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Debunking NIST's calculation of the Kyber-512 security level
[Sidney Harris cartoon used with permission. Copyright holder: ScienceCartoonsPlus.com .]
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
152
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 […]
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Programming with Less Than Nothing
Lambda calculus is for wimps. Real programmers use combinatory logic.
154
Galois Theory
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
155
Ryanair, Hamiltonian Cycles, and using graph theory to find cheap flights
Using graph theory and Ryanair route data to find cheap multi-city flight loops through Europe.
156
Modern SAT solvers: fast, neat and underused
In the previous two parts we used a SAT solver as a black box that we feed input into, and it will (usually quickly) spit out an answer. In this part, we will look at how SAT solvers work and what heuristics and other tricks they employ in their quest for performance.
157
U.S. stock market returns – a history from the 1870s to 2022
Facts and figures on U.S. stock market returns from 1871 to 2024. Annual returns, likelihood of losing money, best / worst months, and more.
158
To be a better programmer, write little proofs in your head
This is a brief write-up of a trick I learned that helps me write code faster and more accurately. I say "trick", but it's really something I started to do without noticing as I moved further into my career. When you're working on something difficult, sketch a
159
Sir, there's a cat in your mirror dimension
Pets do the darndest things, especially if you teach them a bit of math.
160
Solving NP-hard puzzles with the oldest trick in the book
KOITOTO hadir dengan mengutamakan kemudahan akses serta dukungan bagi pengguna yang membutuhkan informasi seputar layanan dan navigasi situs.
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Knuth on Huang's Sensitivity Proof: “I've got the proof down to one page” [pdf]
The Sensitivity Conjecture, which I blogged about here, says that, for every Boolean function f:{0,1}n→{0,1}, the sensitivity of f—that is, the maximum, over all 2n input strings x∈{0,1}n, of…
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37, the median value for the second prime factor of an integer
Chris Grossack's math blog and professional website.
164
Google’s fully homomorphic encryption compiler – a primer
Back in May of 2022 I transferred teams at Google to work on Fully Homomorphic Encryption (newsletter announcement). Since then I’ve been working on a variety of projects in the space, including being the primary maintainer on github.com/google/fully-homomorphic-encryption, which is an open source FHE compiler for…
165
Nvidia Stock Crash Prediction
One of the questions of the 2026 acx prediction contest is whether Nvidia’s stock price will close below $100 on any day in 2026. At the time of writing, it trades at $184 and a bit, so going down to $100 would be a near halving of the stock value of the highest valued company in the world.
166
Xor Filters: Faster and Smaller Than Bloom Filters
In software, you frequently need to check whether some objects is in a set. For example, you might have a list of forbidden Web addresses. As someone enters a new Web address, you may want to check whether it is part of your black list. Or maybe you have a large list of already used … Continue reading Xor Filters…
167
Do Machine Learning Models Memorize or Generalize?
An interactive introduction to grokking and mechanistic interpretability.
168
A generalised solution to distributed consensus
A generalised solution to distributed consensus Howard & Mortier, arXiv’19 This is a draft paper that Heidi Howard recently shared with the world via Twitter, and here’s the accompanying …
169
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…
170
Floating Point Visually Explained
While I was writing the Wolfenstein 3D book [1] , I wanted to demonstrate how much of a handicap it was to work without floating points. My attempts at understanding floating points using canonical [2] articles [3] were met with resistance from my brain. I tried to find a different way. Something far from $(-1)^S *…
171
Skip Lists Done Right
Skip lists are a wonderful data structure, but it is hard to get\ right. This blog post presents various techniques to optimize and\ improve the implementation of skip lists.
172
An update on the campaign to defend serious math education in California
Update (April 27): Boaz Barak—Harvard CS professor, longtime friend-of-the-blog, and coauthor of my previous guest post on this topic—has just written an awesome FAQ, providing his pers…
173
Dijkstra's in Disguise
You can find a PDF version of this blog post here . A weighted graph is a data structure consisting of some vertices and edges, and each...
174
Finding the average of two unsigned integers without overflow
Another code golfing adventure.
175
Random Forests for Complete Beginners
The definitive guide to Random Forests and Decision Trees.
176
NIST Elliptic Curves Seeds Bounty
Announcing a $12,288 bounty (tripled to charity) for cracking the five seeds selected by the NSA in the '90s for the NIST elliptic curve standard.
177
1/999999999999999999999998999999999999999999999999
Divide the number 999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 into 1 and express the result as a decimal expansion, and you’ll find the Fibonacci sequence presented in tidy 24-digit strings: (Thanks, David.)
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Decomposing language models into understandable components
Interpretability research decomposing a transformer layer into thousands of interpretable features that can steer model behavior.
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Introduction to Stochastic Calculus
A beginner-friendly introduction to stochastic calculus, focusing on intuition and calculus-based derivations instead of heavy probability theory formalism.