[bubblyworld]

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]

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].

[1]: https://en.wikipedia.org/wiki/Alexander_Grothendieck [2]: https://hn.algolia.com/?q=Grothendieck

[bubblyworld]

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 =)

[coderatlarge]

in many educational systems, aptitude in math (the more abstract, the better) is conflated with intelligence. so maybe many of us have internalized we should valorize it?

[ssivark]

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]

(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]

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]

Ah those delvers who remember their lock combinations might still visit HN then (hello @Syzygies?

https://raw.githubusercontent.com/Syzygies/log_folders/maste...

And ahem ahem singularities https://johncarlosbaez.wordpress.com/2025/11/05/the-inverse-... )

[aleph_minus_one]

> 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. :-)

[gsf_emergency_4]

Lean4 is "sponsored" by Microsoft

See pages 9-10, 14 https://web.archive.org/web/20250818144653/https://aitp-conf...

Also https://youtu.be/g2--VL2SkMo?t=44m42s

[bubblyworld]

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]

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).