Greg Kuperberg

Uh, you know, and, and so, uh, uh, you know, for me a question is, you know, do I, uh, uh, uh, uh, uh, sort of throw myself into, uh, uh, trying to understand these things, or do I wait for younger people to, uh, uh, to, to understand them, to, uh, you know, re-explain them more comprehensively and then try to understand what's going on? You know, it might, it might, it m- and it, it might be more of the latter, um, uh, for me.

But, uh, uh, you know, so, so, you know, a, a a question that I posed 20 years ago with Greg Kuperberg, which was called the unitary synthesis problem, uh, was one of the, you know, 370 problems that-

Mm

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In 2006, they made partial progress, but they couldn't achieve their ultimate goal, a particularly coveted form of evidence that avoids making unusual assumptions.

That just seemed like a much, much harder problem, said Scott Aronson, a complexity theorist at the University of Texas, Austin, who co-authored the 2006 paper with the mathematician Greg Kuperberg.

In 2025, four researchers finally succeeded.

Quantum forensics.

That contradiction, he suspected, would come from a property of classical proofs that we usually take for granted.

It's possible to read a proof more than once.

Chasing Shadows Outside of spy movies, documents rarely self-destruct after they're read, and fortunately for mathematicians, proofs are no exception.

But in the quantum world, things are different.