Opinion 140: Zvi Artstein's "Mathematics and the Real World" is Destined to become a Classic

By Doron Zeilberger

Written: Oct. 7, 2014

The true mark of a masterpiece is that it makes you think, regardless of the amount of new facts that it teaches you. I just finished reading Zvi Artstein's new book Mathematics and the Real World, the Remarkable Role of Evolution in the Making of Mathematics, and it sure made me think!

I already "knew" most of the content of Artstein's book, but I still could not lay it down. It is a real page-turner! The engaging, often humorous, way that he presents the highlights of current mathematical knowledge, and attitudes, should appeal to a very wide audience, from the "educated layman" (even those who dislike math and science) all the way to Abel and Nobel prize winners. He touches on so many subjects, even social science, economics, and finance, yet he starts at the very beginning, with the cave-dwellers, and in fact even "lower", with mathematical abilities of animals.

But the main significance of this amazing one-in-a-generation summing-up of current mathematical knowledge (the Davis-Hersh "Mathematical Experience", ca. 1980, comes to mind, and also Poincaré's "Science and Method", ca. 1910) is in finally explaining Barbie's complaint

Math is so hard
and not only to "bimbos" like Barbie, but even to nerds like us. Precise mathematical thinking is so unnatural, since evolution did not prepare us to tackle it, and it is amazing that in spite of this fact, we went quite a long way.

But if you take Artstein's message seriously, it could have far-reaching implications, on how to improve our mathematical teaching, to both future mathematicians, and, even more importantly, future scientists (both physical and social), and even Joe the plumber! I found the concluding chapter, on education, particularly insightful, and it gave me hope that if we take Artstein's lessons seriously, we have a chance to teach math naturally, and win over the 99 percent of humankind who (openly!) hate math.

So let's get to work! As a modest first step, I figured out much better ways to prove that the square-root of 2 is irrational. I also have some remarks and short errata.

I am looking forward to reading this masterpiece at least two more times!

Opinions of Doron Zeilberger