Summer of Math Exposition

SoMEπ community edition, summer 2024.

The Summer of Math Exposition (SoME) is an annual competition to foster the creation of excellent math content online. You can participate as either a creator or judge. Learn more

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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.

The 20 honorable mentions

How to Calculate 1^3 + 2^3 + ... + 100^3 By Hand

Latent Space Visualisation: PCA, t-SNE, UMAP | Deep Learning Animated

Penrose Tilings from Five Dimensions

How Many Symmetries Are There

MaVS

Can You Beat The Demon At His Table Game?

The Basics of Circular Motion (and Beyond)!

An entire physics class in 76 minutes

The 4D Julia Set

The algorithm that (eventually) revolutionized statistics

This star almost broke Bohr's atomic model

How good is Advantage in D&D?

Why Quaternions (4d numbers) are useful

Eisenstein Primes Visually

Exploring the wave equation

Math and Living Things

How many times do you ACTUALLY need to shuffle?

Shapley Values: Unlocking Intuition with Venn Diagrams

The Moebius function

Hypergraphs and Acute Triangles

All entries

You can find the whole ranking of entries here: