# Summer of Math Exposition

Results

You can find the winners for the 2024 edition below.

## The top 5 entries are

### What P vs NP is actually about

What if we could run algorithms backwards? We discuss how we could (possibly?) do this by turning them into circuits and turning those into satisfiability problems. If we could do that efficiently, it turns out crazy things would happen!

### What School Didn't Teach You About Mazes

This video provides a painless introduction to the ideas of Maze Generation and the relating Graph Theory. It also highlights an uncommon algorithm that deserves more attention, particularly in the world of ever-changing mazes.

### How To Make a Computer Create Something Beautiful: String Art

This is the second video I've made about string art; a technique to make an artwork from a single thread wrapped around nails along a circular canvas. The first video was received very well. I even had many people throw a bunch of really creative ideas at me. I would have never thought about the radon transform if it wasn't for such an amazing community! Thanks so much!

### Programming with Math: The Lambda Calculus

The Lambda Calculus is a tiny mathematical programming language that has the same computational power as any language you can dream of. In this video, we'll first explore this calculus before seeing how we can flesh it out into a functional programming language. After a brief tour of a simple type system, we'll see why the Lambda Calculus has some surprising applications in the field of mathematical logic, and how the implications of this relationship could alter the way that we study mathematics forever.

### Why is this "Fundamental" to arithmetic?

An animated video about the fundamental theorem of arithmetic and uniqueness of prime factorisation (UPF). The video starts off by giving examples of why UPF is non-trivial and then proceeds to show why it is truly fundamental again using examples. Afterwards a proof of UPF is provided from first principles.