# Tagged Questions

For questions about the motivation behind mathematical concepts and results. These are often "why" questions.

2k views

### Motivation behind the definition of GCD and LCM

According to me, I can find the GCD of two integers (say $a$ and $b$) by finding all the common factors of them, and then finding the maximum of all these common factors. This also justifies the ...
3k views

### Motivation for spectral graph theory.

Why do we care about eigenvalues of graphs? Of course, any novel question in mathematics is interesting, but there is an entire discipline of mathematics devoted to studying these eigenvalues, so ...
1k views

1k views

### Motivation for/history of Jacobi's triple product identity

I'm taking a short number theory course this summer. The first topic we covered was Jacobi's triple product identity. I still have no sense of why this is important, how it arises, how it might have ...
591 views

### Why do we want probabilities to be *countably* additive?

In probability theory, it is (as far as I am aware) universal to equate "probability" with a probabilistic measure in the sense of measure theory (possibly a particularly well behaved measure, but ...
57k views

### Why study linear algebra?

Simply as the title says. I've done some research, but still haven't arrived at an answer I am satisfied with. I know the answer varies in different fields, but in general, why would someone study ...
1k views

### Book ref. request: “…starting from a mathematically amorphous problem and combining ideas from sources to produce new mathematics…”

I couldn't find Charles Radin's Miles of Tiles at the local university library or the public library, and cannot afford its Amazon price right now. Thus, while sorely disappointed for the moment, I ...
5k views

### Uses of quadratic reciprocity theorem

I want to motivate the quadratic reciprocity theorem, which at first glance does not look too important to justify it being one of Gauss' favorites. So far I can think of two uses that are basic ...
3k views

### Motivation of the Gaussian Integral

I read on Wikipedia that Laplace was the first to evaluate $$\int\nolimits_{-\infty}^\infty e^{-x^2} \, \mathrm dx$$ Does anybody know what he was doing that lead him to that integral? Even better, ...
2k views

### Why is the tensor product constructed in this way?

I've already asked about the definition of tensor product here and now I understand the steps of the construction. I'm just in doubt about the motivation to construct it in that way. Well, if all that ...
4k views

1k views

### Fractional Calculus: Motivation and Foundations.

If this is too broad, I apologise; let's keep it focused on the basics if necessary. What's the motivation and the rigorous foundations behind fractional calculus? It seems very weird & ...
2k views

### Why are modular lattices important?

A lattice $(L,\leq)$ is said to be modular when $$(\forall a,b\in L) x \leq b \implies x \vee (a \wedge b) = (x \vee a) \wedge b,$$ where $\vee$ is the join operation, and $\wedge$ is the meet ...
9k views

### Why is it important to study combinatorics?

I was having a discussion with my friend Sayan Mukherjee about why we need to study combinatorics which admittedly, is not our favourite subject because we see very less motivation for it(I am not ...
1k views

### Why study cardinals, ordinals and the like?

Why is the study of infinite cardinals, ordinals and the like so prevalent in set theory and logic? What's so interesting about infinite cardinals beyond $\aleph _0$ and $\mathfrak{c}$? It seems ...
841 views

### Motivation behind the definition of Prime Ideal

Can someone explain what's the motivation behind the definition of a prime ideal? Or why is it exactly called a prime ideal? Has it anything to do it prime numbers?
893 views

### Why the axioms for a topological space are those axioms?

This question might have even been asked here before, I don't really know, so sorry if it's duplicate. I've started to study topological spaces and I've found the axioms for such spaces kind of hard ...
1k views

### What is the motivation behind the study of sequences?

I was discussing some ideas with my professor and he always says that before you work on something in mathematics, you need to know the motivation for studying/working on it. A better way to put this ...
473 views

### A layman's motivation for non-standard analysis and generalised limits

Disclaimer: My apologies for making such a long question. The question is possibly also rather specific, but I hope that (some parts of) it might be useful in general. Background: I have recently ...
473 views

70 views

### Is there a particularly simple example of geometric descent?

I'm looking for a particularly simple and familiar example of descent in geometry or topology in order to motivate the general definition. I'm not counting the definition of the arrow category \$\...