In the Princeton Companion to Mathematics one reads that even pure mathematicians should know some theoretical physics and applied mathematics. What are some well-organized comprehensive companions to theoretical physics for working mathematicians? I have heard of Armin Wachter and Henning Hoeber's, but I don't know if it is rigorous enough (i.e., for example, there are enough proofs of the theorem given).



Companion to theoretical physics for working mathematicians
If you allow such a comprehensive reference to re-introduce basic mathematics, then either as a layman or a working mathematician your prayers are answered by the following (he even prefaces by saying that his intended layman-audience must have some mathematical sophistication): 



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> **The Road to Reality: A Complete Guide to the Laws of the Universe**, by Roger Penrose
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Now let's try to break down the subjects.


Classical Mechanics:  

1) **Mathematical Methods of Classical Mechanics**, by Arnold  

2) **A Mathematical Introduction to Fluid Mechanics**, by Chorin-Marsden


Quantum Mechanics:  

1) **Mathematical Foundations of Quantum Mechanics**, by Mackey  

2) **The Theory of Groups and Quantum Mechanics**, by Weyl


General Relativity:  

1) **General Relativity for Mathematicians**, by Sachs-Wu  

2) **The Large Scale Structure of Space-Time**, by Hawking-Ellis


Electrodynamics:  

1) **Electromagnetic Theory and Computation: A Topological Approach**, by Gross-Kotiuga  

2) **On the Mathematical Foundations of Electrical Circuit Theory**, by Smale  

3) This is a plug for Gauge theory:  

3a) **On Some Recent Developments in Yang-Mills Theory**, by Bott  

3b) **On Some Recent Interactions Between Mathematics and Physics**, by Bott  

3c) **Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields**, by Wu-Yang  

3d) **From Superconductors and Four-Manifolds to Weak Interactions**, by Witten


Standard Model:  

**The Algebra of Grand Unified Theories**, by Baez-Huerta


Quantum Field Theory and String Theory:  

1) **Quantum Physics: A Functional Integral Point of View**, by Jaffe-Glimm  

2) **Geometry and Quantum Field Theory**, 1994 IAS lectures  

3) **Quantum Fields and Strings: A Course for Mathematicians**, 1996 IAS lectures


