Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.
Please help promote PhysicsOverflow ads elsewhere if you like it.
PO is now at the Physics Department of Bielefeld University!
New printer friendly PO pages!
Migration to Bielefeld University was successful!
Please vote for this year's PhysicsOverflow ads!
Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!
... see more
(propose a free ad)
I'm curious as to what sorts of physical problems to which we don't have an answer, because we haven't developed the right mathematics yet (or advanced-enough mathematics).
Related to this question on the Math StackExchange: In what ways has physics spurred the invention of new mathematical tools?
Arthur Suvorov gives a nice comment, I am just going to give a list of a few specific physical problems I can think of from the top of my head.
Lots of real world physics problems contain a huge number of variables and therefore have very complicated equations describing their associated dynamics. An example of this is non-linear partial differential equations, which are notoriously difficult to solve. As an example, take the Navier-Stokes equations. These are real physics equations which describe the motions of fluids and their physical characteristics.
Nobody has yet solved the problem concerning global existence and uniqueness of these equations, and in fact it is one of the millenium prize problems owing to its difficulty. Relating to your question, we effectively have an equation describing a physics phenomena for which the mathematical tools are not yet sufficient to prove is well defined and as such it is difficult to talk about how precise the extracted physics is regarding the solution of this equation.
user contributions licensed under cc by-sa 3.0 with attribution required