Why is this on the front page of hacker news? Hopefully that comes across as a genuine question and not snark. I mean as an ex-mathematician I'm thrilled, but schemes are an incredibly abstract object used in an incredibly abstract branch of mathematics (algebraic geometry).
nhatcher 1 days ago [-]
I have the same question in my mind. Also thrilled though. I think there is a genuine fascination in HN and in general with Grothendieck [1], [2].
Interesting, yeah. I guess he was the mathematical equivalent of the "rogue" archetype. Brilliant, did things in his own way, total lack of respect for authority, shrouded in mystery. I can definitely see the appeal =)
ssivark 1 days ago [-]
Sometimes, the best way to learn about abstruse topics one has a passing curiosity in is to upvote what pops up on HN and hope that some nerd might drop by and comment with a simplified intuitive picture for plebs :-)
gsf_emergency_4 1 days ago [-]
(Edited to be more helpful)
These days, some nerds prefer to ask AI to confirm their "precious" intuitions of why schemes might be needed in the first place. To fix the problems with certain basic geometric notions of old timers? They are then so spooked that the AI instantly validates those intuitions without any relevant citations whatsoever that they decide not to comment
But still leave warnings to gung-ho nerds in the form of low-code exercises
bubblyworld 1 days ago [-]
That's a theory, but I think it's more likely that the few people in the world who deeply understand schemes are locked in the basement of a mathematics department somewhere, and not on hacker news =P
gsf_emergency_4 1 days ago [-]
Ah those delvers who remember their lock combinations might still visit HN then (hello @Syzygies?
>
That's a theory, but I think it's more likely that the few people in the world who deeply understand schemes are locked in the basement of a mathematics department somewhere, and not on hacker news =P
I rather think that because of the very low career prospects in research, quite a lot of people who are good in this area rather left research and took some job in finance or at some Silicon Valley company, and thus might actually at least sometimes have a look at what happens on Hacker News. :-)
I think you overestimate how many people exist in the world with a professional interest in algebraic geometry! The vast majority of mathematicians have no idea how to compute with schemes (and there aren't that many of them to begin with).
aleph_minus_one 5 hours ago [-]
Even though I am from in a different area of mathematics, I know quite many people who work(ed) in algebraic geometry (and at the university where I graduated there wasn't even an academic chair for (Grothendieck-style) algebraic geometry).
The amount of people I know who would love to learn this material is even many, many magnitudes larger (just to give some arbitrary example: some pretty smart person who studied physics, but (for some reasons) neither had any career prospects in research nor found any fullfilling job, who just out of boredom decided that he would love to get deeply into Grothendieck-style algebraic geometry).
(These bloggers as well as creator of M1 may want to chip in a dozen cts)
pixelpoet 2 days ago [-]
What's up with the raccoon on page 67?
Syzygies 22 hours ago [-]
I know both authors, so I wrote them to ask. This is a rogue image that appears in various PDFs posted online, but not on Springer's official PDF or any print copy we've seen.
binarycrusader 1 days ago [-]
Pretty sure that's a ferret.
sam1r 2 days ago [-]
oh yeah! that is insane.
ALLTaken 8 hours ago [-]
I think it's cute!
What if it's steganography or symbolic or a puzzle.
If it's none of that, to complain about it is a bit too harsh.. for something on page 67.
fermigier 1 days ago [-]
Published in 2000.
(I studied schemes 10 years before, but I quit maths in 2000 so this book wouldn't have helped me. It seems like a good introduction, looking at the TOC. Grounded on actual geometry, not just category theory like other textbooks).
Also, the racoon ?!
SherryMarcini 2 days ago [-]
The raccoon has ruined this for me…
Rendered at 16:29:22 GMT+0000 (Coordinated Universal Time) with Vercel.
[1]: https://en.wikipedia.org/wiki/Alexander_Grothendieck [2]: https://hn.algolia.com/?q=Grothendieck
These days, some nerds prefer to ask AI to confirm their "precious" intuitions of why schemes might be needed in the first place. To fix the problems with certain basic geometric notions of old timers? They are then so spooked that the AI instantly validates those intuitions without any relevant citations whatsoever that they decide not to comment
But still leave warnings to gung-ho nerds in the form of low-code exercises
https://raw.githubusercontent.com/Syzygies/log_folders/maste...
And ahem ahem singularities https://johncarlosbaez.wordpress.com/2025/11/05/the-inverse-... )
I rather think that because of the very low career prospects in research, quite a lot of people who are good in this area rather left research and took some job in finance or at some Silicon Valley company, and thus might actually at least sometimes have a look at what happens on Hacker News. :-)
See pages 9-10, 14 https://web.archive.org/web/20250818144653/https://aitp-conf...
Also https://youtu.be/g2--VL2SkMo?t=44m42s
The amount of people I know who would love to learn this material is even many, many magnitudes larger (just to give some arbitrary example: some pretty smart person who studied physics, but (for some reasons) neither had any career prospects in research nor found any fullfilling job, who just out of boredom decided that he would love to get deeply into Grothendieck-style algebraic geometry).
https://web.archive.org/web/20250115224532/http://www.dam.br...
https://golem.ph.utexas.edu/category/2014/12/can_one_explain...
https://liorpachter.wordpress.com/2014/12/30/the-two-culture...
(2014)
With someone actually trying in 2002, using TFB for inspiration & M2 as a very early Jupyter/sage
https://web.archive.org/web/20250000000000*/https://mast.que...
(These bloggers as well as creator of M1 may want to chip in a dozen cts)
What if it's steganography or symbolic or a puzzle.
If it's none of that, to complain about it is a bit too harsh.. for something on page 67.
(I studied schemes 10 years before, but I quit maths in 2000 so this book wouldn't have helped me. It seems like a good introduction, looking at the TOC. Grounded on actual geometry, not just category theory like other textbooks).
Also, the racoon ?!