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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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The latest blog posts to take off on Hacker News. 2,851 posts.
392
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…
394
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…
395
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
398
The cultural divide between mathematics and AI
A reflection on cultural differences observed at the 2025 Joint Mathematics Meeting.
399
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…
400
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…
402
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...
405
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…
406
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...
408
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…
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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.
414
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…
415
Lambda Calculus and Lisp, part 1
The first of a series of envisioned blog posts on lambda calculus, and Lisp. It’s unclear exactly where to start: there is a whole heap of interesting issues, both theoretical and in terms of concrete implementations, which tangle and interconnect. A particular application of lambda calculus is a very salient…
416
Making any integer with four 2s
There's a cute math puzzle that can be interesting to folks on very different levels:
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Five Kinds of Nondeterminism
Or four kinds, or six kinds, I'm not picky about how you count them
418
Relaxed Radix Balanced Trees (2024)
I’m adding immutable vectors to my language, Ivan, and needed to pick a suitable data structure to implement them. Clojure uses Persistent Vectors (PVs) which support lookups, updates, and appends all in ‘effectively’ constant time. However, it doesn’t have efficient insert or merge operations. Relaxed Radix Balanced…
419
The Buenos Aires Constant
Generating primes using the Buenos Aires constant.
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XOR
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.