When I first learned about Diffie-Hellman and especially elliptic curve Diffie-Hellman, I had one rather obvious question: Why elliptic curves? Why use this strange group that seems rather arbitrar…
Psychologically Plausible Deep Learning with Differentiable Tversky Similarity
I have updated this article with new data, better code, and friendlier data visualization. You can read the new version here . Th...
Data, sports, payrolls, and memes
Basketball has evolved into a game of calculated decision-making. From a game of points, assists, and rebounds, it has progressed into using thousands of data points to optimize every element of the game.
Just as I was complaining that we haven't seen many surprising breakthroughs in complexity recently, we get an earthquake of a result to st...
The Legendre transformation tells you how the inverse map acts on integrals
How do we represent a rotation in 3 dimensions? This is a surprisingly deep question, and one we can learn a lot from. Our goal will be to “rediscover” quaternions from first principles, building them up by exploring different representations and fixing the failures along the way.
In this tutorial, we will learn about solving Differential Equations with Julia. Differential Equations are everywhere in Science and Engineering problems. And, being able to solve Differential Equations using computers is very convenient. We will use the DifferentialEquations.jl package for solving Differential…
It is known that mathematics is heavily reliant on set theory, but no one can agree on what set theory is. Many people today understand that we have a choice between set theory and type theory , but they don’t know what type theory is either. Many think that type theory refers to some sort of dependent type theory, as…
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
I remember thinking at school when will I ever in my “real life” use maths. Well much to my utter surprise I’ve come to the stark realisation that there is a link between mathematics and crochet. …
tl;dr. In 2024, pre-election polls were off by about 2 percentage points. Election forecasters were aware of this and incorporated this into their uncertainties. But if you were not following the forecasts carefully, you might’ve not realized this. You might have mistakenly thought that, when predictions happened to…
Hamilton’s quaternion number system $latex {\mathbb{H}}&fg=000000$ is a non-commutative extension of the complex numbers, consisting of numbers of the form $latex {t + xi + yj + zk}&f…
Cantor conceived set theory in a sequence of six papers published in the Mathematische Annalen during the five year period 1879–1884. In the fifth of these papers, published in 1883, 1 he stated as a law of thought ( Denkgesetz ) that every set can be well-ordered or, more precisely, that it is always possible to…
Someone online was solving Advent of Code problems, and had a question about last years’ day 3 . They had a working solution using regular expressions (regexes) on String values, but they wanted to use ByteString values instead for performance reasons. They were surprised, however, that there seems to be a lack of…
A degree in mathematics might not save you from stacking boxes for a living.
Generating primes using the Buenos Aires constant.
Cryptographic schemes are based on the computational difficulty of solving some ‘hard’ problem. For example, RSA (specifically, RSA-2048) is based on the difficulty of a problem like this:
And implications for RLVR progress
This is Jessica. In my Prediction for Decision-making class last quarter we talked about human predictions and decisions relative to algorithmic ones. This led to a discussion about why it’s often hard to demonstrate the value of human knowledge once you have a decent statistical model.
Back in 2021 I looked at OpenEXR lossless compression options (and I think my findings led a change of the default zip compression level , as well as change of the compression library from zlib to libdeflate . Yay blogging about things!) . Then in 2023 I looked at losslessly compressing a bunch of floating point data…
A detailed look at Graph Theory and how it can be applied to video games.
Testing whether a number is composite as an example of a zero knowledge proof. How ZKPs are used more generally.
This post covers the same material as my !!Con 2024 talk , for which the slides are here .
Is a million times a million a billion or is it a trillion ? For my entire childhood, it was a billion, only for me to grow up and realise, as an adult, that it had better be a trillion!
