The famous problem asks whether a map can be filled in with only four colors such that the same color never borders itself. It has been solved with the help of computers, but some experts suggest an...

When I was in graduate school I used to say that a mathematician was someone who would spend two weeks finding a simpler way to do something that could have been finished in two hours.

💬 0  🔁 1  ❤️ 0 · Problem of Points · Mathober Day 11

Sanskrit prosody needed to catalogue every possible metre. Over about fifteen centuries it produced three exact, table-free ways to go between an integer index and a metre: positional (binary), weight-constrained (binomial), and duration-constrained (Fibonacci). This paper states the three schemes precisely as ranking/unranking algorithms, proves them, and checks them exhaustively by machine. It extends the weight-constrained scheme to balanced-ternary vectors with exactly r non-zero digits, and shows that the binomials every scheme needs can be built by Virahāṅka's sūci-prastāra as add-only prefix scans, removing division from the whole path. It corrects several inflations of the historical record, including three errors in the author's own earlier drafts, and maps each scheme onto state addressing in a deterministic integer runtime with measured bounds on where a table-free address pays. No lineage to modern computing and no new mathematics is claimed: every theorem is a known result or a direct composition of known results. What is offered is the reading, the corrections, and the receipts.   Reference implementation (Rust, no_std, allocation-free, 16 exhaustive tests; code MIT OR Apache-2.0): https://github.com/13forge/proofsStatus: release candidate. Open items are listed in §10 of the paper. Related works (Add related work): https://github.com/13forge/proofs → Is supplemented by · Resource type: Software 10.1016/0315-0860(85)90021-7 (Singh 1985) → References arXiv:math/0703658 (Kulkarni 2008) → References 10.1145/363162.363165 (Ingerman 1967) → References

We have become quite used to pronouncements of doom, from scientists predicting the sixth mass extinction due to the measurable effects of climate change, and from religionists declaring the apocalyps...

The math behind your GPS, face unlock, and online banking was worked out by people who never touched a computer — some over a thousand years ago. This piece traces 20 mathematicians to the exact technologies their proofs made possible, and the connections are genuinely surprising.

💬 0  🔁 5  ❤️ 7 · So in this month's Fantastic Four (online reading schedule), aliens invaded in the past and Mr. Fantastic and the Human Torch have to stop them. They travel back to 114 CE Gaul and…

Tangram   is a name of a Chinese puzzle of seven pieces that became popular in England around the middle of the 19th century. It seems...

Math! Science! History! is a podcast about the history of people, theories, and discoveries that have moved our scientific progress forward and spurred us on to unimaginable discoveries. Join…

YouTube video by Alvaro Lozano-Robledo

In Jerusalem of the year 1229, there lived a Greek Orthodox monk named Johannes Myronas.

Discovered alongside unique formulas for the movements of the sun and planets, the attribution proves the importance of such work more than 1,000 years ago

YouTube video by Tom Rocks Maths

Two episodes when technology revealed something familiar as something new

One bad thing about archeologists is that some of the successful ones get a big head. People used to think the Olmecs, who made these colossal stone heads, were contemporary with the Mayans. But in…