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Mathematicians Build Long-Awaited Graph SandwichThe proof of a decades-old conjecture has given researchers a new way to understand complex networks.
Paulina Rowińska explains how Behague, Iľkovič, and Montgomery completed Kim and Vu's sandwich conjecture, letting hard properties of random regular graphs follow from easier binomial-graph results.
7 min · 1,621 words
In April 1542 a letter left Rome for the court of Charles V in Spain. On its first page the Italian stops in the middle of a line and digits begin: Figure 1. The opening of the cipher, f. 70r. Archivio Apostolico Vaticano (AAV), Segr. Stato, Spagna 1A, photograph supplied through DECODE record 92. Detail enlarged from the photograph.
42 min · 9,580 words
English: a vs anWhy vowel letters are the wrong rule for indefinite articles in generated text
Amit Patel (Red Blob Games) digs into when English wants “a” versus “an”: the rule tracks spoken vowel sounds, not written vowel letters, and only a small set of common words need exceptions for procedural text generation.
1 min · 274 words
The author designs a compact binary encoding scheme for national flags using a layered model and Huffman coding. Most flags can be represented in 55–76 bits by exploiting the statistical regularity of flag elements — stripes, stars, crescents, common aspect ratios — while allowing longer codes for complex outliers like Qatar.
2 min · 351 wordsagent-written
Thomas Ahle presents a technique for evaluating polynomials in roughly half the multiplications that Horner's method requires, by preprocessing the coefficients offline. An interactive tool lets users input a polynomial and field to see the optimised evaluation chain.
1 min · 234 wordsagent-written
Optimizing anamorphic sculptures
Thiago Cardoso walks through creating and optimizing anamorphic sculptures—images that resolve only from a specific vantage—using computational geometry techniques.
6 min · 1,436 words
Reservoir SamplingOriginal article link with an AI-written directory summary
An interactive explanation of choosing a fair random sample from a stream of unknown length. Sam Rose develops reservoir sampling with simple arithmetic, visual examples, and an implementation readers can follow.
1 min · 76 wordsagent-written
Bloom FiltersOriginal article link with an AI-written directory summary
A visual introduction to Bloom filters and their tradeoffs. Sam Rose explains how a compact probabilistic structure can answer membership questions, including why false positives are possible and when that compromise is useful.
1 min · 78 wordsagent-written
How Hacker News ranking really works: scoring, controversy, and penalties
Ken Shirriff reverse-engineers Hacker News ranking: the gravity formula, controversy penalties after ~40 comments, title/domain penalties (including historical NSA demotion), and how ~20% of front-page stories are tweaked.
15 min · 3,547 words