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Is chain-of-thought AI reasoning a mirage?
Reading research papers and articles about chain-of-thought reasoning makes me frustrated. There are many interesting questions to ask about chain-of-thought…
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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Bayesians moving from defense to offense
Erik van Zwet, Sander Greenland, Guido Imbens, Simon Schwab, Steve Goodman, and I write :
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Math is an insurance policy
We live in interesting times. For instance, we are witnessing several extinction events all at once. One of them is the massive extinction of species. The other is the extinction of jobs. Both are …
754
Geometry from Another Universe
You start on an enclosed lawn, surrounded by four walls with a doorway in one of them. If you go in and explore, you might begin to feel trapped. You'll find you can visit five different rooms in the house, or go back outside to the lawn, but there's no way to go anywhere else. It's not because there are walls…
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Number of legal Go positions computed
L19 = 208168199381979984699478633344862770286522453884530548425639456820927419612738015378525648451698519643907259916015628128546089888314427129715319317557736620397247064840935
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Shamir’s Secret Sharing Scheme
Consider a scenario in which you are tasked with managing the security of a bank's vault. The vault is considered impenetrable without a key, which you are g...
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Finite state machines as data structure for representing ordered sets and maps
It turns out that finite state machines are useful for things other than expressing computation. Finite state machines can also be used to compactly represent ordered sets or maps of strings that can be searched very quickly.
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Gamedev Tutorial: Dot Product, Rulers, and Bouncing Balls
[latexpage] 本文之中文翻譯在此 Prerequisites Trignometry Basics – Sine & CosineTrigonometry Basics – Tangent, Triangles, And CannonballsInverse Trigonometric Functions, Slope Angles, And Facing Objects Overview The dot product is a simple yet extremely useful mathematical tool. It encodes the relationship between two vectors'…
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How much math you need for programming (2014)
Whenever I wanted to learn Algorithms, Mathematics used there somehow seemed to be an obstacle. I admit my Math is not that good but it ain’t that bad either but this “ain’t bad&#…
760
Euler's Fizzbuzz (2020)
FizzBuzz is a common coding problem asked in technical screenings or interviews. It goes something like this:
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An Intuitive Explanation of Black–Scholes
The Black–Scholes formula is the crown jewel of quantitative finance. The formula gives the fair price of a European-style option, and its success can ultimately be measured by its impact on option markets. Before the formula’s publication in 1973 (Black & Scholes, 1973; Merton, 1973) , option markets were relatively…
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The largest city in each 10x10 degree latitude/longitude box
From the highly eclectic blog of Mark Dominus
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Adding row polymorphism to Damas-Hindley-Milner
Intro to HM
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Quadratic Voting (2014)
Glen Weyl has uploaded a new version of his paper, Quadratic Voting (written with Steven Lalley), to SSRN, which now includes the completed proofs. Quadratic voting is the most important idea for l…
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What mathematicians should know about the Lean Theorem Prover: reliability & AI
[This is a guest post by Thomas Hales. This blog post was initially written in a different file format and converted using AI. — T.] Mathematicians have been weighing in on what they value ab…
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Hamiltonian Monte Carlo explained
Understanding an effective way of sampling from complex distributions with 3d-demonstrations
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Graphical Introduction to Dynamic Programming
I’ve been helping a friend understand dynamic programming (DP for short), so I’ve been on the lookout for good resources. The topic is covered all across the web, but I found many of them focused on the code, and not enough on the beautiful visualizations that shed light into how DP works.
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Quantum mechanics as a generalization of probability (2007)
There are two ways to teach quantum mechanics. The first way -- which for most physicists today is still the only way -- follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then you…
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Why I am learning category theory
Category theory is a domain of mathematics that exerts a strange influence over programmers. One thing that can be said for sure about category theory is tha...
773
How random is xkcd? (2015)
Apparently Randall Munroe gets a lot of messages saying that the “random” button on xkcd is biased.
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How Lewis Carroll computed determinants (2023)
Charles Dodgson (a.k.a. Lewis Carroll) developed a method of computing determinants which has some practical advantages.
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Mona Lisa in 50 polygons, using a genetic algorithm (2008)
This weekend I decided to play around a bit with genetic programming and put evolution to the test, the test of fine art 🙂
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Are deep neural networks dramatically overfitted? (2019)
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Tree traversal without recursion: the tree as a state machine (2007)
I am currently working my way through Higher-Order Perl , a highly recommended tome on effective and practical use of functional programming techniques in Perl. As you’d expect from a book that spends a lot of time discussing such concepts as function composition and recursion, the subject of tree traversal makes a…
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How Advanced Is the NSA's Cryptanalysis, and Can We Resist It?
The latest Snowden document is the US intelligence ‘black budget.’ There’s a lot of information in the few pages the Washington Post decided to publish, including an introduction by Director of National Intelligence James Clapper. In it, he drops a tantalizing hint: ‘Also, we are investing in groundbreaking…
779
Music and Geometry: Intervals and Scales
An article about music and geometry, in particular about musical intervals and scales and their geometric equivalent ...
780
Why Multi-armed Bandit algorithms are superior to A/B testing (with Math)
In a recent post, a company selling A/B testing services made the claim that A/B testing is superior to bandit algorithms. They do make a compelling case that A/B testing is superior to one particular not very good bandit algorithm, because that particular algorithm does not take …