book review

Sherman Stein's motivation for writing this book grew out of a course on the history of calculus for undergraduates he taught for several years. Before that, like most of us, he didn't know where Archimedes' reputation as one of the greatest mathematicians of all time had come from - and now he wants us to know too.
Although some people might find maths deadly boring, very few of us would think it could ever be deadly dangerous. But deadly it was in 16th century England, and one of those who followed the dangerous and mystical path of a mathematician was John Dee, the subject of this book.
If "How to solve it" really contained an infallible recipe for doing so, mathematics would not be mathematics and the world would be quite different. Of course it doesn't - it can't - but it can - and does - contain a great deal of food for thought for the budding mathematician. Like many other Central Europeans, Pólya relocated to the US at the beginning of the Second World War. There he worked at Stanford University and wrote this immensely successful book (more than a million copies sold) in 1945.
This book is built on an extended metaphor, which casts equations as the poetry of science. According to the editor Graham Farmelo (head of Science Communication at the Science Museum in London), great equations and great poems are alike in a number of ways. Both suffer if anything is added, changed, or taken away, both are a rich stimulus to the prepared imagination, and both draw much of their power from their conciseness.
If you watch a steam engine, you may not know how it works but you can soon get a fairly good idea of its behaviour, and you can predict its future behaviour accurately. Even though you don't understand its workings, you can see it's a pretty simple machine, so you can trust it to behave in a simple way: you have confidence in your predictions based on a short sample of its behaviour.
As Tony Gardiner says in at the beginning of this book, "the last ten years or so has seen a remarkable blossoming of public interest in mathematics [but] most of the books produced have been for adults, rather than for students. Moreover, most are in prose format - for those who want to 'read about' mathematics, rather than those who want to get their hands dirty solving problems."
Ever since Watson and Crick worked out the double helix structure of DNA in 1953, the role of genetics in biology has grown and grown. Genetic determinism - the belief that we are controlled by our genes and that no other factor is significant - is now all-pervasive.
Research on the Universe leads to many such startling conclusions and this book attempts to describe some of the surprising phenomena which occupy astronomers and cosmologists. Our Universe, Martin Rees' laboratory, allows its natural laws to be cleverly interpreted at arm's length, by observing the 'extreme' physics which we could never replicate in a laboratory. The biggest questions have an almost philosophical tenor.
"I am certain, absolutely certain that...these theories will be recognized as fundamental at some point in the future." Sophus Lie said these words more than hundred years ago. We know now that he was right, absolutely right. The notions of "Lie groups" and "Lie algebras" are in the vocabulary of every mathematician and physicist today. Lie's theories are indispensable tools for understanding the physical laws of Nature.
A Beautiful Mind is a touching, emotionally charged film detailing the life of a brilliant academic who suffers from schizophrenia. This affliction slowly takes over his mind and we watch as his life crumbles apart around him.
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