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Results tagged with big-picture
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Questions designed to get an overview of a specific subject or body of results or to understand the relations among similar definitions, techniques or concepts appearing in different sub-fields of mathematics. While such questions by their very nature sometimes cannot be made very narrow and focused, it can be helpful to keep in mind that the design of MathOverflow does not make it a good fit for questions that are too broad.
33
votes
Accepted
How do you decide whether a question in abstract algebra is worth studying?
Dear Alex,
It seems to me that the general question in the background of your query on algebra really is the better one to focus on, in that we can forget about irrelevant details. That is, as you've …
13
votes
Logic in mathematics and philosophy
There was some comment in the meta thread to the effect that answers from non-experts are useless.
Nevertheless, I thought to indulge myself with a few remarks (that actually address only a small part …
- 13.6k
31
votes
Why certain diophantine equations are interesting (and others are not) ?
Added 22, October:
While reflecting on this question and the subsequent discussion, I fell again into a
bit of a sermonizing mood. I hope I will be forgiven for inserting two words of
caution.
The …
- 13.6k
97
votes
Thinking and Explaining
Final addition:
Since I've produced many rambles, I thought I'd close my (anti-)contribution with a distilled version of the example I've attempted below. It's still something very standard, but, I ho …
46
votes
Sheaf cohomology and injective resolutions
Even though I'm far from a historian, it seems to me the initial reason for considering injectives is
-prior to derived categories;
-but comes later than the task of extending left exact functors.
…
- 13.6k