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Relearning math as an adult
I recently passed 100 days of practicing math every single day 💯 I’ve wanted to beef up my math chops for a while, but I needed a good reason that would justify the time investment. Plus…
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The latest blog posts to take off on Hacker News. 2,851 posts.
692
AlphaGeometry: An Olympiad-level AI system for geometry
Our AI system surpasses the state-of-the-art approach for geometry problems, advancing AI reasoning in mathematics
693
RSA is deceptively simple and fun
While reading Real-World Cryptography , I came across the "million message attack" . This is an attack that Daniel Bleichenbacher demonstrated in 1998, which effectively broke RSA with a particular encoding function called PKCS #1 . It was only mentioned briefly, so I dug in and decided to try to understand the…
694
When Random Isn't
This post is an anecdote from over a decade ago, of which I lost the actual code. So please forgive me if I do not accurately remember all the details. Some details are also simplified so that anyone that likes computer security can enjoy this article, not just those who have played World of Warcraft (although the…
695
Dynamic programming is not black magic
This year’s Advent of Code has been brutal (compare the stats of 2023 with that of 2022, especially day 1 part 1 vs. day 1 part 2). It included a problem to solve with dynamic programming as soon as day 12, which discouraged some people I know. This specific problem was particularly gnarly for Advent […]
696
Doing First Grade Math in Rust's Type System
MIT student who enjoys performance engineering, compilers, and creating unconventional code
697
Generating SVG for the prime knots
How I created a wall poster of knot diagrams.
698
Solver Performance: 1989 vs. 2024
We estimate the magnitude of speed improvement for optimization solvers and computer hardware in the 35 years from 1989 to 2024.
699
Why Aren't We Sieve-Ing?
Long-time readers of this blog will know that I have mixed feelings about caches. One on hand, caching is critical to the performance of systems at every layer, from CPUs to storage to whole distributed architectures. On the other hand, caching being this critical means that designers need to carefully consider what…
700
When random numbers are too random: Low discrepancy sequences (2017)
Random numbers can be useful in graphics and game development, but they have a pesky and sometimes undesirable habit of clumping together. This is a problem in path tracing and monte carlo integrat…
701
What has a 1 in a million chance? (2010)
If you overheard the phrase "1 in a million chance" in someone else's casual conversation, what might they be talking about?
702
Learning Regular Languages with L* Algorithm
Research in Software Engineering from Rahul Gopinath
703
The Curious Case of MD5
Recently I came across a puzzling fact: the International Criminal Court hashes electronic evidence with MD5, even though MD5 is badly broken. So, why are lawyers using broken, outdated technology? The answer involves the common law system, cultural isolation, and a single man named Don L. Lewis.
704
Understand how transformers work by demystifying the math behind them
Understand how transformers work by demystifying all the math behind them
705
Double encryption: Analyzing the NSA/GCHQ arguments against hybrids
In 2019, Google and Cloudflare ran an experiment where they upgraded HTTPS for many "real users’ connections" to use post-quantum encryption. They then reported statistics on how affordable this was. Google had also run a similar experiment in 2016: "While it's still very early days for quantum computers, we're…
706
What I've learned about flow fields so far
Noise functions and the tiniest bit of trigonometry can take you a long way towards making art.
707
A* tricks for videogame path finding
A* Tricks for Videogame Path Finding, A* (A-star) Search Algorithm
708
Using a Markov chain to generate readable nonsense with 20 lines of Python
Describes a simple Markov chain algorithm to generate reasonable-sounding but utterly nonsensical text, and presents some example outputs as well as a Python implementation.
709
High Precision Mapping from Scratch
The fun of owning rural property is that knowing where your land actually starts and ends is a guess usually. Sure, you have a parcel description, and maybe even an online service with “official” GIS boundaries (for us here in New Brunswick, this is GeoNB ). However, since it’s in the middle of the forest, the odds of…
710
How random is xkcd? (2015)
Apparently Randall Munroe gets a lot of messages saying that the “random” button on xkcd is biased.
711
Formally modeled Dreidel for no good reason
I can mathematically prove the game's not fun.
712
4B If Statements
I recently stumbled upon this screenshot while researching social media on the train. Of course, it was followed by a cascade of spiteful comments, criticizing this fresh programmer’s attempt to solve a classical problem in computer science. The modulus operation.
713
Bayesians moving from defense to offense
Erik van Zwet, Sander Greenland, Guido Imbens, Simon Schwab, Steve Goodman, and I write :
714
How Many People? Ancient Demography
Bret Devereaux (A Collection of Unmitigated Pedantry)2023121 points5 commentscited by 3History & Retro Computing details
One of the first questions anyone asks about past societies is, ‘how many people were there?’ It is one of those basic bits of information and generally speaking those of us who teach t…
715
Math Team
and other horrible things you do to get into stanford
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SVD Image Compression
Singular Value Decomposition (SVD) is a fundamental concept in linear algebra, and it is particularly important in the field of machine learning for tasks such as dimensionality reduction, data compression, and noise reduction.
717
3Blue1Brown Calculus Blog Series
Mathematics with a distinct visual perspective. Linear algebra, calculus, neural networks, topology, and more.
718
Causal Trees
Projects and Ramblings
719
Embeddings, vectors, and arithmetic
An embedding is the representation of a piece of text like a word, sentence, or paragraph. Traditionally this value is in the form of a mathematical vector - a point in space. You can think of it as analogous to coordinates on a map that just happens to have many, many dimensions.
720
FunSearch: Making new discoveries in mathematical sciences using LLMs
We introduce FunSearch, a method for searching for “functions” written in computer code, and find new solutions in mathematics and computer science. FunSearch works by pairing a pre-trained LLM, whose goal is to provide creative solutions in the form of computer code, with an automated “evaluator”, which guards…