An anonymous reader sends in a Science News article that begins: "Human free will might seem like the squishiest of philosophical subjects, way beyond the realm of mathematical demonstration. But two highly regarded Princeton mathematicians, John Conway and Simon Kochen, claim to have proven that if humans have even the tiniest amount of free will, then atoms themselves must also behave unpredictably."
Standard interpretations of quantum mechanics, of course, embrace unpredictability. But many physicists aren't comfortable with that, and are working to develop deterministic interpretations of quantum mechanics. Conway and Kochen's proof argues that these efforts will be fruitless — unless one is willing to give up human free will, in a very strong sense. The article quotes Conway: "We can really prove that there's no algorithm, no way that the particle can give an answer that is unique and can be specified ahead of time. I'm still amazed that we can actually manage to prove that."