I can think of three. Saul Kripke quite famously could only be begrudged to finish his undergraduate degree at Harvard before being hired as a full professor. Donald Martin (the set theorist of Martin's Axiom fame) seems to have been hired into professorship out of a post-baccalaureate fellowship, without pursuing graduate study. Finally, I can't find evidence that Chaitin ever got any graduate degrees.

Are there other famous examples of great logicians or mathematicians making it into the academy while skipping over the PhD? Examples from before the era of the modern academic degree structure are not interesting for the purpose of this inquiry.

One of my professors told me that these days, someone in a similar situation would likely be put into a no-effort PhD program until the residency requirements are met, with some important publication or another of theirs being declared a "dissertation." None of the professors I asked this to could think of a fourth example. Thus, it seems the no-doctorate logician is a dying breed, one worth examining and cataloguing.

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    $\begingroup$ Wittgenstein did not even get a Bachelor's degree, but Cambridge hired him (with the help of Moore and Russell) by counting Tractatus as his PhD, How did Wittgenstein fulfill eligibility requirements for a PhD in philosophy without having a Bachelor's degree in philosophy? $\endgroup$
    – Conifold
    Mar 23 '20 at 0:47
  • $\begingroup$ Although they did not have graduate degrees in Britain at the time, Boole did not even have an undergraduate degree. $\endgroup$
    – Nick
    Mar 23 '20 at 0:51
  • $\begingroup$ Until maybe the late 1950s, a PhD was not a requirement to become a Professor at a college or university. I'm not sure your question really matters. $\endgroup$ Mar 23 '20 at 12:43
  • $\begingroup$ See also hsm.stackexchange.com/questions/5247/… $\endgroup$ Mar 23 '20 at 16:18
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    $\begingroup$ Carl: all three of the figures I refer to in this question were hired as professors after the 1950s and without PhDs, when the requirements you mention were already standard. Whether or not that is interesting is up to you, but I certainly think it is. $\endgroup$
    – jmarvin_
    Mar 23 '20 at 18:35

Thoralf Skolem could perhaps be counted as a quasi example of that. He did not enroll as a PhD candidate before becoming a docent and a member of the Norwegian Academy of Science and Letters, and it seems that he still needed some convincing from his colleagues in order to actually submit a thesis, several years later. When he finally defended it, his formal supervisor, Axel Thue, had already been deceased for no less than four years.

Do note, though, that this could actually be seen as a century-old example of the claim made by your professor.

  • $\begingroup$ This is a great anecdote I wasn't previously aware of. Certainly at least deserves an "honorable mention" on this list! $\endgroup$
    – jmarvin_
    Mar 23 '20 at 6:01

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