Top positive review
3 people found this helpful
I couldn't fully appreciate the beauty
on 1 December 2009
This book has many good points, and some drawbacks. I think my own lack of mathematical knowledge held me back from fully appreciating it. (I got A in O level maths in 1981. I enjoyed maths at school, and felt I was getting to the interesting bits when I was forced towards physics chemistry and biology for A levels- looking back I wish I had the chance to do all four subjects)
The good points are that is well written with a clear narrative showing how our mathematical thinking has developed over time. It shows well how seemingly abstract problems lead on to many insights that may be interesting of themselves (pure maths) or may help solve practical problems. (applied maths) What seems like purely abstract mathematics may later turn out to be the route to new applied knowledge. The "unreasonable effectiveness" of mathematics is shown in many examples throughout the book. The discussion of the relationship between truth and beauty is well nuanced, and it seems likely that truth will be beautiful, and that a current "ugly" or "messy" formulation is one awaiting its simplification. At school I was just beginning to get the idea that graphs, coordinates, geometry, equations and matrices were all ways of expressing the same idea in different formats. This book shows how these relationships come about, and evolve out from one another.
The drawbacks of the book for me was that the final 100 pages largely lost me. I got certain headline points, but I did not understand the ideas behind group theory, Lie groups, Hamilton's work, Killing's work. I think this is a reflection of my ignorance, not the author's writing.
My feeling about this book is that it would be a great read for someone studying maths at A level or university and wanting to get an idea of how maths has developed and where it is going. It would whet the appetite and encourage their studies.