# Kadison–Singer problem

- kind: problem
- status: solved (evidence tier V3)
- year: 1959
- authors: Richard Kadison and Isadore Singer

**Statement.** Does every pure state on the diagonal of B(ℓ²) extend uniquely to a pure state on all of B(ℓ²)?

It started as a question about the foundations of quantum mechanics and was shown equivalent to problems in a dozen fields. The solution came from graph theory, through interlacing polynomials, the same method the authors used to build Ramanujan graphs. A question in operator algebras was settled by a combinatorial method.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Posed 1959, Richard Kadison and Isadore Singer. Closed 2013, Adam Marcus, Daniel Spielman and Nikhil Srivastava.

## Sources

- [Wikipedia: Kadison–Singer problem](https://en.wikipedia.org/wiki/Kadison%E2%80%93Singer_problem)

[Analysis and PDE](/wiki/Space:analysis.md) · [Mathematics](/wiki/Continent:mathematics.md)

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