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Popular Lectures on Mathematical Logic

Hao Wang
Dover Publications
Publication Date: 
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Allen Stenger
, on

This is an introductory work that goes broad and fairly deep; it is much more detailed than a survey, but does not have enough detail to be a text. The present volume is a Dover 1993 unaltered reprint of the 1981 edition from Van Nostrand Reinhold, and includes an 8-page postscript from 1993 that briefly covers progress since 1981 (mostly then-unsolved problems that have since been solved).

Hao Wang (1921–1995) was a China-born US mathematician who received his doctorate at Harvard in 1948 and after that worked primarily in Europe and the US, with occasional trips back to China. The present volume is reworked from a set of lectures he gave in 1977 at the Chinese Academy of Science, and appeared simultaneously in Chinese translation. Wang was one of the first to write computer programs for automated proving of logical statements, including all the propositional logic from Principia Mathematica. He was also one of the first expositors of Kurt Gödel’s work.

The book contains material not just on pure mathematical logic but also a lot on automated proving, set theory, completeness, the continuum hypothesis, decidability, computability, and the P vs. NP question. There are three appendices of material that is farther outside the main topics; the treatment of these is less dense and more elementary. It’s not a book for laymen; I think the “Popular” in the title just means that the lectures were open to the public.

Despite its age the book is still fairly up-to-date. I think it works best for browsing; read the parts that look interesting and skip the rest.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis.


1. One Hundred Years of Mathematical Logic

2. Formalization and the Axiomatic Method

3. Computers

4. Problems and Solutions

5. First Order Logic

6. Computation: Theoretical and Practicable

7. How Many Points on the Line?

8. Unifications and Diversifications

Appendix A. Dominoes and the Infinity Lemma

Appendix B. Algorithms and Machines

Appendix C. Abstract Machines

Postscript (1993)