Linked Questions

232 votes
16 answers
55k views

What elementary problems can you solve with schemes?

I'm a graduate student who's been learning about schemes this year from the usual sources (e.g. Hartshorne, Eisenbud-Harris, Ravi Vakil's notes). I'm looking for some examples of elementary self-...
121 votes
18 answers
14k views

How do you decide whether a question in abstract algebra is worth studying?

Dear MO-community, I am not sure how mature my view on this is and I might say some things that are controversial. I welcome contradicting views. In any case, I find it important to clarify this in my ...
32 votes
8 answers
9k views

Do mathematicians rely on senses other than vision and hearing?

The senses of vision and hearing are commonly recognized as being important for the study of mathematics, with fields like geometry and topology relying heavily on vision, while algebra and number ...
45 votes
8 answers
10k views

A down-to-earth introduction to the uses of derived categories

When I was learning about spectral sequences, one of the most helpful sources I found was Ravi Vakil's notes here. These notes are very down-to-earth and give a kind of minimum knowledge needed about ...
44 votes
9 answers
4k views

Journals and other sources with "easy reading" papers?

Some time ago the journal "Algebra and Analysis" (English translation is published in "St. Petersburg Mathematical Journal") had a special section which was called "easy readings for professional ...
28 votes
7 answers
7k views

Elementary Proof of Riemann-Roch for Compact Riemann Surfaces

I am supposed to give a talk about the Riemann-Roch theorem to a seminar of first and second year graduate students. I want to do Riemann-Roch for compact Riemann surfaces, but I am open to perhaps ...
user avatar
44 votes
6 answers
4k views

Explaining the main ideas of proof before giving details

I'll be the first to admit that this is a risky question to try to get away with on math overflow, but I'm going to give it a shot anyway. Roughly speaking, the question is this: Is it good to try to ...
20 votes
3 answers
3k views

How can Machine Learning help “see” in higher dimensions?

The news that DeepMind had helped mathematicians in research (one in representation theory, and one in knot theory) certainly got many thinking, what other projects could AI help us with? See MO ...
liuyao's user avatar
  • 485
75 votes
1 answer
14k views

What is an étale theta function?

Let me start out by urging you to take seriously that whatever I write about the papers surrounding IUTT really are questions. If you would like to use it as a guide to the mathematics in any way, ...
Minhyong Kim's user avatar
  • 13.5k
31 votes
4 answers
2k views

Expert, Intuitive, Organizing Analogies

In learning a new area it is very helpful to have high-level intuitive analogies that keep track of the various parts of an important argument or strategy. Experts have a store of such things, and ...
31 votes
1 answer
5k views

Why do we use $\varepsilon$ and $\delta$?

My understanding (from a talk by Rob Bradley) is that Cauchy is responsible for the now-standard $\varepsilon{-}\delta$ formulation of calculus, introduced in his 1821 Cours d’analyse. Although ...
13 votes
4 answers
976 views

Source for analysis of identification of structures in learner's mind and mathematical structures?

Concerning the structure of the learner's mind, psychologist Piaget claimed that There exists, as a function of the development of intelligence as a whole, a spontaneous and gradual construction of ...
Mikhail Katz's user avatar
  • 15.1k
13 votes
3 answers
1k views

Cops, Robbers and Cardinals: The Infinite Manhunt

Cops & Robbers is a certain pursuit-evasion game between two players, Alice and Bob. Alice is in charge of the Justice Bureau, which controls one or more law enforcement officers, the cops. Bob ...
Morteza Azad's user avatar
7 votes
1 answer
675 views

Sources of Theorem drafts by the original author

When I look at first time to a theorem and I try to understand it or when I try to memorise a useful theorem I always have difficulties (I am not the only one. For example: I read a question: I always ...