Weird Math

January 15, 2018
Darling (Equations of Eternity), an astronomer and science writer, teams up with a student of his, teenage math prodigy Banerjee, in this enjoyable, wide-ranging volume of essays on such diverse mathematical topics as computing, music theory, prime numbers, and paradoxes. Even math-averse readers should find something to pique their interest here. The authors begin by covering how math is used to visualize multiple dimensions in such fields as popular fiction, modern art, and physics. They move on with a brief discussion of the statistics of random chance that shows how to figure out the odds of winning a lottery as well as understand quantum mechanics. In the most fascinating chapters, student and teacher explore Turing machines and computing, how to build a great chess-playing computer, and the math of really large numbers. They keep their discussion equation-free while delivering thoughtful and accessible explanations with a fair bit of history and many stimulating real world examples. “Mathematics,” Darling and Banerjee write, “is an endless adventure into the weirdest and wildest places ever countenanced by the human intellect”—and there is plenty here to convince even the most skeptical reader that they have a good point.

February 15, 2018
A science writer and astronomer and his student, a teen math prodigy, join forces to elucidate fields of math they find weird.Darling (Mayday!: A History of Flight Through its Martyrs, Oddballs, and Daredevils, 2015, etc.) and Banerjee are struck by how some of the most abstruse findings from math turn out to have practical applications in quantum physics or computer science--or lead to concepts like orders of infinity or yield unexpected patterns of numbers or figures. One could argue that these findings are neither weird nor magical but the inexorable results of logic and the permissible rules of operation of mathematical systems by imaginative thinkers. As subjects, the authors examine selected fields of pure, as opposed to applied, math. The first chapter takes on the idea of seeing in the fourth dimension, with descriptions of the 4-D extension of the cube called a tesseract. There follows a chapter on probability emphasizing non-intuitive findings and then one on fractals, a field that deals with curves that have fractional dimensions. This idea grew out of a paper by the field's inventor, Benoit Mandelbrot, that asked, "how long is the coast of Britain?" Thereafter, the authors' choices are more self-indulgent, with chapters on chess and music, which will be lost on readers who are not game players or familiar with harmonics. Other areas concern computer science and number theory emphasizing primes. There is a particularly wearisome chapter on competitions to generate large and larger numbers, a sport favored by Banerjee. The text concludes with chapters on topology, set theory, infinity, and the foundations of mathematics. This is difficult material, and readers should be familiar with logical paradoxes, the meaning of "proof," and notions of consistency and completeness of axiomatic systems as well as the work Godel and others in establishing the incompleteness of any mathematical system complex enough to embody arithmetic.The authors offer some beguiling insights on what math is about and how it has evolved but no royal road to easy understanding.

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March 1, 2018
Readers seeking nifty facts to wow others won't be disappointed in this unusual presentation by teen math genius Banerjee and his teacher, science writer Darling. Nor will math whizzes, as there is no dumbing down here, with each chapter building to successfully challenging skill levels. One example of the more accessible levels offers a discussion of how ordinary computers, even the Turing Machine conceived in the 1930s, if given enough time, could solve anything a quantum computer can. The chapter on prime numbers is a standout, as the authors illuminate the ongoing inquiry into the Ulam spiral, which established a highly irregular pattern for the occurrence of primes, and the fact that thinkers since the classic Greeks have suspected that a firmer, and probably more useful, understanding of the distribution of such a key building block is tantalizingly close. Another chapter reveals that only people who missed the Large Number Championship at MIT in Boston in 2007 could claim that mathematicians aren't funny. Even the number-challenged will emerge with a stronger appreciation of math.(Reprinted with permission of Booklist, copyright 2018, American Library Association.)