Famous problems, and where each one stands
Qvanta® attacks famous open problems in mathematics with AI agents, Lean formal verification, GPU high-performance computing and quantum computing. These four collections are ordered from hardest to most approachable, with each problem’s status shown clearly: solved, partially solved, or open.
Hilbert's 23 problems
The problems David Hilbert set for the 20th century at the 1900 International Congress of Mathematicians, including the Riemann hypothesis.
Erdős problems
More than 1,200 problems posed by Paul Erdős across number theory, combinatorics and graph theory, many with cash prizes.
Problems posted by OpenAI
Open research problems on which OpenAI has published model-generated manuscripts, some backed by Lean formal proofs.
Ramanujan’s questions
The 58 questions Srinivasa Ramanujan posed in the Journal of the Indian Mathematical Society between 1911 and 1919.
How we read the status
Settled: proved, disproved, or shown to be independent of the axioms. For OpenAI’s problems, this means the main result has a Lean formal proof.
Real progress short of a full answer: solved in some settings, reduced to a finite computation, or a formal proof still awaiting review.
No accepted solution yet. These are the targets.
A published but unverified claim, such as an OpenAI manuscript without a Lean formalization.
How we work
Every problem goes through the same loop, and it keeps running until the problem is settled.
- 1
Hypothesize
Frame a precise conjecture, a special case, or a reduction worth attacking.
- 2
Analyze and build
AI agents study the literature, explore examples, and draft formal proofs.
- 3
Verify in Lean
The Lean proof assistant checks every step. Anything that does not compile is rejected.
- 4
Repeat
Failures and gaps feed the next hypothesis, and the loop runs again.
The same standard as OpenAI
We follow the protocol OpenAI uses for its published problems: a written manuscript for each result, paired with a Lean formalization. A result is marked verified only when its Lean proof compiles.
Many agents, many angles
A variety of AI agents and subagents attack each problem in parallel, from different directions. Their output is a full proof, a partial proof that settles some cases, or a counterexample that disproves the claim.
Solvers on GPU HPC
We run SAT, SMT and search solvers, and the agents themselves, on GPU high-performance computing clusters. That lets us check large finite cases and hunt for counterexamples at scale.
Search where computation decides
Many partially solved problems come down to a finite search for a counterexample or a certificate. That is where quantum and quantum-inspired search can shorten the path to an answer.
Work with us on a problem
Qvanta® partners with researchers and universities on formal verification and computation.
Contact Qvanta®