January 29, 2026
Cosine meets cut, chaos ensues
Networks Hold the Key to a Decades-Old Problem About Waves
Outsiders slice a 60‑year wave riddle with networks — comment war erupts
TLDR: Four researchers made long‑awaited progress on a classic “how low can waves go?” problem by using network‑cut ideas. The comments exploded into awe, pedantry over Max‑Cut vs min‑cut, and memes about outsiders beating decades of tradition — a reminder that fresh tools can crack old puzzles.
Mathematicians just made the first big dent in a 60‑year puzzle about waves — and the internet immediately turned it into a turf war. Four young researchers used network tricks (think: drawing dots and lines, then cutting the picture cleverly) to tackle a classic “how low can a sum of cosines go?” riddle. The twist everyone loves: they hadn’t even heard of the problem until last summer. Cue the comments.
The hype crowd is calling it “speedrunning a math boss fight,” cheering fresh eyes and cross‑pollination. Team Graphs is gloating that a network idea like Max‑Cut — splitting a network into two sides to maximize crossing lines — outfoxed decades of wave‑math orthodoxy. Meanwhile, the “um actually” brigade parachuted in to argue definitions: is this like the max‑flow min‑cut thing from weighted networks? Are we mixing apples and algorithms? One commenter flat‑out asked why “max‑cut” sounds different from the “min‑cut” they learned in class, sparking a mini‑seminar in the replies.
There’s also a vibe war: purists grumble this isn’t “real Fourier wizardry,” while pragmatists celebrate any tool that moves the needle. Jokes flew fast — “cosines having mood swings,” “graph theory cut the vibes,” and “waves got emo, networks brought scissors.” If you came for math, you stayed for the drama: outsiders shake up a dusty riddle, and the comments split like — well — a very good cut.
Key Points
- •Chowla’s 1965 problem asks how small a sum of cosine waves indexed by integers can be, focusing on the minimum of a structured Fourier series.
- •Ankeny and Chowla in 1952 conjectured that the minimum of such sums decreases as the number of integers N grows, a statement later proven.
- •Determining the exact rate at which the minimum drops as N increases remained unresolved and became a benchmark in Fourier analysis.
- •In September, Zhihan Jin, Aleksa Milojević, István Tomon, and Shengtong Zhang posted the first significant advance on this problem in 20 years.
- •The new approach departs from traditional Fourier analysis methods; the authors had not been familiar with Chowla’s problem before last summer.