Does a Hadamard matrix exist for every positive order divisible by four?
github.com contains the excerpt below in a discussion related to Hadamard. Read the source for the surrounding context.
“Research status (2026-07-25): unsolved. This repository does not contain a Hadamard matrix of order 668.”
mathdb.com contains the excerpt below in a discussion related to Hadamard. Read the source for the surrounding context.
“The report supplies no construction details or independent verification, so this is progress on individual orders, not a proof of Hadamard’s conjecture.”
proofatlas.ai contains the excerpt below in a discussion related to Hadamard. Read the source for the surrounding context.
“The universal conjecture remains open: the cited sources do not provide a construction for every positive order divisible by four.”
github.com contains the excerpt below in a discussion related to Hadamard. Read the source for the surrounding context.
“We report on a computational attack on the smallest open case of the Hadamard conjecture: the existence of a Hadamard matrix of order~$668$”
arxiv.org contains the excerpt below in a discussion related to Hadamard. Read the source for the surrounding context.
“A Legendre pair of length 333 would yield a Hadamard matrix of order 668, the smallest order presently unresolved by the Hadamard conjecture.”
mathoverflow.net contains the excerpt below in a discussion related to Hadamard. Read the source for the surrounding context.
“Levent Alpöge has posted on X (formerly Twitter) (without further details) an example of a $668\times668$ matrix”
github.com contains the excerpt below in a discussion related to Hadamard. Read the source for the surrounding context.
“No candidate met this criterion. No final matrix CSV was created.”
github.com contains the excerpt below in a discussion related to Hadamard. Read the source for the surrounding context.
“H.668 verified as genuine Hadamard (Aug 12 2026)”
ion.nechita.net contains the excerpt below in a discussion related to Hadamard. Read the source for the surrounding context.
“Great news: humans have found a Hadamard matrix of order 668”
Jonathan Jedwab's September 22 Bristol seminar describes work with Thomas Pender on quaternary Legendre sequences and their connection to Hadamard matrices.
“It has recently been shown that this conjecture would also follow from the existence of a pair of quaternary Legendre sequences for every even length.”
Epoch's solution update reports that an Anthropic researcher credited three humans and Claude with constructions covering previously missing admissible orders below 2,000, including 668.
“crediting a team of three humans and Claude”
A thread follows Alpöge's announcement and Epoch's update. Commenters ask for more visibility into the prompts and the division of work between the researchers and Claude.