Linked Questions
14 questions linked to/from Thinking and Explaining
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...