Marvellous mathematics

The Best Writing on Mathematics 2012, Mircea Pitici (Ed.), Princeton University Press, Pp 288, $19.95

Dr R Balashankar

THIRD year into publication, The Best Writing on Mathematics gets better and better. The 2012 volume, edited (again) by Mircea Pitici has Foreword by David Mumford, the renowned American mathematician. With twenty-four essays/articles, it shows not just the growing popularity of mathematics but also the increased writings on them. As editor Pitici said he had to choose from a much larger material available.

Some of the most catchy titles are: ‘Mathematics Meets Photography: The Viewable Sphere’ by David Swart and Bruce Torrence, ‘Dancing Mathematics and the Mathematics of Dance’ Sarah-Marie Belcastro and Karl Schaffer, and ‘Mating, Dating, and mathematics: It’s All in the Game’ by Mark Colyvan.

There are quite a few essays on mathematics education: ‘How to Be a Good Teacher Is an Undecidable Problem’ by Erica Flapan, ‘Variables in Mathematics Education’ by Susanna S Epp, ‘Bottom Line on Mathematics Education’ by David Mumford and Sol Garfunkel, ‘Mathematics Teachers’ Subtle, Complex Disciplinary Knowledge’ by Brent Davis, ‘How Your Philosophy of Mathematics Impacts Your Teaching’ by Bonnie Gold and ‘A Continuous Path from High Schol Calculus to University Analysis’ by Timothy Gowers, who has also written on ‘Is Mathematics Discovered or Invented.’

While David Swart and Bruce Torrence explain how maths is related to dance through a series of angles and views, Sarah-Marie Belcastro and Karl Schaffer demonstrate through diagrams and sketches the connection between maths and dance, beyond the obvious keeping count of steps. Both are fascinating. Mark Colyvan asserts that the reason we love, marry and stay married has less to do with love and more to do with mathematics, falling into a mathematical theory known as game theory.
Ian Hacking in his interesting essay ‘Why Is There Philosophy of Mathematics at All?’ says “Mathematics is the only specialist branch of human knowledge that has consistently obsessed many dead great men in the Western philosophical canon. Not all, for sure, but Plato, Descartes, Leibniz, Kant, Husserl, and Wittgenstein form a daunting array. And that list omits the angry skeptics about the significance of mathematical knowledge, such as Berkeley and Mill, and the logicians, such as Aristotle and Russell.”

In the Foreword, David Mumford recounts how earlier mathematicians, (pure and applied), physicists (theoretical and experimental) moved from one field to another seamlessly. But now these have become rigid areas. “It will be difficult to fully repair the professional split between pure and applied mathematics and between mathematics and physics. One reason for this difficulty is that each academic field has grown so much, so that professionals have limited time to read work outside their specialties.” If we build from concrete to the abstract, we would be able to carry the audience and readers with us he says, adding this series is the best way to do it.

Each of the essays is interesting, readable, and purposeful. It is disappointing that there is no contribution from India, especially as we celebrated this year as the centenary of the genius Ramanujam. The contributors are some of the best brains from universities all over world.

|Editor Pitici says, “By editing this annual series, I stand for the wide dissemination of insightful writings that touch on any aspect related to mathematics. I aim to diminish the gap between mathematics professional and the general public and to give exposure to a substantial literature that is not currently used systematically in scholarly settings. Along the way, I hope to weaken or even to undermine some of the barriers that stand between mathematics and its pedagogy, history, and philosophy, thus alleviating the strains of hyperspecialization and offering opportunities for connection and collaboration among people involved with different aspects of mathematics.”
Indeed Pitici has contributed to diminishing the distance between the high academia and the ordinary maths lover. Pitici is a PhD candidate in mathematics education at Cornell University and teaches math. He has also edited the 2010 and 2011 editions of this series.
(Princeton University Press, 41, William Street, Princeton, New Jersey 08540)