Of all the classical functions, the Gamma function still retains much of its mystery and intrigue, since Euler first spotted it as something "worthy of serious consideration". In Gamma, Julian Havil explores Gamma from its birth and in so doing simultaneously deals with many related functions, problems and issues that go beyond the conventional territory of functions alone.
In this well-written book, James Gleick (author of Chaos) tackles the life and work of Isaac Newton. He focuses on the man and his life in the historical context of Britain in the 17th Century, and, although the book is not a light read, he explains Newton's science well without the use of any equations. Newton was born in 1642 in the time of the civil war (King Charles was beheaded when Newton was six years old).
It is not uncommon for physics students to know more about the history of physics than mathematics students do about the history of mathematics. Physical laws often come with a name attached; mathematics constitutes a more homogenous structure, and thus tracing parentage can be harder.
Despite what the innumerate masses may wish, our daily lives are inextricably tied up with mathematics. On the most mundane level, we use basic arithmetic to do such things as tell the time, to count our change, to programme the video. But on a less obvious level we also need a reasonably good grasp of geometry in order to park the car in the garage or to pack the shopping bags carefully at the supermarket; we collect and interpret statistical data when the football results come in and we all seem to know how easily order turns to chaos.
It seems amazing that the universe could be characterised by a mere six numbers, yet, according to Astronomer Royal Martin Rees, this is the case. He makes an excellent case for the necessity of these numbers, though he does not show that they are the only numbers we need.
Early in our mathematical careers, we are introduced to prime numbers. These special integers, which possess no divisors other than themselves and 1, are the building blocks for all the integers. Thus an understanding of the properties of primes, including where to find them, is an essential part of number theory, and any serious discussion of prime numbers will inevitably lead to what is arguably mathematics' greatest unsolved problem: The Riemann Hypothesis.
The Four Colour Theorem - the statement that four colours suffice to fill in any map so that neighbouring countries are always coloured differently - has had a long and controversial history. It was first conjectured 150 years ago, and finally (and infamously) proved in 1976 with much of the work done by a computer. The published proof relied on checking 1432 special cases, which took more than 1,000 hours of computer time.
Many people, when they look back, can pinpoint the precise moment when their interest in mathematics was awakened - it was when they found a puzzle that intrigued them. Perhaps they now realise the puzzle was trivial or insignificant, but at the time something about it captured their imagination and started them on a path that may have led very far - perhaps even into fundamental mathematical research.
Geometric dissection is the mathematical art of cutting figures into pieces that can be rearranged to form other figures, preferably using as few pieces as possible. You may already have come across puzzles such as the Aviary Tangram, the pieces of which can be used to form an egg, a chicken and many other shapes; but the ingenuity of the dissections shown here may still be a revelation to you, as they were to this reviewer.