First a gloss to the way I understand the question : "should everyone read" - I mean that every serious researcher (in theoretical physics) has to refer as to an ultimate resource in searching for truth in natural sciences.
I am aware the fact, that many clever adepts in theoretical physics ignore the following milestones, nevertheless If they hadn't, the landscape of modern (theoretical) physics would have been much more optimistic.
- Astronomia nova - Johannes Kepler (1609)
- Philosophiæ Naturalis Principia Mathematica - Isaac Newton (1687)
- Über die Hypothesen welche der Geometrie zu Grunde liegen - Bernhard Riemann (1854)
These papers/books are indispensable, since no one has mentioned them yet and for their incomparable impact on sciences, more words are worthless.
To mention a modern review paper with many interesting references therein
I could add :
PDE as a Unified Subject by Sergiu Klainerman.
An essay on partial differential equations written by a leading expert in the field, I strongly recommend to anyone attemping to know more on the subject as well as to those who would like to get a grasp of interactions between Mathematics and Physics.