What scientists and mathematicians were afraid to publish their findings?

Question

Background

I am interested in scientists and mathematicians that were afraid to publish their findings during their lifetime, and to what degree such fears hinder scientific progress.

So far, I've identified three famous scientists that were afraid to publish their important findings:

1. Nicolas Copernicus. He delayed the publication of his work on a heliocentric model of the solar system for fear of either astronomical objections, or objections based on religious grounds.
2. Carl Friedrich Gauss. Though fear might not always have been the main reason for him to delay the publication of his work -- he often waited quite some time before he published anything. He was a perfectionist, so perhaps one might describe it as a fear for not publishing something that was up to his high standards.
3. Dan Shechtman. He was afraid of publishing his findings on quasicrystals publishing alone, because he needed the expertise of his coauthors to explain his observations regarding quasicrystals. Moreover, he faced strong opposition from one of the most celebrated scientists of his time: Linus Pauling.

Some also believe Charles Darwin was afraid to publish his theory of evolution and avoided doing so for 20 years, but this has been refuted.

I am also aware of cases of scientists and mathematicians that were scorned for their ideas (Ludwig Boltzmann, Ignaz Semmelweis, Georg Cantor), or ignored (Gregor Mendel, George Zweig). Although these are interesting (albeit tragic) cases as well, for the purposes of this particular question I would like to restrict the examples to those that were afraid of publishing -- for whatever reason.

Question

What other well-known scientists were afraid to publish their findings, and why?

Answer 1

Mikhael Gromov started his career in the Soviet Union. When he decided to try to leave (which was not an easy thing to do at the time, as it is now), he stopped publishing his work, fearful that if the word gets around about him being a great mathematician, the Soviet authorities will prevent him from leaving. His last paper in Russia was published in 1973:

Gromov, M. L. Convex integration of differential relations. I. Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 329–343.

His next paper, already in the West, was published five years later in 1978:

Gromov, M. Manifolds of negative curvature. J. Differential Geometry 13 (1978), no. 2, 223–230.

This was followed by an explosion of publications: by 1981, he published 12 new papers, all of them ground-breaking in their respective field.

Answer 2

The moment I saw this Question , I connected it with $\sqrt{2}$ , which I think is the Earliest Example of hiding ( Mathematical ) Discoveries out of fear.

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https://en.wikipedia.org/wiki/Square_root_of_2#History

Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational. Little is known with certainty about the time or circumstances of this discovery, but the name of Hippasus of Metapontum is often mentioned. For a while, the Pythagoreans treated as an official secret the discovery that the square root of two is irrational, and, according to legend, Hippasus was murdered for divulging it. The square root of two is occasionally called Pythagoras's number or Pythagoras's constant, for example by Conway & Guy (1996).

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That text contains my high-lights :

• Pythagoreans did not "publish" or "publicize" the irrationality of $\sqrt{2}$ ...
• who-ever considered doing so would have the fear of getting murdered ...
• a little fancifully , the secret is still not revealed regarding the who or the when of that Scary Discovery ...
• the truth has been totally buried , lost & forgotten , ensuring that we may never ever know all the facts of that matter ...

Answer 3

Schrödinger was afraid of publishing what is now known as the Klein-Gordon equation because it did not describe experimental data correctly. Instead, he published the nonrelativistic version, which described the data correctly (without relativistic corrections). Reference: Dirac, Recollections of an Exciting Era//History of Twentieth Century Physics: Proceedings of the International School of Physics "Enrico Fermi". Course LVII. - New York; London: Academic Press, 1977. -P.109-146. Dirac recollects his conversation with Schrödinger that took place in (approximately) 1940.

Kronig did not publish the idea of electron rotation as the cause of "duplicity" of atomic spectra because of Pauli's critique. Reference: A. Pais, Phys. Today 42(12), 34 (1989);

If I understand correctly, Pauli was afraid of publishing what is now known as the Yang-Mills field because he believed it implied existence of extra zero-mass particles, which are not observed. Reference: A. Pais, The Genius of Science. A portrait gallery of twentieth-century physicists, Oxford University Press, 2000, pp.243-245.

Answer 4

Newton. Newton was afraid of controversies and of being involved in public disputes. As a result he was reluctant to publish his results, preferring to communicate them to a narrow circle of his correspondents, or just keep to himself. Many of his mathematical works were published with large delay, or after his death. His most important work (Principia) was literally wrestled from him by Halley, who published it at his own expense.

Answer 5

William Thurston did not publish many of his results. Instead he circulated them in unfinished form in some narrow circles. Some reasons for this he explained in his article

On proof and progress in mathematics. Bull. Amer. Math. Soc. (N.S.) 30 (1994), no. 2, 161–177.

Answer 6

(Not sure if this is the kind of answer you're looking for, but since both questions are HNQs, I thought I'd write it.)

duncster94 appears to be doing research related to machine learning as applied to the biology literature. They are hesitant to publish their results, because the data source they used for the research is illegal, and they are afraid of blowback.

I don't know how much this is affecting the field, however.