This question: When did it become a norm for mathematicians not to read proofs of all the results they use?

I would expect answers to include evidence like "Mathematician X wrote that he had not read proofs". However, it was considered opinion-based and was closed. I don't know why.


1 Answer 1


Here is my take on your linked question.

It is impossible to answer it by anything other than an opinion, this is why it was closed.

  1. The current situation. Note that your question is based on quotes from two anonymous sources. How can you be so sure that what's described by these sources represents the current norm? Keep in mind that there are tens of thousands of currently active mathematicians who live in different countries and work in different areas of math.

I have read many math papers and books, I have never came across a statement of the form "I never understood this proof in [X], but I will use this theorem anyway." There are two types of notable exceptions to this (which are widely understood as exceptions):

a. Instances when mathematicians use results where full proofs are not yet available. (I know of two examples: One is in the theory of finite groups and one is in the low-dimensional topology.)

b. Instances when mathematicians use results where the only available proofs are computer-aided. In this case, it is not even clear what does it mean to "read and understand the proof," regarding the computer-aided part. As far as I know, the first such proof is of the 4-color problem, in the mid 1970s.

In these instances, more careful writers might acknowledge this situation, but that's it.

Assuming that my personal experience is a reasonably representative sample, the only way to find out what the current norm is, is to undertake some massive opinion poll of currently active mathematicians. As far as I know, nobody tried to do this and it is very unlikely that anybody will do this in the foreseeable future.

  1. The situation in the past. How are we supposed to find out what proofs mathematicians have read in the "old days"? (Not counting proofs in the first few books of Euclid that everybody was supposed to have mastered.)

Repeating myself: I have never read a paper written before 1960s from which I could infer that the author(s) did not read proof(s) of theorem(s) that they use. In some cases, I can conclude that this did not happen since everything in a paper was proven from scratch, apart from usage of basic algebra/arithmetic, analysis/calculus and elementary geometry. (For instance, Poincare's papers are like that. For the record: Poincare's papers are the only original math papers written in the 19th century that I have read to some extent.) How representative is this (not using any older results by other mathematicians)? Answering by anything other than an opinion, would again require a massive effort, reading a variety of old (say, 19th century) papers, frequently written by obscure mathematicians using obscure terminology, etc. Nobody in their right mind is going to make such an effort.

  • $\begingroup$ Does this mean that questions that require a massive effort are considered "opinion-based", even though answers based on the opinion are not acceptable? $\endgroup$
    – user14400
    Apr 30, 2021 at 16:24
  • 1
    $\begingroup$ @PONPON: No. What I mean is: "A question is inappropriate for this site if its answers have to be either opinion-based or require massive efforts, far beyond what's feasible at SE." $\endgroup$ Apr 30, 2021 at 16:37
  • $\begingroup$ I didn't know that. I think it is better not to close interesting but "big" questions. $\endgroup$
    – user14400
    Apr 30, 2021 at 16:47
  • $\begingroup$ Keep in mind that this is just my take, others may have different opinions. $\endgroup$ Apr 30, 2021 at 18:25
  • $\begingroup$ Regarding the version of your post on math.stackexchange, here is a direct quote from the tour of math.stackexchange: "Don't ask about... Questions with too many possible answers or that would require an extremely long answer." $\endgroup$
    – Lee Mosher
    May 2, 2021 at 15:53

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