Open problems in mathematical physics

TL;DR

This paper compiles a list of open problems across various fields in mathematical physics, highlighting current challenges in classical general relativity, cosmology, and quantum physics to guide future research efforts.

Contribution

It provides a comprehensive overview of unresolved questions in mathematical physics, inspired by recent fundamental questions in physics, to inform and motivate ongoing research.

Findings

Identifies key open problems in classical general relativity.

Highlights unresolved issues in cosmology and quantum physics.

Serves as a roadmap for future research directions in mathematical physics.

Abstract

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment. But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.