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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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Using calculus to do number theory
Calculus is the mathematics of approximations of continuous quantities ; number theory asks exact problems about discrete quantities. These seem, therefore, to be unrelated studies.
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Industrious Dice
I’m a professional mathematician. That means somebody pays me to do math. I’m also a recreational mathematician. That means you might have to pay me to get me to stop. Wearing my recreational mathe…
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Theoretical Machine Learning Lecture Series: Deep Learning and Cognition
Deep learning, which is the reemergence of artificial neural networks, has recently succeeded as an approach towards artificial intelligence. In many fields, including computational linguistics, deep learning approaches have largely displaced earlier machine learning approaches, due to the superior performance they…
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Why Don't Computer Scientists Learn Math?
I recently attended the Heidelberg Laureate Forum , in which some older researchers--mainly Fields Medalists and Turing Award winners--talked to and with young researchers. The young researchers ranged from a few students just entering university to young faculty members, most being graduate students. They came from…
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Math Team
and other horrible things you do to get into stanford
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What is algebra?
NOVEMBER 20, 2011. We hear a lot about the importance that all children master algebra before they graduate from high school. But what exactly is algebra, and is it really as important as everyone …
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Gravitational attraction of stars and cows
One attempt at rationalizing astrology is to say that the gravitational effects of celestial bodies impact our bodies. To get an idea how hard the stars and planets pull on us, let's compare their gravitational attraction to that of cows at various distances. Newton's law of gravity says that the gravitational…
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Busy Beaver Updates: Now Even Busier
Way back in the covid-filled summer of 2020, I wrote a survey article about the ridiculously-rapidly-growing Busy Beaver function. My survey then expanded to nearly twice its original length, with …
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Continuous Diffusion Language Models (CDLM's)
Fully discrete methods dominated for a few years, but language models based on continuous diffusion are making a comeback.
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Solving LinkedIn Queens with SMT
For sure easier than solving it in SAT!
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2025 Turing award given for quantum information science
Bennett, an American physicist at IBM Research, and Brassard, a Canadian computer scientist at the Université de Montréal, are widely recognized as founders of quantum information science, a field at the intersection of physics and computer science that treats quantum mechanical phenomena not merely as properties of…
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Introduction to P vs. NP
Series Introduction In this series of articles I would like to share with you a set of ideas that are meant to help non-technical people build a better intuition as to what the current software and…
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Accidentally writing a SAT solver
where my words occasionally escape /dev/null
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The Flummoxagon
We’re excited to announce Flummoxagon, a new geometric puzzle game that might just leave you flummoxed. Imagine a mash-up of Pentominoes and Sudoku. Your goal is to fit all the pieces into the hexa…
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Five Kinds of Nondeterminism
Or four kinds, or six kinds, I'm not picky about how you count them
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An overview of gradient descent optimization algorithms (2016)
Gradient descent is the preferred way to optimize neural networks and many other machine learning algorithms but is often used as a black box. This post explores how many of the most popular gradient-based optimization algorithms such as Momentum, Adagrad, and Adam actually work.
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Donut.c Without a Math Library
My little donut.c has been making the rounds again, after being featured in a couple YouTube videos (e.g., Lex Fridman and Joma Tech ). If I had known how much attention this code would get over the years, I would have spent more time on it.
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Elliptic Curve Cryptography: A Gentle Introduction – Part II
In the previous post , we have seen how elliptic curves over the real numbers can be used to define a group. Specifically, we have defined a rule for point addition : given three aligned points, their sum is zero ($P + Q + R = 0$). We have derived a geometric method and an algebraic method for computing point…
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Is mathematics about to enter the conservatory?
Math as cultural institution.
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Wolfram Language
Transcript of Stephen Wolfram's talk at SXSW 2015 on the present and future of computing: Wolfram Language, image recognition, language-design philosophy, tweetable programs, computational thinking for kids, natural language as input, symbolic programming, deployment, automation of programming, Internet of Things…
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Derivative at a Discontinuity
Alok Singh's Blog
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The Ruliology of Lambdas
Stephen Wolfram explains the rich ruliology of lambdas, made particularly significant by their connection to practical computing. Covers basic computations to undecidability to multiway graphs and evaluation strategies.
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Softmax, can you derive the Jacobian? And should you care?
Practice machine learning engineering with hands-on coding challenges. Implement neural network components, backprop, and more — from scratch.
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What does the Riemann zeta function have to do with the distribution of primes?
One of the oldest theorems in mathematics is that there are infinitely many primes. Euclid (the geometer!) proved this around 300 BCE, and for centuries afterwards the story ended there. There are infinitely many primes -- so what else is there to ask about them?