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New
The latest blog posts to take off on Hacker News. 2,851 posts.
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NP Complete 3rd Grade Math Problems (2018)
Leo’s third grade class got to try a Noyce Foundation math worksheet [1] the other day. They didn’t fare so well, but I gotta tell you, some of the problems are REALLY hard! In fact, on…
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High Performance Correctly Rounded Math Libraries for 32-Bit Floating Point
Everyone uses math libraries. Surprisingly, mainstream math libraries do not produce correct results for several thousands of inputs. Developers are seldom aware of them, which affects reproducibil…
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The Mathematics of 2048: Optimal Play with Markov Decision Processes (2018)
Finding provably optimal strategies for 2048 using Markov Decision Processes
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Rolling hash; Rabin-Karp string search
This is yet another string search algorithm. (Previously my readers have read about Knuth-Morris-Pratt .)
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Speeding up atan2f
`atan2f` is an important but slow trigonometric function. In this article we'll explain how to approximate it, and implement a version 50x faster than `glibc` on batches of inputs.
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The Inconsistency of Arithmetic (2011)
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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Difficult math is about recognizing patterns
Jeff Bezos tells a great story about the smartest guy he knew at Princeton. He and a classmate were working on a really tough partial differential equation and getting nowhere. They spent 3 hours on the problem and gave up.
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Bloom Filters: More than a space-efficient hashmap
A bloom filter is one of those data structures you are probably already aware of, or have at least heard about. For those looking for a simple recap, they are a probabilistic data structure which can …
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Computational algebraic geometry for high school students
Can high school students really learn algebraic geometry? And what could it teach us about mathematics education?
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The Poincaré Conjecture, Explained
Poincaré began working on what is now considered to be the foundation of topology and algebraic topology in the 1890s with the work Analysis Situs (1895) and five later supplements (1899; 1900, 1902a, 1902b, 1904).
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What time-weighted averages are and why you should care
Learn how time-weighted averages are calculated and why they’re so powerful for data analysis. Read the full article on the Tiger Data blog.
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Using Benford’s Law to Detect Bitcoin Manipulation
Economist Gary Smith sends along this post with the above title and the subtitle, “Market prices are not invariably equal to intrinsic values.” Here’s Smith:
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Types versus sets in math and programming languages
For several years I have been designing and implementing a functional teaching language especially for use in the context of a Discrete Mathematics course. The idea is for students to be exposed to…
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Entropy and Algebra and Topology = ?
Today I'd like to share some math connecting ideas from information theory, algebra, and topology. It's all in a new paper I've recently uploaded to the arXiv (https://arxiv.org/abs/2107.09581), which describes a correspondence between Shannon entropy and functions on topological simplices that obey a version of the…
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0x7FDE623822FC16E6: A magic constant for double float reciprocal (2011)
EDIT: I never expected this post to garner so much interest. Just to be clear, using the constant is a very bad idea in almost every situation I can think of. Even instructions like RCPSS should only be used by people who are convinced that the tradeoffs are worth it (or don’t have any other choice). Subtracting from…
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What is the Axiom of Choice?
One of the easiest ways to start a (friendly) fight in a group of mathematicians is to bring up the axiom of choice. I'll explain what it is, why it's so controversial, and hopefully shed some light on how we choose axiomatic systems and what that means for the math we do.
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Is π the Same in Every Universe?
Mathematician: That depends on what you mean by “universe.” Here’s a framing: A circle of radius R centered at a point P is the set of all points in the plane with distance R fro…
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What Are Diffusion Models?
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Gaussian Processes from Scratch (2019)
This post explores some concepts behind Gaussian processes, such as stochastic processes and the kernel function. We will build up deeper understanding of Gaussian process regression by implementing them from scratch using Python and NumPy.
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Ribbon filter: Practically smaller than Bloom and Xor
What the research is: The Ribbon filter is a new data structure that is more space-efficient than the popular Bloom filters that are widely used for optimizing data retrieval. One of the ways that …