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Mathematics / Millennium problem

Birch–Swinnerton-Dyer Conjecture

Does an elliptic curve's L-function encode its rank and finer arithmetic?

The source trail 8

Findings, with context
DiscussionFound Sep 20, 2026

A source discussing Birch–Swinnerton-Dyer

abel.math.harvard.edu contains the excerpt below in a discussion related to Birch–Swinnerton-Dyer. Read the source for the surrounding context.

“The constant C depends on fancy objects like the torsion order, Tamagawa numbers, regulartor, Shafarevich-Tate group.”
This excerpt is evidence of what the linked page says, not verification of its claims. Publication date has not been established.
Source pageIndirect account · Found Sep 20
abel.math.harvard.edu
RumorSep 13, 2026

Birch–Swinnerton-Dyer in the rumor discussion

boshalfoshal writes the excerpt below in a discussion related to Birch–Swinnerton-Dyer. Read the source for the surrounding context.

“Navier Stokes, and _allegedly_ the Hodge Conjecture and Birch–Swinnerton-Dyer.”
This source discusses a rumor. It does not establish a breakthrough.
boshalfoshalOriginal source · Found Sep 20
Hacker News
PaperAug 26, 2026

A paper related to Birch–Swinnerton-Dyer

arxiv.org contains the excerpt below in a discussion related to Birch–Swinnerton-Dyer. Read the source for the surrounding context.

“we state the conjecture, that is, the equality of these two ranks.”
A linked paper is a research claim, not confirmation that the problem is solved.
Source pageOriginal source · Found Sep 20
arxiv.org
RumorFound Sep 19, 2026

A Reddit comment names Anthropic in a narrower BSD rumor

u/elliotglazer interprets the lab rumors as possibly involving a new case of BSD at Anthropic, rather than a solution of the whole conjecture. He contrasts that with a rumored new Hodge case at OpenAI.

“maybe a new case of BSD by Ant.”
An explicitly tentative account of a possible special case, not proof of BSD or an Anthropic announcement. Reddit's public feed gives September 12 as the source-update date, with no separate publication timestamp. This is the same source linked in the Hodge watch.
u/elliotglazerOriginal source · Found Sep 19
Reddit · r/mathematics
RumorFound Sep 19, 2026

The September megathread also contains a BSD verification rumor

u/imadade reports hearing on Twitter that Hodge and Birch–Swinnerton-Dyer results are being checked. The comment does not identify a BSD author, lab, manuscript, or the case under discussion.

“Hearing on twitter, that there is verification of proof of two problems currently ongoing: Hodge Conjecture & birch and swinnerton-dyer conjecture.”
Unsubstantiated hearsay, preserved as a comment to investigate. No independent corroboration is established. The public feed's source-update date is September 10; the publication timestamp is unavailable.
u/imadadeOriginal source · Found Sep 19
Reddit · r/mathematics
RumorSep 10, 2026

A social post names BSD as a possible AI-lab target

Exact’s timeline attributes a claim to @synthwavedd that OpenAI or Anthropic may be close to a BSD result. The original X post was inaccessible during our check.

Unconfirmed rumor. Date and wording come from a secondary account; repetitions do not establish corroboration.
@synthwavedd, as reported by ExactIndirect account · Found Sep 19
Exact · secondary account
Original X post (may require sign-in)
Upcoming eventEvent · Sep 21, 2026

A workshop on BSD and related recent results

A Clay workshop organized by Chris Skinner and Wei Zhang is scheduled for September 21–25. It is a useful place to look for talks and subsequent papers.

The event dates are known; the listing’s publication date is not. An upcoming workshop does not imply a particular breakthrough.
Clay Mathematics InstituteOriginal source · Found Sep 19
Clay Mathematics Institute