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Succinct data structures
An overview of a class of data structures I didn't know about!
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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How is NSA breaking so much crypto? (2015)
There have been rumors for years that the NSA can decrypt a significant fraction of encrypted Internet traffic. In 2012, James Bamford published an article quoting anonymous former NSA officials stating that the agency had achieved a “computing breakthrough” that gave them “the ability to crack current public…
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Why I Don't Love Gödel, Escher, Bach
Douglas Hofstadter's book Gödel, Escher, Bach: An Eternal Golden Braid is a classic text that's had a strong influence on countle...
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Estimating the chances of something that hasn’t happened yet
A handy rule of thumb for creating a confidence interval for the probability of an event you haven't seen happen yet.
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4D Toys: a box of four-dimensional toys
So I have been working on Miegakure for a long time now, and I have created and accumulated many cool 4D things of all sorts. I think it’s about time that I share some of them, so…
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I don’t understand Graph Theory
Graph theory represents one of the most important and interesting areas in computer science. But at the same time it’s one of the most…
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Reverse engineering a neural network's clever solution to binary addition
While training small neural networks to perform binary addition, a surprising solution emerged that allows the network to solve the problem very effectively. This post explores the mechanism behind that solution and how it relates to analog electronics.
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Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
Stephen Wolfram shares his memories of mathematical physicist Mitchell Feigenbaum. Also a detailed discussion of his work and big discovery of a universal constant for functions approaching chaos via period doubling.
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Decision trees – the unreasonable power of nested decision rules
An introduction to the Decision Trees, Entropy, and Information Gain.
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An intuitive guide to Maxwell's equations (2020)
An Intuitive and Visual Guide to Maxwell's Equations
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AlphaGeometry: An Olympiad-level AI system for geometry
Our AI system surpasses the state-of-the-art approach for geometry problems, advancing AI reasoning in mathematics
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Visual Information Theory (2015)
I love the feeling of having a new way to think about the world. I especially love when there’s some vague idea that gets formalized into a concrete concept. Information theory is a prime example of this.
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Double-entry bookkeeping as a directed graph
In the past couple of years, I’ve been working in billing and payments at Justworks . This experience introduced me to the world of bookkeeping and accounting in ways I didn’t expect: I took a course and read a textbook in accounting, adopted plain text accounting for my personal finances, and worked in a double-entry…
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Machine Learning Crash Course: The Bias-Variance Dilemma
Machine Learning at Berkeley is a student organization at UC Berkeley. Click to read ML@B Blog, by Machine Learning at Berkeley, a Substack publication with thousands of subscribers.
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The Kolmogorov option
Andrey Nikolaevich Kolmogorov was one of the giants of 20th-century mathematics. I’ve always found it amazing that the same man was responsible both for establishing the foundations of …
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Reservoir Sampling
Choosing fairly when you don't know how many you're choosing from.
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GPU Fluid
Benedikt Bitterli's Portfolio
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Gemini with Deep Think achieves gold-medal standard at the IMO
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…
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Eigenvectors from eigenvalues
Peter Denton, Stephen Parke, Xining Zhang, and I have just uploaded to the arXiv the short unpublished note “Eigenvectors from eigenvalues”. This note gives two proofs of a general eige…
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Look, ma, no matrices
Since the 2019 SIGGRAPH course [1], Geometric Algebra, and Euclidean PGA (plane-based or projective geometric algebra) in particular, has been gaining traction within the computer graphics and machine learning communities [2, 3, 4]. Despite its broad applicability, including for higher dimensional geometry and…
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42
In The Hitchhiker’s Guide to the Galaxy by Douglas Adams, the number 42 is the “Answer to the Ultimate Question of Life, the Universe, and Everything”. But he didn’t say wha…
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Render mathematical expressions in Markdown On GitHub
You can now use LaTeX style syntax to render math expressions within Markdown inline (using $ delimiters) or in blocks (using $$ delimiters). Writing expressions as blocks To add math…
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Eigenvectors and eigenvalues explained visually
Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and even Google's PageRank algorithm. Let's see if visualization can make these ideas more intuitive.
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