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Quantum Computers Are Not a Threat to 128-Bit Symmetric Keys
There is no need to update symmetric key sizes as part of the post-quantum transition, due to the details of how Grover's algorithm scales. Most authorities agree.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
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The Truth About Linear Regression (2015)
This is basically a compilation of the lecture notes I wrote when teaching 36-401, Modern Regression, in fall 2015 . I offer it here on the chance that it might be of interest to those learning, or teaching, linear regression. There's no shortage of resources on that, but I have tried to present the subject as though…
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Damn Cool Algorithms: Fountain Codes
Posted by Nick Johnson | Filed under bittorrent , lt-codes , damn-cool-algorithms , fountain-codes
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What3Words – The Algorithm
What3Words is a widely promoted system that is used for sharing a location using just three words. For example, ///wedge.drill.mess is located in Hyde Park.The globe is divided into 3m squares, eac…
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Masterclass on mathematical thinking
About a year ago, I was contacted by Masterclass (a subscription-based online education company) on the possibility of producing a series of classes with the premise of explaining mathematical ways…
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A Gentle Introduction to Bayes’ Theorem for Machine Learning
Bayes Theorem provides a principled way for calculating a conditional probability. It is a deceptively simple calculation, although it can be used to easily calculate the conditional probability of events where intuition often fails. Although it is a powerful tool in the field of probability, Bayes Theorem is also…
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“Why not just use Lean?”
I have been told that when proposing to formalise mathematics these days, you have to explain why you are not using Lean. And that reminds me why I left the dependent-typed world 40 years ago: its cultism, insularity and conformity. Lean is a great language with good tools, a large library and a huge, enthusiastic…
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2^74207281-1 is Prime
GIMPS has discovered a new Mersenne prime number: 2^74207281-1 is prime! Discovered: 2016 Jan 07
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The Wavefunction Collapse Algorithm Explained
The Wavefunction Collapse Algorithm teaches your computer how to riff. The algorithm takes in an archetypical input, and produces procedurally-generated outputs that look like it.
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Functorio
You might have heard people say that functional programming is more academic, and real engineering is done in imperative style. I’m going to show you that real engineering is functional, and …
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A Branchless UTF-8 Decoder
This week I took a crack at writing a branchless UTF-8 decoder: a function that decodes a single UTF-8 code point from a byte stream without any if statements, loops, short-circuit operators, or other sorts of conditional jumps. You can find the source code here along with a test suite and benchmark:
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Why isn't there a replication crisis in math?
The replication crisis is a major problem in medicine and social science; we know that a huge fraction of the published literature is outright wrong. But in math we don't seem to have a similar crisis, despite reasonably frequent minor errors in published papers. Why not, and what can this tell us about the fields…
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BB(3, 4) > Ack(14)
Pavel has found a new 3-state 4-symbol Busy Beaver champion which can compute an “Ackermann-level” function and halts with exactly
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Probabilistic Programming and Bayesian Methods for Hackers (2013)
Bayesian Methods for Hackers : An intro to Bayesian methods + probabilistic programming with a computation/understanding-first, mathematics-second point of view.
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Important machine learning equations
A reference guide to fundamental machine learning equations with correct implementations and clear explanations of how they connect to each other.
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An Interactive Guide to the Fourier Transform (2012)
The Fourier Transform is one of the deepest insights ever made. Unfortunately, the meaning is buried within dense equations:
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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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Knuth changes his mind on Bernoulli number B_1
(I thank Yoshiyuki Kotani for this identity. We'll be able to use the same idea again in 2024 and 2027!)
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Dynamic Progamming: First Principles
Many problems of todays world require multiple decisions made throughout the lifetime of the problem. Choices are made based upon information, including previous decisions made in the problem. This article looks at how Dynamic Programming can be applied to help solve these problems in an efficient manner.
443
The game of life emulated in the game of life
Conway's Game of Life, emulated in Conway's Game of Life: The life simulator used is Golly which has a built-in script to generate these metapixel grids (select a pattern, and choose "metafier.py" from the scripts list). Outer Totalistic Cellular Automata Meta-Pixel: The metacell uses a period 184 tractor beam, which…
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TurboQuant: A first-principles walkthrough
Each mini-demo below covers one concept used later. Skip the ones you already know.
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A high-dimensional sphere spilling out of a high-dimensional cube
Make a square, split each side into two halves, producing four cells. Put a circle into each cell such that it fills it completely. There is a small gap right in the middle of the square. Put a circle there again such that it touches the other four circles. The central circle is obviously inside the square, right?…
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Queueing theory: The science of waiting in line
The math behind how people wait in line
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A Programmer’s Intuition for Matrix Multiplication
What does matrix multiplication mean? Here's a few common intuitions: This is useful when first learning about vectors: vectors go in, new ones come out.…
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Thoughts about what worked in math circles
Thoughts about what worked in math circles After about 7 months of math circles with a group of 7- turning 8-year-old boys and girls, I decided to take a...
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California needs real math education, not gimmicks
A guest post by Armand Domalewski.