The latest blog posts to take off on Hacker News. 238 posts.
The mathematical constant pi represents the ratio of the circumference of a circle to its diameter. It is the most famous ratio in mathematics both on Earth and probably for any advanced civilization in the universe. The number pi, like other fundamental constants of mathematics such as e = 2.718..., is a…
My journey from building cricket bots to building “wind tunnels” with my collaborators — and finding the answer hidden in geometry.
I find myself writing yet another toy parser, as one does during a Christmas break. It roughly follows Resilient LL Parsing Tutorial. Not because I need resilience, but mostly because I find producing a syntax tree and a collection of diagnostics a more natural fit for the problem than bailing out on the first error.
Charles Dodgson (a.k.a. Lewis Carroll) developed a method of computing determinants which has some practical advantages.
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
These days, the most common question I get goes something like this: A decade ago, you told people that scalable quantum computing wasn’t imminent. Now, though, you claim it plausibly is immi…
The informal definition of an elliptic curve is simple. The formal definition is more involved.
Problem 1026 on the Erdős problem web site recently got solved through an interesting combination of existing literature, online collaboration, and AI tools. The purpose of this blog post is to try…
An informal introduction to formality in Lean 4
Crackpots ranging from billionaire Peter Thiel to random YouTube influencers claim that science has been stagnating for the past 50 years. They admit that computing is an exception: they don’t pretend that my personal 32GB laptop is not an advance over the 16MB mainframe that served the whole Caltech community when I…
Educators can show in secondary school maths that AI systems don’t think, making maths more interesting while teaching core concepts of AI.
There are very few universal rules in software engineering, but there are are a lot of near-universal principles. Things like "prefer composition to...
I can't remember where I first saw them, but ever since, I have been unable to forget them: abelian sandpiles. I'm far from the only one . They're remarkably simple, yet produce lovely symmetric patterns. I loved them so much that I adorned the title banner of this blog with an animation of an abelian sandpile. But…
I'm the kind of person who thinks about the design and implementation of hash tables. One design which I find particularly cute, and I think deserves a bit more publicity, is Robin Hood open-addressing with linear probing and power-of-two table size. If you're not familiar with hash table terminology, that might look…
Quanta Books is delighted to announce two new upcoming books by mathematician Terence Tao and theoretical physicist David Tong. Six Math Essentials will be Tao’s first math book written for a popular…
Among a few other integral tricks and techniques, Feynman's trick was a strong reason that made me love evaluating integrals, and although the technique itself goes back to Leibniz being commonly known as the Leibniz integral rule, it was Richard Feynman who popularized it, which is why it is also referred to as…
Testing whether a number is composite as an example of a zero knowledge proof. How ZKPs are used more generally.
In hyperbolic geometry, the sum of a the interior angles of a triangle can be any value less than π. If the sum is zero the triangle has area π.
And implications for RLVR progress
Counting years backwards unlocks faster speed. The first date algorithm to use only 4 multiplications, instead of 7+
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…
A few weeks ago I was minding my own business, peacefully reading a well-written and informative article about artificial intelligence, when I was ambushed by a passage in the article that aroused …
Fizz Buzz is a counting game that has become oddly popular in the world of computer programming as a simple test of basic programming skills. The rules of the game are straightforward. Players say the numbers aloud in order beginning with one. Whenever a number is divisible by 3, they say 'Fizz' instead. If it is…
You will never have enough IQ, nor money, nor time, nor energy.
The survival of our species owes much to our brain, specifically, its ability to observe, analyse, and plan. Planting crops and storing grains for the winter were some of the earliest uses of these abilities. Measuring and calculating are foundational elements of observation, analysis, and planning. Computation, upon…
How would you allocate money to a set of independent assets with to minimize volatility if some assets are more volatile than others?
A modest mathematical framing of language
IBM Slapped the Buzzwords 'AI Interpretability' on Generalized Continued Fractions and their Series Transformations and was awarded a Patent
The tools of linear algebra are extremely useful when working in Euclidean space (e.g. \mathbb{R}^3 ). Wouldn’t it be great if we could apply these tools to additional mathematical constructs, such as functions and sequences? Hilbert space allows us to do exactly this - apply linear algebra to functions.
How a bit of algorithm engineering and low-level details can alter what seems like a straightforward trade-off on a blackboard.
