Kaczynski, the Unabomber. He has been described as a mathematical prodigy and Allen Shields, his doctoral adviser, once told that Kaczynski was the best doctoral student he ever directed.

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    $\begingroup$ I had in mind people with stronger recognized accomplishment in math. $\endgroup$ Aug 4 '18 at 11:49
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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, starting 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.

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Isaac Newton devoted much of his later life to religious speculations that even most religious people regard as having dubious value. In particular, he spent a lot of time on what are now generally termed occult studies such as alchemy and mystical interpretations of the Bible. Martin Gardner wrote an entertaining Skeptical Inquirer article on this topic, entitled "Isaac Newton: Alchemist and Fundamentalist." The article is reprinted in the anthology Did Adam and Eve Have Navels?


EDIT: Here are a few quotes from Martin Gardner's article, to give some sense of how much effort Newton devoted to these studies.

For a large part of his life Newton's time and energy were devoted to fruitless alchemy experiments and efforts to interpret Biblical prophecy. His handwritten manuscripts on those topics far exceed his writings about physics. They constitute several million words now scattered in rare book rooms of libraries and in private collections. … [Newton] read all the old books on alchemy he could find, accumulating more than 150 for his library. He built furnaces for endless experiments and left about a million words on the topic. …

Newton's passion for alchemy was exceeded only by his passion for Biblical prophecy. Incredible amounts of intellectual energy were spent trying to interpret the prophecies of Daniel in the Old Testament and the Book of Revelation in the New. He left more than a million words on these subjects, seeing himself as one who for the first time was correctly judging both books. …

Newton's writings on Biblical prophecy are so huge an embarrassment to his admirers that to this day they are downplayed or ignored. … [John Maynard] Keynes spoke of having gone through some million of Newton's words on alchemy and found them "wholly devoid of scientific value."

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    $\begingroup$ He-he ... I guess even you aren't immune to downvotes (not mine, BTW). Maybe it was because this isn't from the 19th or 20th centuries, or because this devotion in his later life was not considered as crankish then as now, or because his fame didn't diminish over time, etc. $\endgroup$ Jul 15 at 14:47
  • $\begingroup$ @DaveLRenfro Your suggestions are plausible. It could also be that people simply aren't aware of how much time and effort Newton spent on "occult studies." As Wikipedia says, the Portsmouth Papers consisted of "329 lots of Newton's manuscripts, over a third of which were filled with content that appeared to be alchemical in nature." By the way, nowadays such work strikes most people as "harmless crankery," but back then, Newton could have gotten into serious trouble for some of his views. That's probably why much of that work remained hidden from public view until the 20th century. $\endgroup$ Jul 15 at 16:51
  • $\begingroup$ As I was reading your Martin Gardner excerpt I realized those passages sounded very familiar, and then I noticed they (originally) appeared in Skeptical Inquirer. Earlier I somehow I missed your mention of this magazine, probably because I was surprised to see the downvote. I've been a subscriber to SI since early 1979. $\endgroup$ Jul 19 at 14:11
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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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    $\begingroup$ 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. $\endgroup$
    – KCd
    Aug 8 '18 at 9:36
  • $\begingroup$ My thinking is that Schramm and Galois are connected in that they died avoidable deaths. It was their bad decisions that ended their lives and careers abruptly. I accept that these were not a conscious switch to pseudosciences or to violent activism (like Kaczynski). I offered my answer as a different perspective to think about the question. $\endgroup$ Sep 3 '18 at 8:08

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