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Learning more about Claude's mathematical capabilities
An unreleased Claude model improved the lower bound for the fraction of zeroes of the Riemann zeta function that satisfy the hypothesis, raising it from 41.6% to 67.2%.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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Chord progressions of 25,000 songs
Systems thinker who ended up in data. Mostly working out why organisations can't answer their own questions.
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The simple beauty of XOR floating point compression
I recently implemented a small program to visualize the inner workings of a scheme that compresses floating point timeseries by XORing subsequent values. The resulting visualizations are quite neat…
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Exponentially Better Rotations (2022)
If you’ve done any 3D programming, you’ve likely encountered the zoo of techniques and representations used when working with 3D rotations. Some of them are better than others, depending on the situation.
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It’s Time for Some Queueing Theory
Queueing theory is the scientific study of waiting in line. It can apply to familiar lines like those at the grocery store or bank but also to things like web s
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A Zero-Math Introduction to Markov Chain Monte Carlo Methods
For many of us, Bayesian statistics is voodoo magic at best, or completely subjective nonsense at worst. Among the trademarks of the…
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Principia Mathematica is modern and insightful
Notes on Chapter 1 of Principia Mathematica
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Yes, we did discover the Higgs
Ben Recht got my attention with a tweet about his blog post "The Higgs discovery did not take place.” I’m generally a fan of Ben’s writing, but I think he’s off base on a number of issues, and I’ll explain why. [Updated Oct 23rd, 2024] Ben's …
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Dust: Pretraining Transformers Without Backpropagation
Deep learning has been built around backprop, the only credit assignment algorithm capable of training modern neural nets, including transformer-based language models. Backprop requires differentiability and produces first-order gradients, and deep learning’s architectures, optimizers, and hardware have co-evolved…
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Mastering Linear Algebra in 10 Days: Astounding Experiments in Ultra-Learning
The MIT Challenge My friend Scott Young recently finished an astounding feat: he completed all 33 courses in MIT’s fabled computer science curriculum, from Linear ... Read more
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Derivatives, Gradients, Jacobians and Hessians
This article explains how these four things fit together and shows some examples of what they are used for. Derivatives Derivatives are the most fundamental concept in calculus. If you have a funct…
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On AlphaTensor’s new matrix multiplication algorithms
Two acquaintances independently asked about this today, so it seems worth a write-up: recently (as of this writing), DeepMind published a new paper about a new practical fast matrix multiplication …
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Demystifying Fourier analysis
I've started learning about spectrum analysis a long time ago at university, but failed to gain a true insight in how it works under the hood. For me, it was just some magical math formulas I had to memorize and know about. I knew the theory but it didn't really click .
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Reddit’s empire is founded on a flawed algorithm
Reddit has a bug in their code. This bug is currently present in their production platform, and has been for years. It affects one of the most important algorithms in the entire site, the “Hot” ranking algorithm for link popularity. It has real, demonstrable negative effects. It has been reported to Reddit’s technical…
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Backtrack-Free Cursive
Making English more enjoyable to write.
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Generating an infinite world with the Wave Function Collapse algorithm
Generating an infinite world with the Wave Function Collapse algorithm - Personal blog about game development, programming and making
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The Art of LaTeX: Common mistakes and advice for typesetting proofs
When was the first time you had to use LaTeX? If you are like most people, it was probably suddenly forced upon you during your first math or CS class where you had to start writing proofs, with minimal guidance on how to get started. Unfortunately, this meant that while many people have good operational knowledge of…
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Golden powers are nearly integers
As n increases, the distance from phi^n to the nearest integer decreases exponentially where phi is the golden ratio.
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A googol-to-one gear ratio [video]
To celebrate being alive for a billion seconds, Daniel Bruin built a machine with 100 gears with a 10-to-1 gear ratio…meaning that the overall gear ratio is a g
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Solving the “Miracle Sudoku” in Prolog
Writing a solver for “Miracle Sudoku” puzzles in Prolog.
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How to get rid of gerrymandering: the math is surprising
Gerrymandering distorts the will of the people, but the basic math of geographic representation makes it difficult to get rid of, unless we get rid of representation for geographic districts.
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The claimed effect size is about a zillion times higher than is plausible
Some years ago, you blogged about a research article by Hasan and colleagues (2013) .
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A beginning for mathematics
A positive vision for the future of mathematics: how our institutions can deepen human understanding as AI transforms mathematical research.
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Algorithms to Live By – The Computer Science of Human Decisions
What does the math tell us about how many job applicants we should look at before hiring one? While onboarding our new employees, how can ideas from the TCP networking protocol help us to identify the optimal workload for them? Why would giving employees unlimited vacation days most likely lead to less vacation being…