Books

Books : reviews

Mircea Pitici.
The Best Writing on Mathematics 2010.
Princeton University Press. 2011

This anthology brings together the year’s finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics 2010 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there’s more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City’s traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more.

In addition to presenting the year’s most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where its headed.

Mircea Pitici, ed.
The Best Writing on Mathematics 2011.
Princeton University Press. 2012

rating : 3.5 : worth reading
review : 25 December 2013

This anthology brings together the year’s finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schatt-schneider identifies some of the mathematical inspirations of M. C. Escher’s art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more.

In addition to presenting the year’s most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed physicist and mathematician Freeman Dyson. This book belongs on the shelf of anyone interested in where math has taken us—and where its headed.

This is a collection of short pieces covering a wide range of mathematical relevance: about mathematical topics themselves, mathematical art, teaching mathematics, and philosophy of mathematics. The writing is of uniformly high standard: I read and enjoyed even the essays where I didn’t think that I was particularly interested in the topic.

Contents

Freeman J. Dyson. Recreational Mathematics. 2012
Underwood Dudley. What Is Mathematics For?. 2010
Despite the hype, and the attempt to make problems "realistic", most people will not use the specific maths they learn at school in their jobs; mathematics teaches people to reason.
Dana Mackenzie. A Tisket, a Tasket, an Apollonian Gasket. 2010
Lots of interesting things about Apollonian Gaskets, and packing.
Rik van Grol. The Quest for Godís Number. 2010
Solving Rubik's Cube in the minimum number of steps.
Andrew Schultz. Meta-morphism: From Graduate Student to Networked Mathematician. 2010
Good advice for new graduate students, including how to understand seminars, and how to network.
Melvyn B. Nathanson. One, Two, Many: Individuality and Collectivity in Mathematics. 2011
Solitary mathematicians produce better "magic" than massive collaborations.
Martin Campbell-Kelly. Reflections on the Decline of Mathematical Tables. 2010
Ah, the irony: computers were invented specifically to ease the production of mathematical tables, yet have now made them obsolete.
Reuben Hersh. Under-Represented Then Over-Represented: A Memoir of Jews in American Mathematics. 2010
WWII made anti-Semitism unfashionable in the USA, increasing the number of Jewish mathematicians.
David J. Hand. Did Over-Reliance on Mathematical Models for Risk Assessment Create the Financial Crisis?. 2009
The problem is with blindly applying mathematical results out of context, not with the models per se.
Jordan Ellenberg. Fill in the Blanks: Using Math to Turn Lo-Res Datasets into Hi-Res Samples. 2010
Using "compressed sensing" to reconstruct images: it works because images have structure.
Peter J. Denning. The Great Principles of Computing. 2010
Using computational thinking in the natural sciences.
James Hamlin, Carlo H. Sequin. Computer Generation of Ribbed Sculptures. 2010
Capturing existing ribbed sculptures mathematically, and then analysing and varying them.
Barry A. Cipra. Lorenz System Offers Manifold Possibilities for Art. 2010
Artistic representations of the Lorenz manifold: from stainless steel to crochet.
Doris Schattschneider. The Mathematical Side of M. C. Escher. 2010
Escher wasn't a trained mathematician, but his exhaustive analyses influenced mathematicians like Coxeter, and are used to teach mathematical concepts.
Helaman Ferguson, Claire Ferguson. Celebrating Mathematics in Stone and Bronze. 2010
Big, heavy mathematics.
John (2) Mason. Mathematics Education: Theory, Practice, and Memories over 50 Years. 2010
A memoir.
Douglas Fisher, Nancy Frey, Heather Anderson. Thinking and Comprehending in the Mathematics Classroom. 2010
Teaching how to solve mathematical problems by "thinking out loud" and "modelling" the solution approach.
Francis Edward Su. Teaching Research: Encouraging Discoveries. 2010
Teaching how to ask good questions, and other advice.
Alan H. Schoenfeld. Reflections of an Accidental Theorist. 2010
Theories of teaching mathematics.
Hans Niels Jahnke. The Conjoint Origin of Proof and Theoretical Physics. 2010
Why did the Greeks invent mathematical proof?
Ian Hacking. What Makes Mathematics Mathematics?. 2010
Mathematics has such a wide range of subject matter: what, if anything, is the underlying unity?
Feng Ye. What Anti-realism in Philosophy of Mathematics Must Offer. 2010
Anti-realists state that mathematical ideals to not "exist"; since mathematicians are not just acting randomly, these philosophers must provide an explanation of what does actually exist.
Ivan M. Havel. Seeing Numbers. 2009
Mathematical savants seem to be using some kind of direct visual represenation of numbers; what might it be?
Ioan James. Autism and Mathematical Talent. 2010
Several famous mathematicians may have had Asperger's syndrome.
Chris J. Budd, Rob Eastaway. How Much Math Is Too Much Math?. 2010
On giving talks about mathematics to the general public.
Marianne Freiberger. Hidden Dimensions. 2010
Calabi-Yau manifolds and string theory.
Erica Klarreich. Playing with Matches. 2010
How to match doctors to hospitals, under the constraint to the "two-body problem".

Mircea Pitici.
The Best Writing on Mathematics 2012.
Princeton University Press. 2013

Mircea Pitici.
The Best Writing on Mathematics 2013.
Princeton University Press. 2014

This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more.

In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematical physicist Roger Penrose and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Mircea Pitici.
The Best Writing on Mathematics 2014.
Princeton University Press. 2015

This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2014 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here John Conway presents examples of arithmetical statements that are almost certainly true but likely unprovable; Carlo Séquin explores, compares, and illustrates distinct types of one-sided surfaces known as Klein bottles; Keith Devlin asks what makes a video game good for learning mathematics and shows why many games fall short of that goal; Jordan Ellenberg reports on a recent breakthrough in the study of prime numbers; Stephen Pollard argues that mathematical practice, thinking, and experience transcend the utilitarian value of mathematics; and much, much more.