very good. fascinating romp through the history of math and the great mathematicians.

makes me kinda wish I never punked out on math

"not for the sake of any definite answers [...] but rather for the sake of the questions themselves"

A quick read for anyone familiar with the history of mathematics, but a good overview. Gets a little thick towards the end as Livio addresses statistics. Livio recounts in the first chapter that Roger Penrose observed: “First, the world of physical reality seems to obey laws that actually reside in the world of mathematical forms. This was the puzzle that left Einstein perplexed”

... to which I say that's a non starter. Would we not develop the mathematics that describes the physical world? Thus the physical world HAS to obey laws that reside in the math properties we discover and math concepts we invent. Sure, we can invent other mathematics, but they are not useful, therefore are rarely more than a diversion. Had we existed in a universe that conformed to different laws, we'd have invented/discovered different mathematics and then THAT physical world would conform to THOSE mathematical forms.

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The title, which for quite a while made me plan to skip this volume despite the author's fine track record, is a stupid way of asking the otherwise excellent question, à la Wigner, of why mathematics is so well suited to the description of nature. More than half the book covers the same ground as scads of other math/physics popularizations, and it is not entirely free of passages referring to theology. Regarding platonism, it ends up saying that math is both invented *and* discovered (seeing that, e.g., it includes both definitions *and* theorems).

Armonie musicali e patrimonio genetico? Luce delle stelle
e mercato azionario? Tutti ambiti di studio complessi, ma
spiegabili con poche semplici equazioni. Questo spiega
perchè la matematica è così efficace nel descrivere la
natura. Mario Livio ripercorre con vivace curiosità le
avventure, i pensieri e gli accesi dibattiti delle grandi menti
del passato: geni che non a caso furono insieme matematici
e mistici, astronomi, fisici, sociologi e alchimisti.

Eugene Wigner, a Nobel laureate in physics, wondered about the “unreasonable effectiveness of mathematics” in explaining the nature of the universe. Mario Livio, in Is God a Mathematician?, demonstrates how unreasonably effective math (or as the British say, “maths”) is [or is it, “are”?]. Livio shows that Newton’s inverse square law of gravitation has proved to be correct to better than one part in a million, while the measurements available to him were correct only to 4%. Even more extraordinary is the prediction of the magnetic moment of the electron, which the equations of quantum electrodynamics predict with the accuracy of 11 decimal places!!

Livio points out an even more extraordinary power of pure math when he shows how concepts explored by mathematicians with absolutely no application in mind have turned out decades (and sometimes centuries) later to be unexpected solutions to problems grounded in physical reality! For example, “group theory,” developed by Evariste Galois 1832 to determine the solvability of algebraic equations has become the language used by physicists, linguists, and even anthropologists to describe all the symmetries of the world. And a non-Euclidian geometry outlined by Riemann in 1854 turned out to be the tool Einstein needed 60 years later in his general theory of relativity.

Physicist Roger Penrose identified three different kinds of “worlds”: (1) the world of our conscious perception; (2) the physical world; and (3) the Platonic world of mathematical forms. These in turn produce three enigmas: (1) why does the world of physical reality seem to obey the rules of the Platonic forms; (2) how do perceiving minds arise from the physical world; and (3) how did those minds gain access to the Platonic world by discovering or creating and articulating abstract mathematical forms and concepts.

Livio devotes the book to the question that has bedeviled philosophers from Plato to the present: whether the mathematical world we perceive is a preexisting entity that is “discovered” by humans or whether, instead, it is “created” from scratch by mathematicians. Before attempting to answer the question, he takes the reader on a quick (200 or so pages) tour of the history of the great mathematicians. He explores the relationship between math and pure logic, illustrating Russell’s paradox and Godel’s incompleteness theorem.
He treats us to lively descriptions of the biographies and work of many mathematicians from Pythagoras to Godel, ranking Archimedes, Newton, and Gauss as the three greatest. [He also seems to hold rather fond opinions of Galileo, Russell, and Godel.] One suspects that the real purpose of the book is to acquaint the general public with the history of math rather than to answer the deeply profound question of its very nature.

In finally proposing a solution to Wigner’s enigma of whether math is created or discovered, Livio concludes that math is partly discovered and partly created. Since our brains evolved to deal with the physical world, it should not be surprising that they developed a language (math) well suited for that purpose. Mathematical tools were not chosen arbitrarily, but on the basis of their ability to predict correctly the results of the experiments at hand. Livio argues that some math is “created”: “…through a burning curiosity, stubborn persistence, creative imagination, and fierce determination, humans were able to find the relevant mathematical formalisms for modeling a large number of physical phenomena.” On the other hand, for math to be “passively” effective (i.e., solve physical problems that had not been anticipated when the math was first articulated), it was essential that it have eternal validity, and those aspects of math have been “discovered.”

In all, this is a clearly written, fascinating book that is accessible to non-mathematicians.

(JAB) ( )