The story starts in Crosscord, the crossword Discord server. Over 5,000 users strong, the server has emerged as a central hub for the online crossword community, a buzzing, sometimes overwhelming, sometimes delightful town square where total noobs, veteran constructors, and champion solvers alike come together to talk…
A visual introduction to big O notation.
Use the right tool for the job.
Dori | Art Director, Designer, Artist
Celebrating a rare dumpster fire in the kingdom of science.
The ratio 987654321 / 123456789 is very nearly 8. What about the analogous ratio in other bases?
A quick refresher on the maths behind LLMs: vectors, matrices, projections, embeddings, logits and softmax.
Recently I was called on to explain the ‘XOR’ operator to somebody who vaguely knew of its existence, but didn’t have a good intuition for what it was useful for and how it behaved.
An overview of a class of data structures I didn't know about!
Choosing fairly when you don't know how many you're choosing from.
The International Mathematical Olympiad (“IMO”) is the world’s most prestigious competition for young mathematicians, and has been held annually since 1959. Each country taking part is represented by six elite, pre-university mathematicians who compete to solve six exceptionally difficult problems in algebra…
Everything lives on a manifold
Lambda calculus is for wimps. Real programmers use combinatory logic.
This is a brief write-up of a trick I learned that helps me write code faster and more accurately. I say "trick", but it's really something I started to do without noticing as I moved further into my career. When you're working on something difficult, sketch a
A beginner-friendly introduction to stochastic calculus, focusing on intuition and calculus-based derivations instead of heavy probability theory formalism.
Chapter 1: Row vs column picture
Cosine similarity - the duct tape of AI. Convenient but often misused. Let's find out how to use it better.
We have solved a traveling salesman problem (TSP) to walk to 81,998 bars in South Korea. The problem was created using the Open Source Routing Machine (OSRM) to build a table of the 3,361,795,003 point-to-point travel times, one for each pair of bar locations. Our computation produced a tour together with a proof that…
How to test for leap years (until year 102499) in the proleptic Gregorian calendar with just three 32-bit instructions, with detailed explanation of the bit-level tricks.
When seeing the phrase “dynamic programming” in an algorithms class or leetcode study guide, the first question people ask is “what does ‘dynamic’ mean in this context?”.
Counting years backwards unlocks faster speed. The first date algorithm to use only 4 multiplications, instead of 7+
This article is available in German at Heise Online . In 1993, Intel released the high-performance Pentium processor, the start of the long...
There's a cute math puzzle that can be interesting to folks on very different levels:
In a recent 3Blue1Brown video series on transformer models, Grant Sanderson posed a fascinating question: How can a relatively modest embedding space of 12,288 dimensions (GPT-3) accommodate millions of distinct real-world concepts? The answer lies at the intersection of high-dimensional geometry and a remarkable…
We solve 20% of ARC-AGI-1 with no pretraining by minimizing the description length during inference time, with the only data involved being the target puzzle itself.
Craig Gidney's computer science blog
And some novel ideas for bicycle wheel design.
