The Man of the Circular Ruins

May 6, 2021 12:44 PM

An engaging overview of the unusual life of mathematician Alexander Grothendieck, by Luca Signorelli.

Via Peter Woit’s Not Even Wrong, along with a link to Grothendieck’s mystical late 80s work La Clef des Songes (in French), plus a few other items about major figures in recent mathematical history.

Grothendieck previously: in 2008, at his death in 2014.

posted by mubba (24 comments total)

Sadly the article does not mention his most significant contribution, that 57 is a prime number. In his honour the number is now known as the Grothendieck Prime.
posted by phliar at 12:58 PM on May 6, 2021 [15 favorites]

What an interesting story. Thank you for sharing.
posted by Phreesh at 1:23 PM on May 6, 2021 [1 favorite]

I want to hear about Étale cohomology, and goats, and arrows. I expect I'll get as far as goat herding.
posted by sammyo at 2:05 PM on May 6, 2021

(Just to know: how did you identify the author of this piece? I don’t see it mentioned anywhere on that blog... Incidentally, Luca Signorelli is a lofty name for a “mere” cartographer, albeit one with such a gift for crafting portraits ;-)
posted by progosk at 2:48 PM on May 6, 2021

Was this ever interesting. Then 57 divided by 3 =19. I guess I have to relearn what prime number means.
posted by Oyéah at 2:52 PM on May 6, 2021

I had the same notion about 51. That seemed obviously prime. I just love that it isn't.
posted by chavenet at 2:55 PM on May 6, 2021

That's a really fascinating piece, thanks for linking it mubba!
posted by tavella at 3:27 PM on May 6, 2021

I learned in math class long ago, if you add up the numbers of a number and that sum is divisible by three, then the number is divisible by three. So 49, 4+9=12 1+2=3, the number is divisible by three. I thought this was miraculous! This otherwise secret property. Anyway this mathematician!
posted by Oyéah at 3:41 PM on May 6, 2021 [4 favorites]

Here's a trick: A number is divisible by 3 if the sum of its digits is divisible by 3. So, 57 = 5 + 7 = 12 = 3 x 4 is divisible by 3; as is 51 = 5 + 1 = 6 = 3 x 2. Also randomly chosen 710366298285411 = 7 + ... + 1 = 63.

Edit: Oyeah beat me to it.
posted by axiom at 4:10 PM on May 6, 2021

Absolutely fascinating! I'm tempted to describe the story as a tragedy but whatever was going on within him in his hermit years seems to have been so opaque to anyone else (and it appears that he vastly preferred it that way) that I wouldn't feel comfortable making that judgment. Also, as I was reading the latter part of the story, I kept thinking of U.G. Krishnamurti (previously)
posted by treepour at 4:22 PM on May 6, 2021

Just to know: how did you identify the author of this piece?

Just going by the Via link to Peter Woit’s blog (where Signorelli has a comment)
posted by mubba at 4:29 PM on May 6, 2021

So 49, 4+9=12 1+2=3, the number is divisible by three.

Checks out -- after all, 49 = 9².
posted by aws17576 at 4:34 PM on May 6, 2021 [6 favorites]

I guess I have to relearn what prime number means.

Oyéah, Phliar's link says that a Grothendieck prime is a number that looks like it's prime but isn't. They're not really primes, just ones that people might assume are prime. It's based on this anecdote:

In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.” [source: PDF]

In the case of 57, I think it's because we're more used to composite (not-prime) numbers being either even, or a multiple of 5. We've memorised some exceptions to this but mostly for multiples of small numbers - for instance, we know that 9=3x3, and 27=3x9. And we probably recognise low odd multiples of 11, because they are symmetrical: 33,55,77,and 99. In contrast, 57 is 3*19, and most people don't know their 19-times table. So it looks prime, and it's a low enough number that most people wouldn't think to check by factoring it, in contrast to, say, 5007 (which is also 3 times a prime number). Both 57 and 5007 are therefore 2-almost primes, a category of numbers which is of great interest to mathematicians.
posted by Joe in Australia at 5:03 PM on May 6, 2021 [2 favorites]

With all my frequent personal faux pas the famous examples of insanely brilliant mathematicians making silly mistakes (when likely a bit lubricated) is just reassuring to my sense of humanity... and then as I go looking for another example I run into many, I assume are perfectly embarrassing, like:

Poincare defined the fundamental group and the homology groups and proved that H1 was π1 abelianized. So the question came up whether there were other groups πn whose abelianization would give the Hn. Cech defined the higher πn as a proposed answer and submitted a paper on this. But Alexandroff and Hopf got the paper, proved that the higher πn were abelian and thus not the solution, and they persuaded Cech to withdraw the paper.

Like obviously...
posted by sammyo at 5:15 PM on May 6, 2021

I’ve long maintained that 91 is the smallest non-obvious composite - all smaller composites are squares or divisible by 2, 3, 5, or 11 and thus easily recognized. But I’m better at arithmetic than Grothendieck was.
posted by madcaptenor at 6:07 PM on May 6, 2021 [3 favorites]

So 49, 4+9=12 1+2=3, the number is divisible by three.

Well, you can correct this just by changing the two nines to eights:

So 48, 4+8=12 1+2=3, the number is divisible by three.
posted by WalkingAround at 1:01 AM on May 7, 2021 [1 favorite]

I searched Grothendieck's English Wikipedia page for the string "57", only to learn that his mother died from tuberculosis in 1957.
posted by WalkingAround at 1:21 AM on May 7, 2021 [1 favorite]

Excellent find, WalkingAround!
posted by jamjam at 1:55 AM on May 7, 2021

Wow. Just wow. Thank you very much for this.

Somehow it is an encouragement, a reassurance, an inspiration and a reminder to cleave to one's path, something which demands fortitude, resilience and courage in a world which so loudly and insistently trumpets the wrong road.

I had never heard of Grothendiek. I have now. It's one to the humans! Hehe.
posted by dutchrick at 4:36 AM on May 7, 2021 [1 favorite]

Grothendieck

You should probably know that you pronounce the last syllable 'deck'
posted by srboisvert at 4:47 AM on May 7, 2021

Thank you!
posted by dutchrick at 4:53 AM on May 7, 2021

Checks out -- after all, 49 = 9^2.

Not to red line but on the other hand...
posted by waving at 5:48 AM on May 7, 2021

Great article, I was really captivated. I had a friend at University that got their degree in Mathematics at the age of 20. They were rigorous and disciplines but read a ton of literature, especially Camus, and poetry. I think they were trying to find balance to the analytical world in which they lived. They went on to get a PhD and later on co-founded a successful startup. We lost touch after their PhD. I saw them suffer immensely with depression and anger at politics and social injustice. They were estranged from their parents, one of whom was a war veteran obsessed with automatic rifles. Such a lonely yet very sought after person. I wonder what they are doing and hope they found a place or people providing safety and comfort outside of mathematics.
posted by waving at 5:59 AM on May 7, 2021 [2 favorites]

Thanks for posting this, mubba. Grothendiec’s life was like a bewitched Pinball Wizard, playing inside a limitless, spherical machine that neither balls (nor Wizard) can escape, but who remain in perpetual motion until their next collision.
posted by cenoxo at 8:37 AM on May 7, 2021