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50 Visions of Mathematics

Sam Parc, editor
Oxford University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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The title would be a bit more accurate if it were to be “50 Brief Visions of Mathematics”: the longest “vision” is six pages long, with most being only 2 to 4 pages. The breadth of coverage is extensive, from brief biographies of some of the major mathematicians of the twentieth century to humor, recreational mathematics, major technical problems and their mathematical solutions and some mathematical philosophy.

While most amateur and professional mathematicians will be familiar with the majority of topics, the editor is to be commended for including some articles describing people and problems that are not as well known. I was unfamiliar with Sir James Lighthill, for example, yet he is described as arguably the preeminent applied mathematician of his generation.

The authors and editors make the excellent decision to include equations when they are needed to explain the topic, yet even with that nearly all of the visions will be clear and understandable to readers with a high school mathematics background. Crisp and understandable diagrams are also used to great effectiveness. The four page entry “Conic Section Hide and Seek” is simultaneously the best simple introduction to how GPS satellites work and a response to the student that says, “Why do we need to study conic sections?” In clear language and diagrams the reader learns the basics of how GPS works and why three satellite signals are needed.

There are many uses for this book; one of the best that I can think of is in high school mathematics classes. The instructor could assign most of these visions as a homework reading and then use it as the basis for a class discussion that the students would find interesting. It beats the sawdust out of having to constantly answer the question, “Why do we need to learn this math stuff?” Or equivalently, “What’s the use of this?”

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

1. What's the problem with mathematics?, David Acheson
2. The mathematics of messages, Alan J. Aw
3. Decathlon: The art of scoring points, John D. Barrow
4. Queen Dido and the mathematics of the extreme, Greg Bason
5. Can strings tie things together?, David Berman
6. Grooves and knuckleballs, Ken Bray
7. Pigs didn't fly but swine flu, Ellen Brooks-Pollock and Ken Eames
8. Bill Tutte: Unsung Bletchley hero, Chris Budd
9. What's the use of a quadratic equation?, Chris Budd and Chris Sangwin
10. Tony Hilton Royle Skyrme, Alan Champneys
11. The mathematics of obesity, Carson C. Chow
12. It's a small world really, Tony Crilly
13. How does mathematics help at a murder scene?, Graham Divall
14. Mathematics: The language of the universe, Marcus du Sautoy
15. The troublesome geometry of CAT scanning, Richard Elwes
16. The mathematics of sports gambling, Alistair Fitt
Pythagoras's Theorem: a2
17. A conversation with Freeman Dyson, Marianne Freiberger and Rachel Thomas
18. A glass of bubbly, Paul Glendinning
19. The influenza virus: It's all in the packaging, Julia Gog
20. Mathematicians at the movies: Sherlock Holmes vs Professor Moriarty, Derek Moulton and Alain Goriely
21. Solving the Bristol bridge problem, Thilo Gross
22. All ravens are black: Puzzles and paradoxes in probability and statistics, David Hand
23. The Tower of Hanoi: Where mathematics meets psychology, Andreas Hinz and Marianne Freiberger
24. Career: A sample path, Philip Holmes
25. Sweets in the jar, Steve Humble
26. Mary Cartwright, Lisa Jardine
27. The fallibility of mathematics, Adam Jasko
28. Anecdotes of Dr Barrow, Tom Korner
29. Finding Apollo, Adam Kucharski
30. The golden ratio in astronomy and astrophysics, Mario Livio
31. The high-power hypar, Peter Lynch
32. This is not a carrot: Paraconsistent mathematics, Maarten McKubre-Jordens
33. The mystery of Groombridge Place, Alexander Masters and Simon Norton
Pythagoras's Theorem: b2
34. Mysterious number 6174, Yutaka Nishiyama
35. Percolating possibilities, Colva Roney-Dougal & Vince Vatter
36. Milestones on a non-Euclidean journey, Caroline Series
37. Simpson's rule, Simon Singh
38. Risking your life, David Spiegelhalter
39. Networks and illusions, Ian Stewart
40. Emmy Noether: Against the odds, Danielle Stretch
41. Of catastrophes and creodes: How maths benefits from collaboration with other fields, Paul Taylor
42. Conic section hide and seek, Rachel Thomas
43. Sir James Lighthill: A life in waves, Ahmer Wadee
44. Fail safe or fail dangerous, Ahmer Wadee and Alan Champneys
45. Leapfrogging into the future: How child's play is at the heart of weather and climate models, Paul Williams
46. Motorway mathematics, Eddie Wilson
47. The philosophy of applied mathematics, Phil Wilson
48. Mighty Morphogenesis, Thomas Woolley
49. Called to the barcode, Andrew Wrigley
50. Roughly fifty-fifty?, Gunter Ziegler
Pythagoras's Theorem: c2