Open problems 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.

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• Undecidability of the Spectral Gap (full version)
• Light, the universe, and everything -- 12 Herculean tasks for quantum cowboys and black diamond skiers
• The sounds of science a symphony for many instruments and voices part II
• Some Remarks on Wang-Yau Quasi-Local Mass
• Strong field behavior of Wang-Yau Quasi-local energy