I came across the following quote by the famous mathematician Paul Halmos:

A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better.

What does it mean, and what is the context? It seems as if Halmos wasn't fond of Archimedes' methods of reasoning, which is quite intriguing.

  • $\begingroup$ @RodrigodeAzevedo Apparently, Paul R. Halmos, I Want to Be a Mathematician, Springer 1985, p. 205 (at the bottom of the page) $\endgroup$
    – njuffa
    Nov 11, 2022 at 18:11
  • 1
    $\begingroup$ Points out the difference between knowing things and being able to deduce things (solve problems). $\endgroup$
    – MBN
    Nov 16, 2022 at 10:27

1 Answer 1


The meaning of the quote is more likely to be, that Archimedes' reasoning was on such a high level, that no one (example: the clever graduate student) could teach him to reason better because Archimedes knew all about how to do that already.


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