Here is a rough approximation of float multiplication (source): float rough_float_multiply(float a, float b) { constexpr uint32_t bias = 0x3f76d000; return bit_cast<float>(bit_cast<uint32_…
Earlier this year I decided to put my main project Tangerine on hold indefinitely and began prototyping a new renderer in an unfamiliar language using a totally new graphics API with the goal of overcoming all of Tangerine's technical shortcomings. The new renderer is an eccentric CPU ray tracer called Star Machine…
On June 30, 2025, Mark Brittenham and Susan Hermiller uploaded a preprint to the arXiv called “Unknotting number is not additive under connected sum” (and an updated version on Septembe…
Fourier Transform
You will never have enough IQ, nor money, nor time, nor energy.
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…
From Multi-Head to Latent Attention: The Evolution of Attention Mechanisms What is attention? In any autoregressive model, the prediction of the future tokens is based on some preceding context …
Discovering Atari Games in Randomly Generated Data
Look at this orange: Now look at this orange: It’s the same orange. But, look how much more orange it looks with the red mesh on top of it: If you buy bags of oranges (at least at many places in the US), they frequently come in this red mesh bag. This bag makes the oranges look more orange. Oranger. Here’s what that…
Through a couple of different avenues I wandered, yet again, down a rabbit hole leading to the topic of this post. The first avenue was through my main focus on a particular machine learning topic th
IBM Slapped the Buzzwords 'AI Interpretability' on Generalized Continued Fractions and their Series Transformations and was awarded a Patent
My journey implementing a new dithering algorithm in the Racket programming language.
A modest mathematical framing of language
Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density…
Deriving the basic mathematical properties of the Smith chart from electrical engineering
Transformer-based large language models are relatively easy to understand. You break language down into a finite set of “tokens” (words or sub-word components…
An article about the John Coltrane Tone Circle, a 5-octave Circle of Fifths and a double-ring Hexatonic Circle as well. Interpretation, explanation ...
When you resize, rotate, or in any way transform an image; or more generally when you resample some discrete signal, the software you are using must _interpolate_ between the discrete points to produce a result. Linear and cubic interpolation are easy to explain, but Lánczos interpolation, one of the most popular…
A Penn State engineering student's work on a century-old math problem that expands research in aerodynamics, unlocking new possibilities in wind turbine design, was recently published in Wind Energy Science.
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
With the concern that “Moore’s Law is dead,” new interest has grown for unconventional forms of computing. This includes:
In the comments on my recent post on books on the history of maths Fernando Q. Gouvêa jumped in to draw attention to the book Math Through the Ages: A Gentle History for Teachers and Othe…
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 …
Large language models like ChatGPT & Claude have become ubiquitous in today’s world. I visited a friend for the New years eve and was impressed by how ChatGPT was being extensively used within the family. The friend’s little kid is going to grow up in a world, where turning to large language models (LLM) for quick…
Update: this post was discussed on Hacker News I completed a Computer Science degree at uni, and bundled a lot of maths subjects in as electives: partial differential equations, vector calculus, discrete maths, linear algebra.
A geometric framework for co-designing neural net optimizers with manifold constraints.
Chris Grossack's math blog and professional website.
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…
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…
