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The Mathematics of Crochet
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. …
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The latest blog posts to take off on Hacker News. 238 posts.
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Animals Made from 13 Circles (2016)
Dori | Art Director, Designer, Artist
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Accessible open textbooks in math-heavy disciplines
The challenge The authoring platform of choice in many math-heavy disciplines is LaTeX. It produces typeset documents of excellent quality and handles formulas and mathematical diagrams extremely w…
184
Decomposing a Factorial into Large Factors
I’ve just uploaded to the arXiv the paper “Decomposing a factorial into large factors”. This paper studies the quantity $latex {t(N)}&fg=000000$, defined as the largest quanti…
185
Entropy Attacks
The conventional wisdom is that hashing more entropy sources can't hurt: if H is any modern cryptographic hash function then H(x,y,z) is at least as good a random number as H(x,y), no matter how awful z is. So we pile one source on top of another, hashing them all together and hoping that at least one of them is good.
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A (Long) Peek into Reinforcement Learning
[Updated on 2020-09-03: Updated the algorithm of SARSA and Q-learning so that the difference is more pronounced. [Updated on 2021-09-19: Thanks to 爱吃猫的鱼, we have this post in Chinese].
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Numbering should start at zero (1982)
To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots, four conventions are open to us
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Derivatives and Logarithms of 3D Transforms
Understanding derivatives and logarithms of transforms
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Zero-knowledge proofs, encoding Sudoku and Mario speedruns without semantic leak
We published our video on zero-knowledge proofs! Surprisingly, making this video took a lot of work. Zero-knowledge proofs for coloring are one of those algorithms that, in hindsight, seem beautifu…
190
The exceptional Jordan algebra (2020)
In the early 1930s, Pascual Jordan attempted to formalise the algebraic properties of Hermitian matrices. In particular: Hermitian matrices form a real vector space: we can add and subtract Hermiti…
191
Lemma for the Fundamental Theorem of Galois Theory
This post illustrates a key lemma that is used in proving the fundamental theorem of Galois theory (FTGT). Note that FTGT is not covered in this post. The focus of this post is on understanding and proving this lemma only. Here is the lemma from the book Galois Theory , 5th ed. by Stewart (2023):
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History of Maths for Beginners
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…
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A new Sudoku layout with 81 uniquely shaped cells
My journey making a Sudoku variant that doesn’t have rows or columns
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The cultural divide between mathematics and AI
A reflection on cultural differences observed at the 2025 Joint Mathematics Meeting.
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Sorting algorithms with CUDA
Building on my previous post on sorting algorithms, I implemented the same algorithms using CUDA to explore performance improvements through parallel computing. The goal is to see how we can leverage the power of parallel computing to speed up our sorting algorithms. I went for a NVIDIA recruiting event some days ago…
196
An election forecast that’s 50-50 is not “giving up”
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…
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Discovering errors in Donald Knuth's TAOCP
As Donald Knuth has just published Volume 4, Fascicle 7 of The Art of Computer Programming (TAOCP), on constraint satisfaction, I would like to provide…
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Succinct data structures
An overview of a class of data structures I didn't know about!
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ARC-AGI without pretraining
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.
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The inspection paradox is everywhere (2015)
I have updated this article with new data, better code, and friendlier data visualization. You can read the new version here . Th...
201
Solving First Order Differential Equations with Julia
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…
202
Math Academy pulled me out of the Valley of Despair
Here’s to being a preserving student for life.
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The Pentium contains a complicated circuit to multiply by three
This article is available in German at Heise Online . In 1993, Intel released the high-performance Pentium processor, the start of the long...
204
Rediscovering Quaternions
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.
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Iterated Log Coding
I've created a new format for encoding real numbers on computers. I'm proud of it! Let's dive in.
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Closing the “green gap”: energy savings from the math of the landscape function
I recently returned from the 2025 Annual Meeting of the “Localization of Waves” collaboration (supported by the Simons Foundation, with additional related support from the NSF), where I…
208
Student refines 100-year-old math problem, expanding wind energy possibilities
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.
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Introduction to Stochastic Calculus
A beginner-friendly introduction to stochastic calculus, focusing on intuition and calculus-based derivations instead of heavy probability theory formalism.
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Why are QR Codes with capital letters smaller than QR codes with lower case?
Take a look at these two QR codes. Scan them if you like, I promise there's nothing dodgy in them. Left is upper-case HTTPS://EDENT.TEL/ and right is lower-case https://edent.tel/ You can clearly see that the one on the left is a "smaller" QR as it has fewer bits of data in it. Both go to the same URl, the only…