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Paul Erdős (2000)
Erdős posed and solved problems in number theory and other areas and founded the field of discrete mathematics.
New
The latest blog posts to take off on Hacker News. 163 posts.
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The Joy of Condensed Matter
I published a slightly different version of this article in Nautilus on February 24, 2021. Everyone seems to be talking about the problems with physics: Woit’s book Not Even Wrong, SmolinR…
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The solution of the Zodiac killer’s 340-character cipher
See how Mathematica was used to solve one of the cryptograms sent in a letter by the Zodiac Killer.
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Apple’s M1 processor and the full 128-bit integer product
If I multiply two 64-bit integers (having values in [0, 264)), the product requires 128 bits. Intel and AMD processors (x64) can compute the full (128-bit) product of two 64-bit integers using a single instruction (mul). ARM processors, such as those found in your mobile phone, require two instructions to achieve the…
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Claude Shannon: The Mathematical Theory of Cryptography
The foundation of modern cryptography.
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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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Fitting Cubic Bézier Curves
Blog of Raph Levien.
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Trapped priors as a basic problem of rationality
P(A|B) = [P(A)*P(B|A)]/P(B), all the rest is commentary.
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No, RSA Is Not Broken
I have been seeing this paper by cryptographer Peter Schnorr making the rounds: “Fast Factoring Integers by SVP Algorithms.” It describes a new factoring method, and its abstract ends with the provocative sentence: “This destroys the RSA cryptosystem.” It does not. At best, it’s an improvement in factoring—and I’m not…
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The Most-Used Mathematical Algorithm Idea in History (2016)
Stephen Wolfram shares a glimpse into his conversations with Solomon Golomb, developments on shift registers, polyominoes, scientific contributions.
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Review: The Book of Why
The Book of Why: The New Science of Cause and Effect is a collaborative effort aimed at a general audience by Judea Pearl , a professor of computer science at UCLA, and Dana Mackenzie , a science writer. As a medical student with a laughably poor formal education in statistics, I believe I qualify as a card-carrying…
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How does your programming language handle “minus zero” (-0.0)?
The ubiquitous IEEE floating-point standard defines two numbers to represent zero, the positive and the negative zeros. You also have the positive and negative infinity. If you compute the inverse of the positive zero, you get the positive infinity. If you compute the inverse of the negative zero, you get the negative…
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Did Schnorr destroy RSA? Show me the factors
Schnorr has claimed new factoring methods that “destroy RSA”. This should be easy to demonstrate with well known challenges.
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What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
[Photo by Alejandra Mavroski.] Myrtle called it The article that launched a thousand posts…, and counting comments on this and several other blogs, that may not be too much of an exaggeration…
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An Introduction to Hierarchical Modeling
A visual explanation of multi-level modeling
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Translating My Z3 Tutorial to Coq
A blog about life, programming, math, logic, and physics.
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Ancient Babylonian Algorithms: The Earliest Programs
An interactive, illustrated timeline of historic moments in humankind's quest for information. With annotations by Jeremy Norman.
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Formalising Mathematics: An Introduction
An introduction to the TCC course “Formalising Mathematics”
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Finite State Machines
To infinity and beyond!
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Native Type 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…
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Cleaner parallel curves with Euler spirals
Blog of Raph Levien.
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Functorio
You might have heard people say that functional programming is more academic, and real engineering is done in imperative style. I’m going to show you that real engineering is functional, and …
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(Very) Basic Intro to Elliptic Curve Cryptography
Learn cryptography in Go by building ciphers, hashes, password security, and encryption tools. Understand security beneath the library call.
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Implementing the Elo Rating System (2020)
In this article we’ll look at how to implement the Elo rating system in code.
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Foldable Words
Packing up the household for a recent move, I was delving into shoeboxes, photo albums, and file folders that had not been opened in decades. One of my discoveries, found in an envelope at the back of a file drawer, was the paper sleeve from a drinking straw, imprinted with a saccharine message:
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Gradient Descent Models Are Kernel Machines
This paper shows that models which result from gradient descent training (e.g., deep neural nets) can be expressed as a weighted sum of simi...