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Mathematicians work a lot and are usually inspired by many things. In their lifetimes they get to publish only portions of their results. There have been stories of how Gauss, Euler, Ramanujan, Einstein, Hilbert etc kept notebooks and in it we can find glimpses to their thought processes and glimpses to results they did not publish and nevertheless would have turned to be important if in fact they had done. These are known classical examples.

  1. Are there notable example of recent mathematicians who kept such notebooks?

  2. I find lot of mathematicians have blogs but these are on published results. Do mathematicians still have such notebooks and if so when do they transfer their results usually to their notebooks and when do they transfer such results to publication (in other words I am asking for organizing principles for organizing thought processes and progress)?

YCor
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Turbo
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    Since publications are only distillations of parts of our work, we do need to save all of our work somewhere. In the old days, we did this in paper notebooks or pads, and I'm sure many mathematicians still do. Others prefer to type them up in LaTeX. I do this, so I have a git repository containing all of my math work. – Deane Yang Nov 01 '20 at 01:25
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    It would be nice to know organizing principles. – Turbo Nov 01 '20 at 01:29
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    I think that one of the motivating ideas of the nLab is closely relevant to what you are asking (although i do not now if this answers -at least partially your question). – Konstantinos Kanakoglou Nov 01 '20 at 01:57
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    Quillen's notebooks were put online a few years ago: https://www.claymath.org/publications/quillen-notebooks – Dan Ramras Nov 01 '20 at 02:05
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    My friend Jim Dolan (of Baez-Dolan fame) has hundreds of notebooks. – Todd Trimble Nov 01 '20 at 02:10
  • @DanRamras Excellent answer. – Turbo Nov 01 '20 at 02:14
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    I'm on the opposite end of the spectrum from Deane: I keep nothing except occasionally a pile of scratch paper related to the most current project. If I accidentally stumble upon a new idea worth remembering, I usually merely try to remember it. Part of it is a decent memory that started to fail me only after 50 and part of it is a clear understanding that I'm no Gauss or Euler, so I'd better be rather restrictive in choosing when to add my voice to the choir unless I want just to increase the noise component in the music. :-) – fedja Nov 01 '20 at 02:18
  • @fedja I feel most are that way (to harshly put it undisciplined) and I feel organizing what you have come across is important – Turbo Nov 01 '20 at 03:06
  • @fedja, I used to be more like you. Anything I found worth remembering I would redo over and over, partly to check it but mostly to enjoy it. So it would be burned in my memory and I didn’t need to keep any of the written versions. Alas, that’s not possible anymore. – Deane Yang Nov 01 '20 at 04:53
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    I am a disaster in this respect. Have a folder called worktex where I start some tex file every time something in my head manages to attract my attention. The result is above 1 gb, almost 30 folders with some of them having up to 10 subfolders, and if I pick something at random, as a rule I can make no more sense out of it than of some dream I might have one of the nights from that time. Moral: only keep notebooks if you really know what you are doing. – მამუკა ჯიბლაძე Nov 01 '20 at 05:40
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    Federico Ardila kept notes for five years of work that was unfortunately stolen from his car by a thief! The story has a happy ending though. https://www.quantamagazine.org/mathematician-federico-ardila-dances-to-the-joys-and-sorrows-of-discovery-20171120/ – Tony Huynh Nov 01 '20 at 08:16
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    Although the question "How do you keep your research notes organized?" was asked 11 years ago, the answers may nevertheless prove insightful. See https://mathoverflow.net/q/1785/965. – grshutt Nov 01 '20 at 08:24
  • @todd if only that could be distilled into published/-able form! I've read his blog posts... – David Roberts Nov 01 '20 at 09:09
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    “ ... have blogs but these are on published results” - I think sometimes people blog about not published results. Sometimes even in comments section quite interesting problems are solved, and sometimes new solutions are found to some old problems. – Paata Ivanishvili Nov 01 '20 at 10:53
  • @PaataIvanishvili True certain of these comments never become authority for coauthorship even though the results could not be solved at that time without the comments. – Turbo Nov 01 '20 at 12:19
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    I use random scraps of paper which I then lose. – Brendan McKay Nov 01 '20 at 12:22
  • Rob Lazarsfeld advises early career mathematicians to keep a mathematical journal. – Zach Teitler Nov 01 '20 at 13:24
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    This post is obviously popular, but it also pretty obviously has nothing more to do with mathematical research than "who uses Aeron chairs while doing their research?" That is to say, it's an interesting question, but it's hard to see why it belongs here rather than on someone's blog. – LSpice Nov 01 '20 at 14:31

1 Answers1

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  1. Yes, mathematicians keep notebooks. Sometimes, after their death, notebooks are published. Here is an example: http://www.claymath.org/publications/quillen-notebooks

Here is another example, though not so recent: https://www.math.uu.se/collaboration/beurling/unpublished-manuscripts/

I believe many mathematicians have a lot of unpublished stuff. Sometimes their friends and students publish this after their death, exactly as it happened in the past.

  1. Mathematicians discuss on their blogs and web pages not only published results. There are many examples. Much material exists in the form of correspondence, lecture notes, and preprints which are not officially made public (not available to everyone, like blogs) and which mathematicians share among their colleagues.
Alexandre Eremenko
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