Experimental Blog #95

Comments on the books "A Strange Wilderness" - The Lives of the Great Mathematicians by Amir D. Aczel and "Is God a Mathematician?" by Mario Livio

This book begins over 2500 years ago in Ancient Greece and Alexandria describing the lives and works of Thales, Pythagoras, Archimedes, Euclid, and others, who were especially outstanding in geometry. The author, Amir Aczel, then provides some very interesting information on the mathematical accomplishments of India, Arabia, and Persia from around the 5th to the 12th centuries AD, who were very inventive, or original, in algebra and trigonometry. A few pages contain some information on the Chinese mathematical achievements from about the 3rd century BCE to the 15th century.

The author's attention then goes back to Italy and the rest of Europe beginning in the 12th century and culminating in the "great heresy" of Johannes Kepler, Galileo Galilei, and others of "heliocentrism".

Although the author describes many Italian, French, German, and other European mathematicians and their achievements, he seems to concentrate on Rene Descartes, Gottfreid Leibniz, Isaac Newton, Evariste Galois{who died at 20 years of age in a duel}, Georg Cantor{who died in a mental hospital, where he had often been a patient}, and Nicolas Bourbaki and his group who published papers and books even though Nicolas Bourbaki was a ficticious person who never lived.

The whole second book, "Is God a Mathematician", revolves around the never ending debate about whether mathematics is a science of "discovery" of the "absolute truth of the universe" that exists independently outside the human mind, which is often called the "Platonic" point of view; or whether mathematics is only an "invention", or creation, of human imagination, and would, and could not exist without the human brain.

Among much other information the author points out how virtually timeless mathematics seems to be; that is, it rarely really changes over time. For instance, Euclid's geometry is as true and useful today as it was 2300 years ago. Mario Livio also describes how so many things are not only explained, but have been, and can be predicted by mathematics to extraordinary degrees of accuracy.

By contrast, however, the science of biology is limited to our planet Earth, to an infinitesmal place in the universe with no known relationships to anywhere else. Mathematics seems to apply consistently and everywhere in space and time.