The Geometry of Schemes [pdf]
Posted2 months agoActiveabout 2 months ago
webhomes.maths.ed.ac.ukResearchstory
calmmixed
Debate
40/100
Algebraic GeometryMathematics EducationSchemes
Key topics
Algebraic Geometry
Mathematics Education
Schemes
A PDF on the geometry of schemes is shared, sparking discussion about its abstract nature and relevance to non-mathematicians, with some users humorously fixating on a raccoon image in the document.
Snapshot generated from the HN discussion
Discussion Activity
Active discussionFirst comment
6d
Peak period
15
Day 7
Avg / period
5.5
Comment distribution22 data points
Loading chart...
Based on 22 loaded comments
Key moments
- 01Story posted
Oct 31, 2025 at 7:06 PM EDT
2 months ago
Step 01 - 02First comment
Nov 6, 2025 at 8:06 PM EST
6d after posting
Step 02 - 03Peak activity
15 comments in Day 7
Hottest window of the conversation
Step 03 - 04Latest activity
Nov 11, 2025 at 10:18 AM EST
about 2 months ago
Step 04
Generating AI Summary...
Analyzing up to 500 comments to identify key contributors and discussion patterns
ID: 45777701Type: storyLast synced: 11/20/2025, 8:56:45 PM
Want the full context?
Jump to the original sources
Read the primary article or dive into the live Hacker News thread when you're ready.
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.
[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
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. :-)
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).
I believe that the masses don't have a deep understanding of Schemes because of enemy action by the sufficiently advanced stupidity (aka loneliness) of the intelligent :)
Some (ex-)academics get triggered by the so-thought foolhardy Buzzard & his undergrads, but B+Co are, at least, not being that kind of imbecile https://spiral.imperial.ac.uk/server/api/core/bitstreams/012...
https://github.com/ramonfmir/lean-scheme
Their interest is "pro" and they are not a hypothesis
(& I'd NOT bet against that they understand deeper than Sturmfels and his students)
Schemes (like cat theory) have become a sort of religion-- it's sad because Grothendieck himself might not have understood them intuitively.. and it won't be the first time.. Feynman didn't understand Path Integrals, nor Archimedes integration!! BECAUSE they were all loners whose first resort was WRITING LETTERS
Ps: as with Jobs.. I hesitate to call Buzzard a full-time salesman
If you want to hang out in meatspace: do you have a public key?
> The amount of people I know who would love to learn this material [...]
I am one of them =) but my point wasn't really about people who want to learn the material (which I assume includes many orders of magnitude more humans) it was about people who already deeply understand it.
See pages 9-10, 14 https://web.archive.org/web/20250818144653/https://aitp-conf...
Also https://youtu.be/g2--VL2SkMo?t=44m42s
https://raw.githubusercontent.com/Syzygies/log_folders/maste...
And ahem ahem singularities https://johncarlosbaez.wordpress.com/2025/11/05/the-inverse-... )
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)
(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 ?!