Does anybody know who was Atle Selberg's advisor?

I find it interesting to know the advisor's impact on his students. Unfortunately, in Selberg case, this information (even his advisor's name) seems to be nowhere to be found.

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It also says that he had a PhD. – Charles Staats Jul 22 '10 at 1:51
Both the notion of advisor (in the recent US sense) and the tradition of thanking him in your early papers are comparatively new phenomenae. If you go back 80 years, many people in the German system started publishing when they were in their early 20s and they wrote a Habilitation after they already became established mathematicians. So the right notion of "advisor" is closer to the Russian one (undergraduate, or diploma thesis advisor), but in many cases, instead of a formal advisor, there would be a professor running a seminar that included other, "non-tenured", faculty playing this role. – Victor Protsak Jul 22 '10 at 8:08
So if you are interested about scientific influences on Selberg, you should investigate where he studied (another common tradition from those times was to travel to Goettingen or another big center for a semester or a year and work with someone there) and who his professors were. – Victor Protsak Jul 22 '10 at 8:10
I can certainly confirm that when I was a student at the University of Oslo in the 1970s, there was no formal PhD program in the modern sense. To obtain a degree, you just handed in a thesis. The faculty would then appoint a committee to evaluate the thesis, and if it passed muster, they would declare it “worthy of defense for the dr.philos. degree”. Then there would be an official defense, and the degree awarded. But there was no advisor, formally speaking. In practice, there would typically be a mentor of sorts. – Harald Hanche-Olsen Jul 22 '10 at 8:39
As an amusing aside, since there was no formal requirements for course work or previous education to hand in a thesis for the dr.philos. degree, there certainly were crackpot theses. The math department had a number of them in their archive. I have looked at one of them, a gentleman from western Norway who claimed to have solved angle trisection and the doubling of the cube. All neatly handwritten in French with religious commentary interspersed. It took me about an hour to find the mistake in the angle trisection part. – Harald Hanche-Olsen Jul 22 '10 at 8:44

I'm a student at the university of Oslo, so I thought I'd have a go at this. I just talked to Erling Størmer (Carl's grandson) who is a professor emeritus here. He said that in practice Atle had no advisor. Of course someone must have signed the papers but he doesn't know who (I don't really see what difference it makes anyway). Erling told me that according to Atle the reason why so many Norwegian mathematicians at the time worked in number theory is that they were all self-taught, and number theory is more accessible to the autodidact.

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Here is a quote from the translated interview, with a little emphasis from me: "It was Størmer that presented it to the Norwegian Academy of Science and Letters in Oslo, of course. As opponent Harald Bohr was the obvious choice because there was nobody in Norway that had any real competence in that field." Elsewhere in the interview, Selberg says, "There were others that were helpful in their way, my brother Henrik and Professor Størmer, in particular." He also talks about reading Størmer's lecture notes when he was in grade school, and meeting him when he first came to Oslo as an undergraduate.

It is not clear whether the University of Oslo formally required an "advisor". But we can conclude this from the interview: On the one hand, Størmer was Selberg's undergraduate mentor and the communicator of his PhD thesis. On the other hand, by the time Selberg filed his PhD thesis, he was really an independent mathematician with several great publications, with no one else working in his field in Norway. Selberg is not very charitable on this point. The arrangement with Bohr was more striking than Will's comment suggests. Bohr would ideally have come to Oslo for the thesis defense, but since he couldn't, he received Selberg's report in absentia in Sweden, and "Størmer read Harald Bohr's report." It's clear enough that Bohr wasn't Selberg's advisor either. Selberg generally has more to say in the interview about what he read than who he met.

The other guy on Selberg's committee was the Skolem, who as Selberg points out worked in logic rather than number theory. In fact, I only found evidence of one other well-known mathematician in Oslo in that period, Heegaard. But Heegaard retired in 1941, and decades earlier he had left Copenhagen in a huff because they had hired Harald Bohr!

So probably the right answer is that Størmer was Selberg's nominal advisor, if he had one, but he was actually self-advised as a graduate student. Selberg gives little room for other possibilities in the interview.

