Philosophy of science:
- How to think about science. A series of broadcasts from the Canadian Broadcasting Corporation. Though I don’t agree with all of them, they are all interesting, except for the one about Rupert Sheldrake, who was just a crank.
- David Hume, An Enquiry Concerning Human Understanding. A clear exposition of the basic problem of connecting pure reason to reality.
- Robert Sokolowski, Introduction to Phenomenology. A condensation of the important ideas of the philosophical movement of phenomenology.
- G. Polya, How to Solve It: A New Aspect of Mathematical Method. One of the few books written on how to learn and teach how to solve mathematics problems. Simple language, almost deceptively so, but horrendously accurate.
- E.W. Dijkstra and C.S. Scholten, Predicate Calculus and Program Semantics. Among the first texts espousing calculational mathematics, that is, making logic as easy to use as the algebra of real numbers we all learn in school, and then calculating proofs, theorems, and functions as we would numbers. This is an elegant, streamlined, and terse exposition, with no exercises, but beautifully written. See also the EWD archive.
- R. Boute, Formal Logic for Practical Use (PDF) is a different notation for calculational logic, and an actual textbook. More material using this notation is available from Funmath.
- R.P. Feynman, The Feynman Lectures on Physics. The most beautiful introductory lectures ever given on physics for advanced practitioners of the field. In particular, volume 3 on quantum mechanics is among the most gorgeous expositions of this field ever given, on a par with Schwinger and Dirac.
- Landau and Lifshitz, Course of Theoretical Physics. Ten volumes of terse exposition and insight. As usual, the clearest derivation of anything discussed in Landau and Lifshitz is in Landau and Lifshitz, with the exception of thermodynamics.
- G.N. Gatsopoulos and J.H. Keenan, Principles of General Thermodynamics. The only clear exposition of this subject I am aware of, but the book uses Imperial units for some incomprehensible reason.
- G.J. Sussman and J. Wisdom, Structure and Interpretation of Classical Mechanics. An exposition of Lagrangian and Hamiltonian mechanics focused on modern tools and a formulation sufficiently unambiguous to be programmed into a computer without human interpretation.
- P.G. de Gennes, F. Brochard-Wyart, D. Quéré, Capillarity and Wetting Phenomenon. A gorgeous volume of surface tension and the dynamics of boundaries of liquids, including most of the information you need to actually use it for experiments sprinkled into the text.
- P.J. Bickel, K.A. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I (2nd Ed). A gorgeous, clear exposition of most of what you need to know about statistics with real motivation, derivation, and understanding.
- J.C. Kiefer, Introduction to Statistical Inference. A publication of lecture notes by the man who created randomized statistical procedures. The notation is Baroque, the exercises unrevealing, but the first four chapters are among the clearest expositions of what statistics is all about you will find anywhere.
- J.W. Tukey, Exploratory Data Analysis. A book about what comes before formal regression or hypothesis testing, when you are faced with raw data. A life changing book, with amusing and dated rants about different kinds of graph paper.
Biographies and Histories:
- Erwin Chargaff, Heraclitean Fire: Sketches from a Life Before Nature. A beautifully written autobiography by an idiosyncratic but very cultured biochemist.