# Tagged Questions

Questions to get the "big picture" about a subject.

0answers
167 views

### Why would I learn modern category theory if my interest mainly is structured sets, what would I have to gain? [on hold]

A long time ago I studied mathematics at the University of Stockholm. I had a romantic view of modern algebra and manage to make the first two algebra courses by self studies in order to immediately ...
0answers
138 views

### Are all theorems usable? [closed]

The (revised) question to answer: Can anyone give an example of a serious proof using this funny (revised) theorem? For any natural number $n$ and prime $p<n-1$ there exist a prime $q$ ...
1answer
35 views

### Problems reducible to polynomial root finding

In the past, I have noticed several problems for which the solution goes something like this: Reduce the problem to a polynomial equation Find the roots of the polynomial Interpret appropriately in ...
1answer
61 views

### Theoretically, can mathematical equations be used to graph any picture imaginable? [duplicate]

I know that quadratic formulas make parabolas, linear makes straight lines and sin, cos and tan make cool curves but after messing around with WolframAlpha and online equation graphing tools I can ...
1answer
29 views

### Combinatorial interpretation of multinomial function. [closed]

Given $n$ items if we pick $k$ we use binomial function. What is the analogy with multinomial function?
1answer
42 views

### Significance of Rank of Matrix

Why we determine the Rank of Matrix ? Instead of this just asking for my info : What is the easiest way to find Rank of Matrix ?
1answer
51 views

### Foliations vs Laminations

What's the big difference/similarity between foliations and laminations? What kind of theorems hold for both of them? Is there something that makes them essentially the same/different?
2answers
86 views

### Algebraic topology & Riemannian geometry project idea?

I'm taking a first course on Riemannian geometry this semester. For a final project, I would like to do something that involves algebraic topology. However, the only results I know in algebraic ...
1answer
82 views

### Categorical formulations of basic results and ideas from functional analysis?

I'm taking a first (undergrad) course on functional analysis. Though the material is nice, the approach seems very ad hoc and in a sense, near-sighted (?). I was wondering whether the/a big picture ...
0answers
87 views

### Synthetic differential geometry and algebraic geometry

I am reading here and there about basic synthetic differential geometry. One of the central ideas seems to be that it should be developed in a suitable topos, hence, in particular, a cartesian closed ...
1answer
37 views

### Geometric intuition for homotopy invariance of fiber bundles?

There's a nice result in algebraic topology saying that given a fiber bundle, its pullbacks along homotopic maps are isomorphic as bundles. Thinking of a bundle as a comb with the "teeth" as its ...
1answer
2k views

### Eilenbergâ€“Zilber as abstract nonsense - why is it important?

The Eilenbergâ€“Zilber theorem in singular homology, relating the monoidal structure of the category of chain complexes with the chain complex of the cartesian product of the underlying spaces, is used ...
2answers
351 views

1answer
67 views

6answers
745 views

### How is the concept of the limit the foundation of calculus?

My casual study of mathematics and calculus introduced me to the notion that calculus didn't find a firm foundation until Cauchy, Weierstrauss (et al) developed set theory some ~100 years after Newton ...
1answer
210 views

### What is the prerequisite knowledge for Navierâ€“Stokes Existence and Smoothness problem?

I am highly interested in the Millennium Problem of Navierâ€“Stokes Existence and Smoothness (also here) and my aim is to reach some level of knowledge to do research on it. The problem seems simple to "...
3answers
1k views

### What's so special about the group axioms?

I've only just begun studying group theory (up to Lagrange) following on from vector spaces and I am still finding them almost frustratingly arbitrary. I'm not sure what exactly it is about the ...
1answer
40 views

14answers
4k views

### Largest “leap-to-generality” in math history?

Grothendieck, who is famous inter alia for his capacity/tendency to look for the most general formulation of a problem, introduced a number of new concepts (with topos maybe the most famous ?) that ...
1answer
135 views

### Why are infinite sums so much harder to calculate than the associated infinite integral?

It seems that with continuous functions, we have in calculus an apparatus for "short cutting" an infinite sum. However, when we move to the discrete case, it seems that we don't have the equivalent ...
1answer
115 views

### Relationship between measure theory and real analysis

Does measure theory generalize real analysis to abstract spaces? For example, you can now talk about convergence even on unordered fields.
1answer
422 views

### What is the overall idea of Galois theory?

I am a third year undergraduate, doing a course on Field and Galois theory. Now, while I seem to understand most of the concepts locally, I do not seem to get the 'Whole picture' of what is happening ...