~/ on Max's blog

~/about-me/

Mon, 01 Jan 0001 00:00:00 +0000

Hi! I am Max Ambaum, a student at the University of Warwick in the UK where I study discrete mathematics (mathematics, computer science and the large intersection) and I am just starting second year. I love pure mathematics as well as most things software (including Nix and Rust), which I suppose makes my university course a good fit? Also, I play trumpet and violin, and I enjoy classical music (perhaps by extension).

Your type checker may be wrong - an introduction to formal proof verification and the Curry-Howard Correspondence

Sat, 25 Jul 2026 09:50:01 +0100

Contents

When writing code many of us have been saved time and time again by type checkers: the useful piece of software that ensures you aren’t adding a string to an integer ¹ or returning a reference to a value instead of the owned value. However, while useful, and sometimes annoying, it seems that the humble type checker has limited capability beyond its noble task of saving our asses…

Zero knowledge Tolstoyan art

Sat, 11 Jul 2026 00:00:00 +0000

Contents

In this post I hope to prove to you (get it 😉) in rather uncertain terms, that:

Tolstoyan art has the structure of a zero knowledge proof.

Currently, this statement is a big nothing-burger, so first we will discuss the high level ideas of Tolstoyan art and zero knowledge proofs.

Tolstoyan art

In Tolstoy’s 1897 book, what is art? ¹, he discusses what it means for some piece of work to be art. In chapter V, he states that the activity of art is

Some intuition behind the contrapositive

Sat, 27 Jun 2026 00:00:00 +0000

Contents

Introduction

While quite a fundamental law in logic, the contrapositive is certainly not immediately intuitive (or at least it was not to me). After someone else expressed a similar feeling, I decided to try and derive some intuition to explain the rule, the results of which can be found here! This blog could also be treated as an introduction to the contrapositive.

Before we begin, I would like to show how the formal definition of the contrapositive looks. I like to think that definitions codify intuition, but it only goes one way. That is, we can turn intuition into definitions, but trying to gain intuition from a definition is a faux pas. Towards the end of this post we will revisit it, and hopefully, you will see your newfound intuition reflected in the definition.

An introduction to Turing machines and computation

Sat, 04 Apr 2026 00:00:00 +0000

Contents

Introduction

This blog aims to provide a short (but slightly longer than intended), and potentially useful, introduction to Turing machines. Turing machines are so fundamental to Computer Science and the study of computability (i.e. can this thing be computed? In finite time?), that an understanding of the key elements and results can only further one’s appreciation for the field.

Minimising the product of sums chosen from intervals

Sun, 07 Sep 2025 00:00:00 +0100

Contents

What a catchy name! I’d like to explain this problem, and then provide a wordy proof for a general case. All the proofs are hidden in drop downs to motivate you to try them yourself and to make the blog less dense, if you have any questions about the proofs (or anything else), please leave them below!

The main components of the MLP

Sun, 17 Aug 2025 00:00:00 +0100

Contents

This is the second iteration in the series where we are building a Multi-Layer-Perceptron (MLP) from scratch! This post will consider the main sections of the code in the MLP, which are the:

The maths behind the MLP

Wed, 13 Aug 2025 00:00:00 +0000

Contents

This blog(/tutorial maybe?) is the first part in a walk-through of the process I followed to build a multi-layer-perceptron (MLP) from scratch in rust. Followed by using it to classify the MNIST dataset. The source code for the MLP can be found here.