There is a well-known story about Grothendieck being asked to explain concretely some result involving prime numbers and of his answering "You mean an actual number? All right, take 57".
See here.
Unfortunately there seems to be no written trace of this anecdote and it it is not clear whether it happened or not.
But did he make a written assertion in the same vein?
$\begingroup$
$\endgroup$
8
asked Jan 11, 2023 at 19:15
-
4$\begingroup$ Possibly you're joking, but this is not of a "controversy" but just thoughtlessness, and, in the written example $344/133$, just a careless typo. Fortunately not every typo by an important mathematician is a controversy. $\endgroup$– YCorCommented Jan 12, 2023 at 8:56
-
$\begingroup$ Dear @YCor: yes, it had not escaped my attention that there is no actual controversy about 57 being or not prime nor about 344/133 being or not a good approximation of $\pi$... $\endgroup$– Georges ElencwajgCommented Jan 12, 2023 at 10:53
-
$\begingroup$ In Grothendieck's paper Hodge's general conjecture is false for trivial reasons example the last paragraph on page 300 before the start of section 2. I believe that every statement in that paragraph is in some way incorrect. There is a typographical error in line 1. In line 2 he asserts something about the vector space generated $j$-fold products of distinct elements of a collection of complex numbers which is incorrect without additional assumptions.... contd. below $\endgroup$– KapilCommented Jan 12, 2023 at 16:04
-
1$\begingroup$ By "controversial statement" do you mean a purely mathematical one? Because otherwise the list would not be short. $\endgroup$– polfosolCommented Jan 12, 2023 at 17:09
-
1$\begingroup$ @Franz "He wrote that he and other established mathematicians had no need for additional financial support and criticized what he saw as the declining ethics of the scientific community that was characterized by outright scientific theft that he believed had become commonplace and tolerated". I find the first sentence to be highly controversial. But I think it's the nature of a controversial statement that some might not consider it as one. $\endgroup$– polfosolCommented Jan 14, 2023 at 12:32
|
Show 3 more comments
1 Answer
$\begingroup$
$\endgroup$
4
Yes, he did.
In his Récoltes et semailles, volume I posthumously edited by Gallimard in 2022 he reminisces (in footnote 68, page 522) about his first encounter with $\pi$ as a child:
"La valeur approchée 344/133 trouvée dans un livre (...) m'avait frappé-elle était si jolie que j'avais du mal à croire qu'elle ne soit qu'approchée!"
which I translate as:
"The approximate value 344/133 found in a book (...) had struck me-it was so pretty that I could hardly believe that it was only approximate !"
This is interesting because $344/133=2.586466...$, certainly the worst approximation of $\pi$ in the history of Mathematics!
Needless to to say his unnamed book certainly had $\pi\cong355/113=3.14159...$, with all digits correct.
What I find amusing is that neither Grothendieck in his fifties when he wrote Récoltes et semailles, nor the people at Gallimard, nor the numerous mathematicians who retyped the manuscript, nor any of my colleagues who read the book noticed this egregious blunder...
As a bonus, here is the retyped manuscript , with the footnote on page 318.
answered Jan 11, 2023 at 19:15
-
12$\begingroup$ Not surprising since many mathematicians are apparently averse to giving actual numerical results, doing numerical checks, etc., preferring to deal mostly only with algebraic proxies/expressions and tossing about theorems. $\endgroup$ Commented Jan 11, 2023 at 22:10
-
$\begingroup$ That's arithmetic, not mathematics. I tried to drill the difference into my school age kids - they never got it. $\endgroup$ Commented Jan 13, 2023 at 5:40
-
3$\begingroup$ This isn't even the worst approximation of $\pi$ on the StackExchanges. $\endgroup$ Commented Jan 13, 2023 at 8:12
-
4$\begingroup$ I guess Serre's Course in Arithmetic is not mathematics, then... $\endgroup$ Commented Jan 13, 2023 at 18:43