Dude, Can You Count?

Dude, Can You Count? is a 25-chapter polemic against, among other things, the state of mathematical education in the US, although many of the complaints will be familiar on this side of the pond. The author is a mathematician with an eminent career in areas including elasticity, integral equations and non-linear problems, and one who will be familiar to many in applied mathematics.

The book is a series of discursive encounters at US universities between an academic narrator and the proverbial "man from Mars" - actually a Ganymedean - called J.J. Moon. Each chapter, or Scam (Stories, challenges and adventures in mathematics), is a forthright conversation about a specific subject, including a mixture of mathematical diversions, jokes and challenges.

The message may appeal to schoolteachers and academic mathematicians looking for confirmation of their educational views. The style may appeal most to gifted sixth formers and early-year undergraduates. However, anyone with an interest and some experience in mathematics could also dip in and out.

Subjects dealt with include "The public school system" (in the US sense of "public"), "Mathematical education", "Political correctness", "TV advertising", "Percentages and living on debt", "Averages and buying cars", "The criminal legal system", "Academic politics", "Mathematicians versus engineers" and "The virtues of mathematics".

The questions posed at the start of the chapter are a mixture of interesting problems and theorems (some of them are also jokes). "Notes after the meeting" provides solutions to the mathematical challenges. The "Word to the wise" section at the end of each chapter provides guidance on the avoidance of mathematical errors commonly made by pupils at secondary school, or by early-year undergraduates. There is plenty of good mathematical source material for teachers and first-year mathematics lecturers to use.

Some of the "jokes" are rather (too) old, such as the politically incorrect "proof" that girls are evil and the demonstration that "the less one knows the more one is paid". Their inclusion gives the faint air of a Benny Hill rerun. The author suggests that readers may disagree with, or be offended by, some of the statements. At least one technical and one political statement had me squirming.

In Scam 23, engineers are criticised for not checking whether a series representation of a function is convergent before using it. But for all the perceived mathematical faults of engineers, the addiction of mathematicians to often slowly convergent series held back mathematics for more than a century. Divergent expansions litter the physical sciences. The issue is not whether a series is convergent, but whether one can estimate the error of a truncated approximation and so decide if it is a useful approximation in the context - to the engineer's relief, quite often it is! Even Newton summed series beyond their radius of convergence, and planes still use his mechanics to fly (unless volcanic ash and the more fundamental Universal Law of Health and Safety grounds them).

Christian Constanda presents Margaret Thatcher as a suitable example of feminism who "took a country left by her male predecessors in a sorry state and turned it around ... whether you liked the colour of her politics or not". For younger or non-UK readers, the author omits to mention that under Thatcher, British universities suffered a prolonged period of funding cuts and, as a result of her free-market approach, the UK became over-reliant on the financial sector. This is a legacy that is about to have potentially dire consequences for the very subject the author is trying to promote.

Appeasement followed, however, as I read the epilogue: "When the book is published, expect all kinds of reactions to it, from full agreement to fierce criticism ... My objective is simply to make people aware of the issues discussed ... (and) form their own opinions."

Last summer, some were shocked by soundbites such as "healthcare is a privilege, not a right" in the US debates on President Barack Obama's healthcare reforms. More surprising to British citizens, though, was that an open discussion of the existence of limits to the funding of healthcare was even taking place. This is a debate that, even in the current economic situation, no UK politician has been prepared to engage in publicly. Constanda's book sits firmly in the tradition of open debate that is perhaps lacking in Britain.

Hence, if you can come to grips with the style and are prepared to disagree in some parts, there is a definite and valid point to this book, underpinned by a solid mathematical base containing plenty of entertaining examples of interest - as well as some inappropriate jokes for more private moments.