• Please include evidence in your answer. This question is not opinion-based.

I've heard that mathematicians sometimes don't read proofs.

The following is a quote from mathoverflow.

... I think a vast number of mathematicians do not read the proofs, in particular do not verify the details of (all of) the results they cite.


A mathematician I know also says that he sometimes uses theorems without understanding the proof.

I guess that mathematicians in the old days (~19th Century?) read proofs.

  • 1
    $\begingroup$ It is said that „research in pure mathematics is all about writing proofs”. If one doesn't read, or reads and doesn't understand proofs, how can he generate new results?? $\endgroup$ – DanielC Apr 24 at 22:16
  • 1
    $\begingroup$ @DanielC Even if a mathematician doesn't read or understand the proof of theorem $A$, he can write a proof of $A\Rightarrow B$. $\endgroup$ – PONPON Apr 25 at 2:46
  • 1
    $\begingroup$ This is your question, but, a more reasonable question would be: "When did it become a norm for mathematicians not to read proofs of all the results they use?" However, I do not think your question has a definitive answer. One can reasonably conjecture that most mathematicians in 19th century could prove "cold" all the results they were using. The longest "hierarchy" of the math results at the time was contained in Euclid's "Elements" and all trained mathematicians (and not only them) had to learn all of these at some point. As the complexity of math proofs increased in the late 19th-early $\endgroup$ – Moishe Kohan Apr 25 at 21:26
  • 1
    $\begingroup$ @Danu Why do you think so? Please leave some constructive comments. $\endgroup$ – PONPON Apr 30 at 9:48
  • 1
    $\begingroup$ @Danu It's the appropriate way because there is the message "Update the question so it can be answered with facts and citations. This will help others answer the question. You can edit the question or post a new one.". I'm not trying to start a discussion. You are wrong. $\endgroup$ – PONPON Apr 30 at 12:34