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Bilinear interpolation on a quadrilateral using Barycentric coordinates
A new algebraic method for hardware-accelerated bilinear interpolation on convex quadrilaterals is presented, using the Barycentric coordinate feature of modern GPUs.
New
The latest blog posts to take off on Hacker News. 460 posts.
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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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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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Visual explanations of mathematics (2020)
It is thought that Euclid wrote Elements in about 300 BC, but Oliver Byrne turned it into one of the true gems of visualization — and made it about 100 times more readable. By seamlessly combining typeset text (Caslon, if you’re interested) with minimalist geometric drawings in primary col
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There's Math.random(), and then there's Math.random() (2015)
V8’s Math.random implementation now uses an algorithm called xorshift128+, improving the randomness compared to the old MWC1616 implementation.
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Nearly all binary searches and mergesorts are broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
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Kelly Can't Fail
Introduction You may have heard of the Kelly bet allocation strategy. It is a system for correctly exploiting information or bias in a gambling situation. It is also known as a maximally aggressive…
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The Deceptively Asymmetric Unit Sphere
The deficiencies of the Unit Sphere and an exploration of Lie groups.
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Tog's Paradox
Tog’s Paradox (also known as The Complexity Paradox or Tog’s ComplexityParadox) is an observation that products aiming to simplify a task for users tend toinspire new, more complex tasks. It’s one ...
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The centrality of stupidity in mathematics
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Better-performing “25519” elliptic-curve cryptography
Automated reasoning and optimizations specific to CPU microarchitectures improve both performance and assurance of correct implementation.
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Learning to Reason with LLMs
We are introducing OpenAI o1, a new large language model trained with reinforcement learning to perform complex reasoning. o1 thinks before it answers—it can produce a long internal chain of thought before responding to the user.
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Galois Theory
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
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Qwen2-Math
GITHUB HUGGING FACE MODELSCOPE DISCORD 🚨 This model mainly supports English. We will release bilingual (English and Chinese) math models soon. Introduction Over the past year, we have dedicated significant effort to researching and enhancing the reasoning capabilities of large language models, with a particular focus…
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AI solves International Math Olympiad problems at silver medal level
Breakthrough models AlphaProof and AlphaGeometry 2 solve advanced reasoning problems in mathematics
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Prover-Verifier Games improve legibility of language model outputs
Discover how prover-verifier games improve the legibility of language model outputs, making AI solutions clearer, easier to verify, and more trustworthy for both humans and machines.
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A practical introduction to constraint programming using CP-SAT and Python
We discuss constraint programming, an approach to solve discrete optimization problems, and illustrate how it works with a scheduling code example implemented in Python with the CP-SAT solver.
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Researchers develop the fastest possible flow algorithm
Rasmus Kyng has written the near-perfect algorithm. It computes the maximum transport flow at minimum cost for any kind of network – be it rail, road or electricity – at a speed that is, mathematically speaking, impossible to beat.
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B-Trees Require Fewer Comparisons Than Balanced Binary Search Trees
A blog by and for database architects.
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New work extends the thermodynamic theory of computation
In a paper published in Physical Review X on May 13, a quartet of physicists and computer scientists expand the modern theory of the thermodynamics of computation. By combining approaches from statistical physics and computer science, the researchers introduce mathematical equations that reveal the minimum and maximum…
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U-M finds students with alphabetically lower-ranked names receive lower grades
Knowing your ABCs is essential to academic success, but having a last name starting with A, B or C might also help make the grade.
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2023 ACM Turing Prize awarded to Avi Wigderson
Avi Wigderson is the recipient of the 2023 ACM A.M. Turing Award for foundational contributions to the theory of computation, including reshaping our understanding of the role of randomness in computation, and for decades of intellectual leadership in theoretical computer science.