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Results tagged with motivation
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user 3106
9
votes
Are large cardinals about more than just consistency?
Asaf Karagila already wrote an excellent answer at math.SE, but here is a simple point that may be helpful. In any area of math, the natural course of research leads one to ask questions, pose conjec …
- 82.7k
17
votes
Accepted
Is modern computability theory "really" about algorithms?
But they become more abstract, and it takes a broad perspective to see their motivation and to be able to tell which problems are still of importance today. …
- 82.7k
6
votes
Simple motivation to study arithmetic geometry
Which integers are the sum of three cubes?
This question remains unanswered in general. You may have heard of this problem in the popular press because there was recent computational progress, but the …
- 82.7k
28
votes
Why study finite topological spaces?
As Uri Bader's answer notes, finite $T_0$ topological spaces are equivalent to finite partially ordered sets (posets). Now, combinatorialists who are interested in the topology of finite posets most c …
- 82.7k
76
votes
How do you decide whether a question in abstract algebra is worth studying?
I'm going to interpret your question in the language of Gowers's "two cultures" essay as follows:
How does one get good at theory-building?
The process of developing a good theory can seem decep …
7
votes
What's the use of group cohomology for class field theory?
This is not a full answer, but is a bit too long for a comment. I recommend the introduction to the second part of Lang's Algebraic Number Theory, where he discusses several different approaches to cl …
- 82.7k