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Although Skolem worked primarily in set theory, he had done work in number theory (Skolem's p-adic method for solving Diophantine equations). See Borevich--Shafarevich's Number Theory. According to his Wikipedia page it looks like this may have been the topic of his thesis (and unlike Selberg he had a definite advisor: Thue). – KConrad Jul 22 '10 at 5:28
Yeah, okay, but this is what Selberg says: "The second opponent was Skolem, who had struggled with this material, of course. It was not really his field, it is safe to say." As for Skolem's advisor Thue, Wikipedia says this: "His notional thesis advisor [for his 1926 thesis] was Axel Thue, even though Thue had died in 1922." – Greg Kuperberg Jul 22 '10 at 7:17
Gentlemen, you are arguing about something that is not well-defined (see my comments to the question) and making seemingly plausible, but faulty assumptions. Example 1: My official diploma thesis advisor was not present at my (and another student's) defense. Moreover, he wasn't even our first advisor, who had left the university two years earlier, or even a faculty member at the U! Example 2: John Tate supervised Ph.D. theses of George Bergman and Robert Warfield, Jr at around the same time. There are some comments in print as to how uncomfortable he felt reading their theses. – Victor Protsak Jul 22 '10 at 8:27

It appears that no single mathematician at Oslo had that much influence on Selberg. There is a long translated interview. He defended his dissertation on October 22, 1943. The Germans closed the university on November 30. Given the kind of people with whom he was corresponding and the comparatively little time he actually spent at Oslo, it may be that the professors flipped a coin after his defense as to the order of signatures.

Well, this may be an injustice to someone we currently do not know about, but Selberg seems to have done everything himself.

There may be reason to think Carl Størmer (1874–-1957) was the adviser. He was present at the defense and presented the paper to the Norwegian academy of Sciences. Evidently the expert asked to comment was elsewhere, Harald Bohr (1887-–1951), brother of Niels.

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A good point, Will! – Wadim Zudilin Jul 22 '10 at 2:20
Thanks for the edit, Wadim. I couldn't figure out the punctuation. Evidently Skolem is regarded as not having been comfortable with the material, although he helped with the English. – Will Jagy Jul 22 '10 at 2:43

I could assume that Fritz David Carlson (1888–-1952) was at least his informal advisor, although Carlson was a Swedish mathematician. Note that he is not represented in the Mathematics Genealogy Project.

Selberg's first contribution to the Polya-Gelfond problem was very close in style to Carlson's famous theorem (see, for example, [P.J. Forrester and S.O. Warnaar, The importance of the Selberg integral, Trans. Amer. Math. Soc. 45 (2008) 489--534]).

EDIT. This was only my guess (as I indicate in my comments above to the question, I have believed that Selberg was self-educated). I asked the question Gert Almkvist, who knows a lot of Scandinavian math history. He answers:

It is evident that Selberg had no advisor, but somebody had to sign the papers. Harald Bohr fled to Sweden when the Germans invaded Denmark. He was in Lund and Stockholm. But he did not dare to go to Oslo for the thesis defense.

Then Gert adds that he has a huge biography of Harald Bohr but this could serve for a different question. $\ddot\smile$

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This is very interesting. Yes, I suspect too one of the Scandinavian analysts to be his advisor. This is plausible because on coming to the states Selberg listed "function theory" and not "number theory" as his interests. Besides Carlson, what about Beurling? (Note that Selberg did work on the "Beurling majorant" , but this is definitely not enough even to make an educated guess...) – anon Jul 22 '10 at 2:14
It does not seem that Selberg's first contributions are related to Beurling's stuff but clearly they could be in correspondence at that time. I was wondering whether Siegel could be one of Selberg's correspondents... – Wadim Zudilin Jul 22 '10 at 2:26
Hi, Wadim. There has got to be an actual biography somewhere, although possibly in Norwegian. The people mentioned as being present at the defense are Skolem and Stormer. But the opinion that counted was Harald Bohr, who sent a report. – Will Jagy Jul 22 '10 at 2:34
A short biography of Atle, www-history.mcs.st-andrews.ac.uk/Biographies/Selberg.html, says that he was influenced by Ramanujan's work and by Hecke's lecture at the International Mathematical Conference in Oslo in 1936. – Wadim Zudilin Jul 22 '10 at 2:46