Hedonistic Calculus
Hello and welcome to my blog! This blog is intended as an expository and non-rigorous treatment of some maths problems and topics at ~undergraduate level.
A Note On Notation
2026-10-19 · 1 min read
Terence Tao has written extensively about the way that good notation can “relieve the brain of all unnecessary work” ...
Eigenvalues On A Donut
2026-09-02 · 2 min read
This is the first in a (hopefully) three part series, building up to the Fourier Transform on a (locally compact) abe...
Top 7 Types Of Derivative
2026-05-22 · 5 min read
Welcome to Watchmojo where I’ll be counting down my top 7 favourite types of derivative.
Sums Of Squares For Kids
2026-05-21 · 4 min read
This post arose out of an extended conversation I had with my 13 year old sister. By the end of the conversation she ...
Derivatives and linearity
2026-05-20 · 4 min read
I’d like to share three examples where I was pleasantly surprised by the interplay of derivatives and linearity.
Three Proofs of The Infinitude of the Primes
2025-11-04 · 3 min read
A friend recently asked me “Have you seen the topological proof that there are infinitely many primes?” and I’m possi...
Why is it called Spectral Theory?
2025-10-03 · 4 min read
When I meet other PhD students and the unavoidable question ‘What area of research are you in?’ is asked, my answer v...
Misuses of Probability in Legal Cases
2025-07-07 · 1 min read
O.J. Simpson In 1995 O.J. Simpson was acquitted of the murder of his ex-wife Nicole Brown and her friend Ronald Goldm...
Topology I: Snake on a Donut
2025-03-21 · 3 min read
I’m of the age where my first phone housed only one game, snake. Snake is played in a rectangular world: if you try t...
PDEs: Explain it like I'm 5
2025-03-14 · 3 min read
This post is for Mum who asked for an r/explainlikeim5 style post on what I study. My PhD is very closely related to ...
Time Reversibility and How E.Coli Swim
2025-03-09 · 4 min read
If I let a ball roll down hill then it’ll reach the bottom with some velocity. If I kick it back up the hill with the...
Maxwell's bright idea
2025-02-19 · 2 min read
Our starting point is going to be Maxwell’s equations for a magnetic field $\mathbf{B}$ and an electric field $\mathb...
Navier-Stokes Equations
2025-02-10 · 7 min read
This post is dedicated to BK. Fluid mechanics is an interesting and important area to study in its own right: everyth...
Some infinities are bigger than others
2025-01-31 · 5 min read
This post is dedicated to RA and this meme he sent me. This post is a little longer than usual, but hopefully it seem...
Ant on a rubber rope: part 2
2025-01-27 · 2 min read
In the Ant on a Rubber Rope post I mentioned a discrete solution that I found very pleasing and I plan to present it ...
Imaginary numbers aren't imaginary
2025-01-26 · 3 min read
Please enjoy an alternative motivation of the extension from the real numbers to the complex numbers.
Paradox 3: ant on a rubber rope
2025-01-25 · 3 min read
In the previous post we mercilessly mocked an ant who was condemned to spend its entire life falling and so couldn’t ...
Why Time is a Dimension
2025-01-15 · 3 min read
This post is dedicated to KP and our relentless debate on this matter.
Paradox 2: ravens and apples
2025-01-14 · 3 min read
Just as the last paradox was an excuse to talk about proof by induction, this is an excuse to talk about some basic l...
The Robin Boundary Condition
2025-01-10 · 2 min read
My fourth year project concerns, succinctly, the equation which is common to both wave propagation and heat flow. I p...
Paradox 1: All horses are the same colour
2025-01-08 · 2 min read
Before getting into the paradox, lets talk about proof by induction, a handy tool that is great for proving (or verif...
A Probability Problem That Uses No Probability: part 3
2025-01-07 · 3 min read
Now it’s time to address the title of this trilogy: how can we solve a probability problem without using probability?...
A Probability Problem That Uses No Probability: part 2
2025-01-06 · 2 min read
In the previous post I deprived you of a derivation and I now plug that hole. On reflection, I much prefer the method...
A Probability Problem That Uses No Probability: Part I
2025-01-05 · 5 min read
I’d like to share a problem which was covered in 3blue1brown’s lockdown math lecture series and I found particularly ...
Dogs Chasing One Another: Part 2
2025-01-04 · 4 min read
Following the problem from yesterday, I thought it’d be an insightful activity to model the situation in python. Here...
Dogs Chasing One Another
2025-01-03 · 3 min read
Over the summer I spent a week or so playing with a problem Steven Strogatz proposed on an episode of the 3B1B podcas...