I remember reading that Grothendieck didn't care much about foundational issues and didn't want to be 'stuck all the way down there'.

Does anybody know if he ever actually said this? Did he have any thoughts on foundations?

Why was he able to so brush it aside? did he simply want to be ignorant of it?

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    $\begingroup$ It would help if you can edit to tell us what research you have done yourself and what, if anything, it found so people do not spend a lot of time duplicating what you have already done. $\endgroup$
    – mdewey
    Commented Jul 5 at 13:01
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    $\begingroup$ There are many, many branches of mathematics about which Grothendieck said nothing. Why do you single out foundations (a relatively obscure part of mathematics)? $\endgroup$ Commented Jul 6 at 1:21

1 Answer 1


I don't know about what you read, but in practice Grothendieck expressed thoughful concerns about foundations.

See for example the concept of a Grothendieck universe, invented by Grothendieck to avoid certain foundational issues in set theory (i.e. the concept of a proper class), albeit at the expense of adding a strong axiom to ZFC set theory (existence of strongly inaccessible cardinals).


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