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Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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Differential Heuristics
In 2005 Google showed off Google Maps, which lets you drag the map around instead of reloading the page like MapQuest and others used. That’s the feature that got everyone’s attention. But what got my attention was a feature they added in 2007 where you could drag the start/end points on a route [1] , and it would…
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Goodhart’s law isn’t as useful as you might think (2023)
Goodhart's Law is useless. It tells you about a phenomenon, but it doesn't tell you how to solve it. We look at how organisations actually prevent Goodhart's Law, and illustrate this with Amazon's Weekly Business Review as an example.
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Optimizing a Math Expression Parser in Rust
Optimizing a math expression parser for speed and memory.
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The sum of all the positive integers is not -1/12
I haven't been blogging recently because my new startup is taking up all my time, but someone needs to stand up and say the emperor has no c...
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Cistercian Numerals
Cistercian numerals were invented by the Cistercian order of monks in the 13th century. Giuseppe Frisella explains how the notation system works: A vertical str
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A reckless introduction to Hindley-Milner type inference (2019)
(I've been editing this post on and off for almost a year. I'm not really happy with it, but I suspect I never will be.)
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Can guitar frets perform multiplication?
I’m sure that some pictures are worth a thousand words, but others trigger a whole lot of puzzlement. Such was the case with the cover of a book I recently bought entitled Calculating with Tones: The Logarithmic Logic of Music:
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Why Philosophers Should Care About Computational Complexity
Update (August 11, 2011): Thanks to everyone who offered useful feedback! I uploaded a slightly-revised version, adding a “note of humility” to the introduction, correcting the footnot…
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Black Hole Tech?
In celebration of the detection of gravitational waves, Stephen Wolfram looks forward and discusses what technology black holes could make possible.
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The probability of a hash collision (2022)
Exploring the math behind hash collisions.
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Gaussian Distributions Are Soap Bubbles
This post is just a quick note on some of the pitfalls we encounter when dealing with high-dimensional problems, even when working with something as simple as a Gaussian distribution. Last week I wrote about mixup [https://www.inference.vc/mixup-data-dependent-data-augmentation/] a new data-augmentation...
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Math Exposition on YouTube
This summer, 3Blue1Brown launched the third installment of the Summer of Math Exposition contest. Every year, I’ve been impressed and inspired by the quality of some of the videos in this con…
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The adder at the heart of Intel's 8087 floating-point chip
In 1980, Intel released the Intel 8087 floating-point coprocessor, a chip that could make math up to 100 times faster. As well as arithmetic...
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When will the eclipse happen? A multimillennium tale of computation
Wolfram tech and its dedicated website now easily predict eclipses. A look at advances in understanding and science from ancient eclipse data thousands of years old through current eclipse calculations.
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An equation that takes Pythagoras to a new level
Unbelievably enough, it all comes back to Pythagoras.
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Bayes' Theorem with Lego
Find Bayes' Theorem confusing? Let's break down this famous formula using Lego to help you build up a better intuition for this foundational concept!
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An easy-to-implement, arena-friendly hash map
My last article had tips for for arena allocation . This next article demonstrates a technique for building bespoke hash maps that compose nicely with arena allocation. In addition, they’re fast, simple, and automatically scale to any problem that could reasonably be solved with an in-memory hash map. To avoid…
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How has mathematics gotten so abstract?
What's the meaning of "numbers" and "arithmetic operations"? We consult Georg Cantor's turtles and look at Giuseppe Peano's code.
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What do we mean by "the foundations of mathematics"?
The phrase “foundations of mathematics” is bandied about frequently these days, but it’s clear that there is widespread confusion about what it means. Some say that a proof assistant must be based on a foundation of mathematics, and therefore that the foundations of mathematics refers to some sort of formal system…
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A seventh-grader student found a beautiful proof to Thales' Theorem (2002)
A useful theorem attributed to the probably first mathematician ever, Thales of Miletus (ca. 624 BC-ca. 546 BC) is one of most elementary and intuitive ever stated.
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A Nerd’s Way to Walk Up the Stairs (2011)
Mathematics, applications of mathematics to life in general, and my life as a mathematician.
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Using Benford’s Law to Detect Bitcoin Manipulation
Economist Gary Smith sends along this post with the above title and the subtitle, “Market prices are not invariably equal to intrinsic values.” Here’s Smith:
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On Norbert Blum’s claimed proof that P does not equal NP
Edited 8/16 to correct attributions to Alon and Boppana and to Tardos, thanks to an anonymous commenter for the correction Yesterday, Norbert Blum posted a preprint with a claimed proof that $latex…
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The power of two random choices
In many large-scale web services, multiple layers of stateless and stateful services are seperated by load balancers. Load balancing can be done with dedicated hardware, with dedicated software load balancers, using DNS trickery or through a load-balancing mechanism in the client. In large systems, the resources and…
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Hash tables
In this post you will learn what hash tables are, why you would use them, and how they are used to implement dictionaries in the most popular Python interpreter—CPython.
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Decomposing a Factorial into Large Factors
I’ve just uploaded to the arXiv the paper “Decomposing a factorial into large factors”. This paper studies the quantity $latex {t(N)}&fg=000000$, defined as the largest quanti…