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Math on GitHub: Following Up
About six weeks ago, on May 19, 2022, GitHub released Math support on Markdown. At the time of the release, it received criticism for being ill-designed and buggy. I, too, wrote a blog post about it.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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Improving math performance in glibc
Read the most recent Red Hat Developers blog content. Explore our featured monthly resource as well as our most recently published items.
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A Perl Regular Expression That Matches Prime Numbers
Take a look at this Perl regular expression: perl -lne '(1x$_) =~ /^(11+?)\1+$/ && print "$_ is composite"' This regular expression matches only the composite numbers (and doesn't match prime numbers). Can you figure out how it works? I'll give the explanation below but try to figure it…
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Understanding Convolutions in Probability
In this post we take a look a how the mathematical idea of a convolution is used in probability. In probability a convolution is a way to add two random variables. Using a slightly ridiculous, mad-science, example we walk through multiple way to compute a convolution and ultimate arrive at the formu
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Ray tracing massive amounts of animated geometry using tetrahedral cages
Animate compact tetrahedral cages and reuse static mini-BLASes to ray-trace hundreds of millions of triangles in real time, dramatically cutting per-frame update and memory costs for dense foliage, grass, and crowds.
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The Math Required for Machine Learning
For the past year, I’ve been working on implementing well known model architectures and building web applications, so I have a fair amount…
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100 years of Zermelo's axiom of choice: What was the problem with it? (2006)
Cantor conceived set theory in a sequence of six papers published in the Mathematische Annalen during the five year period 1879–1884. In the fifth of these papers, published in 1883, 1 he stated as a law of thought ( Denkgesetz ) that every set can be well-ordered or, more precisely, that it is always possible to…
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Case study: Creative math – How AI fakes proofs
Many AI enthusiasts debate whether Large Language Models actually "reason." My research indicates that a reasoning process does indeed occur, but its goal is different than we assume.
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Parser Combinators Beat Regexes
Someone online was solving Advent of Code problems, and had a question about last years’ day 3 . They had a working solution using regular expressions (regexes) on String values, but they wanted to use ByteString values instead for performance reasons. They were surprised, however, that there seems to be a lack of…
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P < 0.05 Considered Harmful
The unreasonable persistence of an old standard
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Breaking Bell's Inequality with Monte Carlo Simulations in Python
The article explains the Bell inequality using Monte Carlo simulations in Python, and shows how non-local action-at-a-distance can be used to break it with entangled qubits.
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Doing First Grade Math in Rust's Type System
MIT student who enjoys performance engineering, compilers, and creating unconventional code
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Backpropogation Is Just Steepest Descent with Automatic Differentiation (2013)
Preface The intended audience of this article is someone who knows something about Machine Learning and Artifical Neural Networks (ANNs) in particular and who recalls that fitting an ANN required a…
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Deterministic thinking: a problem in how we think, not just in how we act
– Basketball Stats: Don’t model the probability of win, model the expected score differential.
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Exploring the design space of binary search trees
Open-source research project that explores the design space of binary search trees to implement persistent and concurrent linear list data structures.
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The Shape of Inequalities
…symmetry isn’t just a preference for “pretty” shapes. Contents Introduction The HM-GM-AM-QM Inequality The two circles The Semicircle The Container The 3D container The Sum of Squares Inequality Nesbitt’s Inequality Conclusion Introduction While I was randomly browsing the web, I came across this nice picture: Roland…
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Bounty to Recover NIST's Elliptic Curve Seeds
This is a fun challenge: The NIST elliptic curves that power much of modern cryptography were generated in the late ’90s by hashing seeds provided by the NSA. How were the seeds generated? Rumor has it that they are in turn hashes of English sentences, but the person who picked them, Dr. Jerry Solinas, passed away in…
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Hacking physics from the back of a napkin (2020)
February 24, 2020. The computational power of a humble napkin is awesome. I discuss three napkin algorithms — dimensional analysis, Fermi estimates, and random walks — and use them to figure out why rain falls, the length of the E. coli genome, and the mass of a proton, among other things. These examples suggest a…
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Visualizing Diffs: The Myers difference algorithm (2020)
In 1986, Eugene Myers published An O(ND) Difference Algorithm and Its Variations , which unified the problems of finding the longest common subsequence of two sequences (the LCS of "driftwood" and "artwork" is "two") and finding the shortest edit script for transforming one sequence into another. Myers showed that…
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