Frontier mathematics
New structures, conjectures, proofs, counterexamples, and connections—supported by systems that can search beyond a single familiar route.
VDL / Research
Research
We choose problems with a precise mathematical core, a genuine obstruction, and room for verification to change what can be discovered.
Research directions
What we work on
Verification methods
Exact computation, proof auditing, formalization, and reproducible workflows that keep the checked claim aligned with the original target.
Mathematics in use
Hard problems across science, engineering, and industry whose mathematical structure has not yet been fully used.
Yang–Mills existence and mass gap
A public working repository concerned with the Yang–Mills existence and mass gap problem. It records research materials in progress; the existence of a repository is not a claim that the problem has been resolved.
View repositoryDiscovery loop
How the work moves
- 01
Frame
State the problem precisely and separate the intended result from nearby, weaker claims.
- 02
Explore
Combine structure, literature, computation, and automated reasoning. Pursue more than one route.
- 03
Challenge
Search for counterexamples, hidden assumptions, boundary failures, and target drift.
- 04
Verify
Match each result to an exact claim using proof, exact computation, formal checking, and review.
- 05
Release
Publish the result with its evidence, status, dependencies, and unresolved limits.