For example, is Probability and Statistics theory only a part of Mathematics or maybe Physicians consider this knowledge from both fields simultaneous? And one really crazy question: is there any possible circumstances (like other reality with other Physics or maybe kind of non-Euclid mathematical framework) which makes Pi non equal to 3.14~ ?
OMNI
There’s another thing that seems to happen a lot in modern physics: the discovery of applications for kinds of mathematics that were previously “pure,” such as matrix algebra or group theory. Are physicists more receptive now than they used to be? Is the time lag less?
Feynman
There never was any time lag. Take Hamilton’s quaternions: The physicists threw away most of this very powerful mathematical system and kept only the part — the, mathematically, almost trivial part — that became vector analysis. But when the whole power of quaternions was needed, for quantum mechanics, Pauli reinvented the system on the spot in a new form. Now, you can look back and say that Pauli’s spin matrices and operators were nothing but Hamilton’s quaternions . . . but even if physicists had kept the system in mind for ninety years, it wouldn’t have made more than a few weeks’ difference.