Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
Ramanujan came up with an approximation for factorial that resembles Stirling's famous approximation but is much more accurate. As with Stirling's approximation, the relative error in Ramanujan's approximation decreases as n gets larger. Typically these approximations are not useful for small values of n. For n = 5…
Words by Rob Rix.
Poincaré began working on what is now considered to be the foundation of topology and algebraic topology in the 1890s with the work Analysis Situs (1895) and five later supplements (1899; 1900, 1902a, 1902b, 1904).
Note The latest version of this document can be found online at https://dr-knz.net/categories-from-scratch.html. Alternate formats: Source, PDF. Prologue The concept of category from mathematics happens to be useful to computer programmers in many ways. Unfortunately, all “good” explanations of categories so far have…
A machine learning craftsmanship blog.
The geometry puzzles that are lighting up Twitter.
Erdős posed and solved problems in number theory and other areas and founded the field of discrete mathematics.
A visual and intuitive intro to complex number system providing a historical overview of how it was developed and why it is useful.
Random numbers can be useful in graphics and game development, but they have a pesky and sometimes undesirable habit of clumping together. This is a problem in path tracing and monte carlo integrat…
A brief overview of the formal specification landscape
ConvNets Match Vision Transformers at Scale
Knights in chess move in an L-shape: 2 squares in one direction and 1 square perpendicular. But what if it didn't have to be like that?
There is a new feature of Pages and Keynote, not mentioned in any of Apple’s publicity nor in any press coverage I’ve seen, that is really very interesting. Perhaps it will even one day prove to ha…
Have you ever given up working on a math problem because you couldn’t figure out the next step? Wolfram|Alpha can guide you step by step through the process of solving many mathematical problems, from solving a simple quadratic equation to taking the integral of a complex function.
In the early days of computing, 1 + 1 didn’t always equal 10
About a weird, lovely short story
What log scales tell us.
This is mathematical section of the parent essay Gödel Incompleteness for Startups Gödel Numbering A formal system is just a collection of axioms and rules. Just like we did before we can record ax…
Presentation-quality math with Three.js and WebGL.
How Devin and a Cognition researcher built the world’s highest-performance GPU lattice siever, to make factoring numbers 10x cheaper than the previous…
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
Research in Software Engineering from Rahul Gopinath
Student performance across OECD countries has continued to decline, reaching the lowest average ever recorded by the OECD Programme for International Student Assessment (PISA) in mathematics and reading. Across the OECD, one in five 15-year-old students is now a low performer in science, mathematics and reading, up…
My problem is not just with the methods—although I do have problems with the method—but also with the ideology.
Intro I recently worked through a problem from a theory of computation textbook that asked me to prove a property of a language using finite automata. The informal proof is a simple constructive proof where you build an automaton and show that it recognizes the language. This is kind of similar to program…
P(A|B) = [P(A)*P(B|A)]/P(B), all the rest is commentary.
A common example of recursion is the function to calculate the $n$-th Fibonacci number: def naive_fib(n): if n < 2: return n else: return naive_fib(n-1) + naive_fib(n-2) This follows the mathematical definition very closely but it’s performance is terrible: roughly $\mathcal{O}(2^n)$. This is commonly patched up with…
