Seventeen Equations that Changed the World

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Qualities: It was informative, credible (with citations to peer-reviewed evidence), well-written, entertaining, and well-organized. Stewart provides the "historical background" to explain "how the equation was anticipated", how people then "generalized the ideas and formalized the results". He has published more than 120 books including the US bestseller Flatterland, and the bestselling Professor Stewart's Cabinet of Mathematical Curiosities and follow-up, Professor Stewart's Hoard of Mathematical Treasures. Since nowadays you can do an A level in Physics without studying calculus it seems that this book can only be aimed at undergraduate students or people who have studied these interesting areas. Important work by mathematicians Vladimir Arnold and Stephen Smale helped with the realization that chaos is a consequence of differential equations.

For example, a right triangle drawn on the surface of a sphere need not follow the Pythagorean theorem.The square root of -1, usually written i, completes this process, giving rise to the complex numbers. However, he personally would have preferred a less "discursive style" but acknowledged that Stewart's writing was appropriate for his intended audience.

French engineer Claude-Louis Navier and Irish mathematician George Stokes made the leap to the model still used today.Allegedly, Prime Minister William Gladstone asked whether anything of practical consequence would come from it. El resto del libro es una gran lectura acerca de cómo las matemáticas viven, cómo son creadas y cómo (para sorpresa de muchos escolares que creen saberlo todo) las matemáticas sí se usan en la vida cotidiana. Like with most popular science books it is not important that the reader understand all the logical implications of maths, but to get some understanding of the general nature of these equations.

Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery.The reviewer, a mathematician, said that Stewart was "generally successful in getting the essential points across in a nontechnical way without too much distortion. Stewart's expertise and his well-developed style (enhanced by a nice sense of humor) make for enjoyable reading. So Pythagoras and his Greek successors would decode the theorem as an equality of areas: ‘The area of a square constructed using the longest side of a right-angled triangle is the sum of the areas of the squares formed from the other two sides. Algebra works perfectly the way we want it to — any equation has a complex number solution, a situation that is not true for the real numbers : x 2 + 4 = 0 has no real number solution, but it does have a complex solution: the square root of -4, or 2 i . Word of the method spread across Europe, reaching the ears of the Danish nobleman and astronomer Tycho Brahe.

The left side is the acceleration of a small amount of fluid, the right indicates the forces that act upon it. Newton's law is a remarkable piece of scientific history — it explains, almost perfectly, why the planets move in the way they do.While we take the idea of universal laws for granted today, in earlier eras the idea that the terrestrial and celestial worlds shared the same properties was revolutionary.