A 1940 Letter of André Weil on Analogy in Mathematics (2003) [pdf] | Hacker News Reader

A 1940 Letter of André Weil on Analogy in Mathematics (2003) [pdf]

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88 pointsgone3533 comments

> Keep in mind that the letter was not written for a mathematician, even though Simone could not understand most of it.

I'd love to see a citation here. Simone Weil referenced mathematics a lot in her philosophical writing, and, growing up in the shadow of her brother, had been exposed to mathematics all her life.

> The unwritten laws of modern mathematics forbid writing down such views if they cannot be stated precisely nor, all the more, proven. To tell the truth, if this were not the case, one would be overwhelmed by work that is even more stupid and if not more useless compared to work that is now published in the journals. But one would love it if Hilbert had written down all that he had in mind.

Here we've had some (technical) progress since 1940: modern Hilberts may publish their proven results, arxiv their useless work, and blog their work that is even more stupid?

I truly believe that there is an ideal point of efficiency for every human process. Make something too easy and too mechanical, and it loses its charm because it is lost in a sea of mediocrity. Publishing and producing work is like that these days. Yes, in absolute number, more work might be done, but is that worth the overall decline in the attraction of a discipline?

Personally, I believe the world would be a better place if scientific research weren't a race for citations.

A few decades ago, pure mathematics was a genuine exception to the "race for citations". Hiring committees were more interested in the profundity of results than their number. For various understandable reasons, this last bastion fell and now PhD students and postdocs are expected to have many on top of ground-breaking results. It is important to emphasize to young researchers that the vision of getting tenure after a few ground-breaking results is a relic of the past (exceptions always exist).

Sadly, I was enraptured by the romanticism of the old style research loop as a PhD student, and being not-very-savvy to say the least, I missed the bullet train by mistaking it for a horse carriage.

Yes, that is a very interesting point. You are very right though, that the trend has changed and there's a pressure now. I don't think your own experience is necessarily a bad thing. It's best to stick with your own ideals rather than bend to the will of others.

This ideal point of efficiency, is it computable ;)?

haha. Maybe not, if our instinct-for-efficiency brains are the computers.

"however it is beautiful and surprising that the prime numbers p for which m is a residue are precisely those which belong to certain arithmetic progressions of increment 4m; for the others m is a non-residue"

Fascinating. At first I was confused because I thought he was referring to the law of reciprocity. But it's actually a different law:

  m = 3
  = not a square mod 5. (reciprocal)
  = not a square mod 7. (not reciprocal)
  = 5² mod 11.          (not reciprocal)
  = 4² mod 13.          (reciprocal)

  Add 4*3 = 12:

  = not a square mod 17 (reciprocal)
  = not a square mod 19 (not reciprocal)
  = 7² mod 23.          (not reciprocal)

  Add 4*3 = 12:

  = not a square mod 29 (reciprocal)
  = not a square mod 31 (not reciprocal)

This easily follows from the law of reciprocity.

Is an interesting read, but it's striking how condescending he is at the outset. How about let the reader decide what they understand or not? There's no use in saying anything regarding that.

The intended reader was his sister, who he sent the letter to. This was a private letter, not a publication.

His sister had evidentially asked him about his work (maybe to give him something positive to talk about given that he was in prison).

"Some thoughts I have had of late, concerning my arithmetic-algebraic work, might pass for a re- sponse to one of your letters, where you asked me what is of interest to me in my work. So, I decided to write them down, even if for the most part they are incomprehensible to you."

It might seem condescending to speak to his sister like this, but perhaps he understood her intent well enough, and was essentially acknowledging it.

Likely even less so... That was likely just how colloquially he is saying to his kin "Tahnks for prodding me about what I thought of my work... so Ill put some write it out here, for good measure, so dont worry if you dont get it..."

Basically he is saying, let me document this for myself, at the appreciated behest of sis.

Do not get upset on behalf of his sister. You do not know either her or him. Besides, she was perfectly able to get upset and make it known on her own.

> let me document this for myself, at the appreciated behest of sis.

Tell me you live in the information age without telling me you live in the information age

Maybe not everyone knows that the sister was Simone - much better known than her brother in the world outside mathematics.

(native french) It is also a letter originally written in french in 1940: http://denise.vella.chemla.free.fr/transc-AWSW.pdf . It uses "tu" which is the affectionate/intimate version of you, the language used is as is quite common in educated households (and the weil's certainly was) is "language soutenu", which is quite formal sound and elaborate (french people love their language), and while I can see how it could strike one as cold, especially in english-speaking countries, it doesn't seem condescending to me in the least, on the contrary.

> french people love their language

as well as their anglicisms, mdr:

> ... il avait aussi un theorema egregium, et je ne sais plus which is which.

Lost in Translation: it is gliding for me https://www.dailymotion.com/video/x2rdc71

unfortunately subtitles are never going to do LNA HO justice: https://www.dailymotion.com/video/xefrls

(wait, did M Polnareff invent the lyric video here?)

I expected a No True Belgian response and was instead pleasantly surprised.

I'd have guessed he invented Boggle, the intertubes have that at 1972, 18 years earlier.

I have no words for the French here in '67: https://www.youtube.com/watch?v=3LZbw6YCcm4

1967? 22 years before the release of unrelated belgian Techno anthem "Pump Up the Jam"...

Yes, '67, six years before Bowie covered Brel on the stench of fish and whores in Zeebrugge. (A syllable was added and Amsterdam was used as "it sounded better to the ear")

The sailors are a bit more appreciative than the scientists: https://www.youtube.com/watch?v=1e1eLe1ihT0

(Les Horribles Cernettes lineup appears to have been far more anglophone than francophone over the years, but all of them —as it was a founding member in 1954– have at least tenuous ties to belgium)

That I did not know! (Although I've been a fan of the Cernettes since d/loading that first image on the web in a mosaic browser way back when).

Kids now will never know the salad days of "discovery" being reading the "What's New" page at NCSA.

https://images.computerhistory.org/revonline/images/50000487...

One would think that he would know whether his own sister, the recipient, would have sufficient mathematical background to understand his work.

Exactly, so why take the time to remind her of that? Ego is why.

A more positive interpretation could be something like "I can't express what I want to say without going into topics that I know you have no familiarity with. But I'm aware of that and am not just insensitively bombarding you with jargon."

Indeed. This is a six (printed) page letter, and already at a page or two in I wouldn't be surprised if it would take that many textbooks (how many printed pages?) to get SAW from where ever she left off (I don't recall maths being very prominent in classics/philosophy departments; note AW's description of a field) to where she could have a hope of seeing the moon itself, beyond the finger pointing at it.

Did you read the introduction? It says: Weil wrote this fourteen-page letter to Simone Weil, his sister ... (Keep in mind that the letter was not written for a mathematician, even though Simone could not understand most of it.)

Yes I did. And?

And without that context, his sister may have been perplexed as to why he would dive into complicated math that he should have known she wouldn't understand. Consider that sometimes when you read ego or aggression into writing, it's not coming from the author's mind but is a projection of your own.

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