7
votes
2answers
406 views

Surprising applications of cohomology

The concept of cohomology is one of the most subtle and powerful in modern mathematics. While its application to topology and integrability is immediate (it was probably how cohomology was born in the ...
61
votes
20answers
3k views

What are some examples of mathematics that had unintended useful applications much later?

I would like to know some examples of interesting (to the layman or young student), easy-to-describe examples of mathematics that has had profound unanticipated useful applications in the real world. ...
2
votes
1answer
128 views

Accessible Applications of Graph Ramsey Theory

I am giving a short lecture series on graph Ramsey theory to a group of gifted high school seniors. The brief outline is to start with the "six people at a dinner party" question, transition into the ...
3
votes
4answers
775 views

Sports that use Mathematics

What kind of sports and games use mathematics beyond simple arithmetic? How is math applied to build strategies for these games? Sailing could use mathematics in terms of astronavigation, tying ...
14
votes
8answers
8k views

What is the real life use of hyperbola? [closed]

The point of this question is to compile a list of applications of hyperbola because a lot of people are unknown to it and asks it frequently.
4
votes
4answers
4k views

How does linear algebra help with computer science

I'm a Computer Science student. I've just completed a linear algebra course. I got 75 points out of 100 points on the final exam. I know linear algebra well. As a programmer, I'm having a difficult ...
44
votes
8answers
3k views

Are there real world applications of finite group theory?

I would like to know whether there are examples where finite group theory can be directly applied to solve real world problems outside of mathematics. (Sufficiently applied mathematics such as ...
91
votes
33answers
8k views

Can you provide me historical examples of pure mathematics becoming “useful”?

I'm trying to think/know about something but I don't know if my basis premise is plausible, here we go. Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because ...
2
votes
3answers
344 views

Applications of the number of spanning trees in graphs

Let $G$ be a simple graph and denote by $\tau(G)$ the number of spanning trees of $G$. There are many results related to $\tau(G)$ for certain types of graphs. For example one of the prettiest (to ...
4
votes
1answer
2k views

Large numbers in real world

I am a high school math teacher and I am looking for a comprehensive list of large numbers which occur in real world. For example There are $10^{14}$ cells in the human body $10^{100}$ is called ...
12
votes
6answers
669 views

In what fields would you like to see applications of mathematics?

There are very few disciplines which mathematics has not penetrated. As a pupil finds such gem in the calculus problem of theory of rumors, he wonders if such field has application in vaudevillian ...
1
vote
0answers
163 views

Problems and conjectures that have positive practical consequences for society, once solved

This question made me think a bit about how mathematics can be used in such a way that society benefits from it. I think there are quite a lot of good answers to the aforementioned question. Still, ...
6
votes
3answers
2k views

Group theory applications along with a solved example

As I asked in previous question, I am very curious about applying Group theory. Still I have doubts about how I can apply group theory. I know about formal definitions and I can able to solve and ...
10
votes
3answers
2k views

Real-world uses of Algebraic Structures

I am a Computer science student, and in discrete mathematics, I am learning about algebraic structures. In that I am having concepts like Group,semi-Groups etc... Previously I studied Graphs. I ...
1
vote
3answers
218 views

Recent practical advances

I love interesting and deep mathematical results, but on the other hand I cannot object when someone says that most likely all these complicating abstract theorem will not make a change to human kind ...
6
votes
8answers
2k views

Applications of Probability Theory in pure mathematics

My (maybe wrong) impression is that while probability is widely used in science (for example, in statistical mechanics), it is rarely seen in pure mathematics. Which leads me to the question - Are ...
10
votes
12answers
2k views

Applications of algebraic topology

What are some nice applications of algebraic topology that can be presented to beginning students? To give examples of what I have in mind: Brouwer's fixed point theorem, Borsuk-Ulam theorem, Hairy ...
12
votes
7answers
1k views

Real world uses of homotopy theory

I covered homotopy theory in a recent maths course. However I was never presented with any reasons as to why (or even if) it is useful. Is there any good examples of its use outside academia?
16
votes
15answers
4k views

Applications of the Fibonacci sequence

The Fibonacci sequence is very well known, and is often explained with a story about how many rabbits there are after $n$ generations if they each produce a new pair every generation. Is there any ...
11
votes
9answers
12k views

Real world uses of hyperbolic trigonometric functions

I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful. Is there any good examples of their uses ...
13
votes
6answers
3k views

Real world uses of Quaternions?

I've recently started reading about Quaternions, and I keep reading that for example they're used in computer graphics and mechanics calculations to calculate movement and rotation, but without real ...
24
votes
8answers
2k views

Real life usage of Benford's Law

I recently discovered Benford's Law. I find it very fascinating. I'm wondering what are some of the real life uses of Benford's law. Specific examples would be great.