You may have noticed our recent announcement of the proof of the Kadison-Singer conjecture, in which we weren’t able to go into that much detail about what the conjecture actually entails. Well, having been contacted by one of the authors of that paper, Adam Marcus, who emailed to congratulate us on the complete absence of any typos in our coverage, and in particular the correctness of the spelling of all the proper nouns, we’re now able to give a little more detail. Quoth Adam:

To be honest, I don’t think I could do a better job at explaining the conjecture than some people have already done, so I would rather point you at their expositions. The physics one is especially easy to follow, and is accessible with freshman-year physics. The other two are also quite good, but require a bit more math.

- An article by Nikhil Srivastava (spelt correctly this time), a coauthor of the proof, explaining the relationship between the conjecture and discrepancy theory.
- A piece from Notices of the AMS written by Christopher Heil, which relates the conjecture to Frame Theory.
- A relatively accessible article by Bryan Roberts on the physics which originally inspired the question (as physics has a tendency to do).

Adam Marcus was an Assistant Professor of Applied Mathematics at Yale and is now the co-founder of a tech startup. Nikhil Srivastava is at Microsoft Research. Daniel A. Spielman is a Professor of Computer Science, Mathematics, and Applied Mathematics at Yale.