Conjectures.io

(Bittensor Subnet 66) rewards anyone who can solve open mathematical problems and advance the frontier of mathematics.

[Conjectures.io @conjectures_io]

We believe incentivization of mathematical breakthroughs is one of the most important and exciting problems a Bittensor subnet has ever addressed. This educational video explains why.

[Conjectures.io @conjectures_io]

@Crypto_McKenna We already do this, and incentivize it 😉

[Conjectures.io @conjectures_io]

@MacroBombastic @Crypto_McKenna We provide incentivization to solving these problems and create a shared resource layer, check us out @ https://t.co/2j5iFNnB7U

[Conjectures.io @conjectures_io]

AI is now driving the most significant progress in 50 years on what many consider mathematics’ hardest open problem.

Conjectures fuels breakthroughs like this and rewards the people pushing them forward.

[Anthropic @AnthropicAI]

We asked an unreleased research version of Claude to take a stab at the Riemann hypothesis.

It didn’t solve it, but it did make strides on a related problem: it increased the lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis from 41.6% to 67.2%.

https://t.co/aZDvqqhHRi

[Conjectures.io @conjectures_io]

For more context on the software optimization side, which is a future contest that will run alongside our breakthrough competition, check out this article by Vitalik Buterin
https://t.co/Uvdwj0mtTP

[Conjectures.io @conjectures_io]

We’ve recently published our roadmap:

https://t.co/wTU64kOQXI

This explains simply our 2 paths to revenue: scientific breakthroughs and software optimization. Formal verification connects them both by making every result objective, trustworthy and rewardable.

[Conjectures.io @conjectures_io]

@RonXLabs Don't trust, verify 😉

Erdős #10, Grechuk variant: https://t.co/LFUvCMJoki

Green #29: https://t.co/5FXxCdAJ3o

[Conjectures.io @conjectures_io]

We’re excited to announce that our miners have closed two published open-conjecture targets with Lean-verified submissions: the Grechuk variant of Erdős Problem #10 and Ben Green’s Problem #29. This comes less than one day after opening mining!

1. Erdős #10, Grechuk variant: Are there infinitely many even integers that cannot be written as a prime plus at most three powers of 2? A miner proved yes by formalizing Crocker’s covering-congruence construction and the required parity reduction.

2. Green's problem #29: Must every K-approximate group A contain a polynomially large S ⊆ A with S⁸ ⊆ A⁴? A miner proved no, constructing a counterexample with K=3 in ℤ × H for sufficiently large finite H.

Both submissions passed our production verifier and Lean’s kernel. The Erdős result formalizes an older mathematical construction; the Green #29 counterexample gives a negative answer to the published question. Our open competition turned open conjectures into machine-checked solved mathematics.

[Conjectures.io @conjectures_io]

Mining is live on Conjectures!

Prove open mathematical conjectures in Lean and earn bounties for accepted solutions. Use any model or tooling, and check your proof bundle for free before submitting.

Start mining: https://t.co/yN7GTsHKYZ

[Conjectures.io @conjectures_io]

OpenAI is doing it right now, Conjectures will be doing it soon.

[OpenAI @OpenAI]

An internal version of our next major model produced 10 new results on long-standing open problems in mathematics and theoretical computer science, using roughly $2,000 worth of tokens at GPT-5.6 Sol API rates.

[Conjectures.io @conjectures_io]

OpenAI believes in AI’s ability to make important mathematical breakthroughs.

Do you?

[Sebastien Bubeck @SebastienBubeck]

yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model.

We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more.

More thoughts here: https://t.co/8SjXONeh38

[wejh @Wejh69]

150 year old conjecture proved false by AI. Imagine the results we see when @conjectures_io starts incentivizing this type of breakthrough 🤔

[Conjectures.io @conjectures_io]

Anthropic breaking cryptography with their proprietary models begs the question, is stronger and newer cryptography a must?

The answer is yes, and at Conjectures we are incentivizing the mathematical breakthroughs that makes new and stronger cryptography possible.

[Anthropic @AnthropicAI]

New Anthropic research: Discovering cryptographic weaknesses with Claude.

Claude Mythos Preview has helped our researchers find weaknesses in cryptographic algorithms—the mathematical methods that are used to keep data private.

Read more: https://t.co/TYKLjb3Q7V

[Mark Jeffrey @markjeffrey]

AI is cracking math proofs left and right.

Now there's a subnet for that.

[Conjectures.io @conjectures_io]

https://t.co/Hiq26lQFS3