Another mathematician, Roger Penrose, made a similar claim, but with "consciousness" instead of "free will".
I find this very implausible. So does Douglas Hofstadter, probably, though I've not yet read his main book on the subject.
Thought experiment: You make a mathematical model of how neurons work, you cut up a human's brain, and you build a machine that simulates it. Wherever the model required randomness, you use pseudorandom numbers, generated cryptographically, so the entire system is deterministic. You connect it up to some kind of humanoid robot. Does the resulting system behave roughly like a human, and, if so, does it have free will, and is it conscious?
People who believe that consciousness or free will depends on fundamental physics have to believe:
* Either that the simulated human won't work like a human: it will mysteriously fail to function, but how exactly?
* Or that the simulated human will seem to work like a real human, but nevertheless it won't be conscious; it will be a mere "zombie".
The first option seems intuitively implausible to me, and the second option sounds like silly sophistry.