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.
"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.
Over the last decade, the discipline of neuropsychology has shed light on many aspects of human thought. Brain scans, carefully structured behavioural experiments, and the study of individuals who have suffered brain damage, have taught us much about which abilities are native to humans and which learned; which abilities can be lost and what happens when they are.
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.
ver the last hundred years, human understanding of the nature of the universe has expanded at a mind-boggling rate; and over the last forty, Kip Thorne, along with Stephen Hawking, who wrote the foreword to this book, have been among the group of people shining most light into the darkness. But, aware that his research is carried out on behalf of us all, Thorne has not neglected the task of explaining its results to the rest of us.
What is the nature of the universe that we live in? This is a question that has exercised philosophers and scientists for as long as people have been able to think. Almost everyone has asked it at one time or another, in one form or another. It is hard to imagine a more fundamental question.
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.