E.T. Bell (1883-1960), attended Stanford and Columbia, taught at U. of Washington and Cal Tech, was president of the Math. Assoc. of America, and a National Academy of Science member. This gift book is for math lovers.

A renowned mathematician, E.T. Bell formulated the Bell polynomials and the Bell numbers of combinatorics. As the front flap says: “First published in 1937, Men of Mathematics introduced millions of readers to the tenets of mathematics – and the extraordinary, often bizarre, lives of history’s greatest mathematicians. Many people find algebra, calculus, logic and arithmetic intimidating, but E.T. Bell conceived that in order to truly understand the theories behind mathematics, one had to take a creative approach to this complicated subject. In his most controversial and ingenious work, Men of Mathematics, Bell helps readers to comprehend concepts and theorems by describing how modern mathematical theory came to be and who created it.

“With humor and remarkable candor, Bell provides a classic introduction to the craft and history of mathematics. Including the geometry of the Greeks, Newton’s calculus, the laws of probability, the concepts of symbolic logic and more, the book goes beyond ideas and numbers. It presents a unique, biographical approach to the great mathematicians who had a hand in shaping the academics of the future – and who happened to live extraordinary, often unusual, lives. Tracing the development of mathematical thought from ancient times well into the twentieth century, this enduring work’s clear and often witty way of dealing with complex ideas makes this an ideal read whether your interest in mathematics is professional or personal. Men of Mathematics will give you a look beyond the numbers and theories into the minds of their creators.”

When I was taking plane geometry as a sophomore in high school, my teacher let me read from her 1937 copy of this book. She used half the class time to cover plane geometry in nine months. Those who learned quickly he let go at a faster pace. She let me go into trigonometry and solid geometry. She also showed my what to read from this book. I loved it then and now, with much higher math in advancing to a Ph.D. in physics, I was fortunate to receive this book from a good friend. So I reread it cover-to-cover with much joy and a deeper understanding of math concepts beyond those than I had learned in high school under her wonderful part-tutorial teaching style.

The book’s Contents require seven pages, as they include several lines of short phrases of the topics discussed in each of its last 28 chapters, but including them would be too much for a review. Ch 1 is the INTRODUCTION, from which I quote a few lines: “Only some of the conspicuously new things each man did are described, and these have been selected for their originality and importance to modern thought. Of the topics selected for description we may mention the following (among others) as likely to interest the general reader: the modern doctrine of the infinite (Ch 2, 29); the origin of mathematical probability (Ch 5); the concept and importance of a group (Ch 15); the meanings of invariance ((Ch 21); non-Euclidean geometry (Ch 16 and part of 14); the origin of the mathematics of general relativity (last part of Ch 26); properties of the common whole numbers (Ch 4); and their modern generalization (Ch 25); the meaning and usefulness of so-called imaginary numbers (Ch 14, 19); symbolic reasoning (Ch 23). But anyone who wishes to get a glimpse of the power of the mathematical method, especially as applied to science, will be repaid by seeing what the calculus is about (Ch 2, 6).”

To see the “cast of characters” for Ch 2-29, I present each chapter’s title and the mathematicians involved: Ch 2 – Modern Minds in Ancient Bodies – ZENO (5th century BC), EUDOXES (408-355 BC), ARCHIMEDES (287?-212BC); Ch 3 – Gentleman, Soldier, and Mathematician – DESCARTES (1596-1650); Ch 4 – The Prince of Amateurs – FERMAT (1601-1663); Ch 5 – “Greatness and Misery of Man” – PASCAL (1623-1662); Ch 6 – On the Seashore – NEWTON (1642-1727); Ch 7 – Master of All Trades – LEIBNIZ (1646-1716); Ch 8 – Nature or Nurture? – The BERNOULLIS (17th and 18th centuries); Ch 9 – Analysis Incarnate – EULER (1707-1783); Ch 10 – A Lofty Pyramid – LAGRANGE (1736-1816); Ch 11 – From Peasant to Snob - LAPLACE (1749-1827); Ch 12 – Friends of an Emperor – MONGE (1746-1818), FOURIER (1768- 1830); Ch 13 – The Day of Glory – PONCELET (1788-1867); Ch 14 – The Prince of Mathematicians – GAUSS (1777-1855); Ch 15 – Mathematics and Windmills – CAUCHY (1789-1857); Ch 16 – The Copernicus of Geometry – LOBATCHEWSKY (1793-1858); Ch 17 – Genius and Poverty – ABEL (1802-1829); Ch 18 – The Great Algorist – JACOBI (1804-1851); Ch 19 – An Irish Tragedy – HAMILTON (1805-1865); Ch 20 – Genius and Stupidity – GALOIS (1811-1832); Ch 21 – Invariant Twins – SYLVESTER (1814-1897), CAYLEY (1821-1895); Ch 22 – Master and Pupil – WEIERSTRASS (1815-1897), SONYA KOWALEWSKI (1850-1891); Ch 23 – Complete Independence – BOOLE (1815-1864); Ch 24 – The Man, Not the Method – HERMITE (1822-1901); Ch 25 – The Doubter – KRONECKER (1823-1891); Ch 26 – ANIMA CANDIDA – RIEMANN (1826-1866); Ch 27 – Arithmetic the Second – KUMMER (1810-1893), DEDEKIND (1831-1916); Ch 28 – The Last Universalist – POINCARÉ (1854-1912); Ch 29 – Paradise Lost? – CANTOR (1845-1918).

With so many well-known names (to mathematicians and lovers of math) I focus only on some aspects they had in common. First, many of them showed great ability in math at very early ages – they were truly many math prodigies. Second, most needed a sponsor to give them the funds to support themselves in order to focus their great promise on mathematical advances. Third, with only a few exceptions, it was older, well-established mathematicians who recognized great promise in young aspiring mathematicians and helped them, directly or indirectly, obtain wider recognition and a position that allowed them to pursue their mathematical efforts. Fourth, there was, for the most part, recognition of ability and accomplishments, even by mathematicians who were competitors in that field of mathematics. Recommendations by older, well-established mathematicians often led to invitations to become a member of an academic institution or to one (or more) nation’s Academy of Mathematics.

Other than these significant commonalities, there were great differences in the lives of the great mathematicians who E.T. Bell covered. His collection of stories describes both the lives and the mathematical accomplishments of the great mathematicians from ancient times up to his era – the first third of the 20th century. I hope that someone will extend Bell’s style of math history to include more recent mathematicians. I give this book my highest recommendation to those who love math or who wish to become aware of the history of this exceptionally wonderful field to which so many owe so much for the advances in non-mathematical areas of endeavor, such as physics, that depends very heavily on the beautiful language of mathematics.