Seventeen Equations that Changed the World

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The square root of -1, usually written i, completes this process, giving rise to the complex numbers.

Some of the explanations are quite complex, especially where Stewart is exploring the most recent applications of older ideas. Maxwell's equations were for classical electromagnetism what Newton's laws of motion were for classical mechanics. There's not enough detail to interest people studying maths or physics at university, but it becomes too obscure in a number of places for the general reader.British mathematician Ian Stewart, author of the 2012 book entitled In Pursuit of the Unknown: 17 Equations That Changed the World, said that Black–Scholes had "underpinned massive economic growth" and the "international financial system was trading derivatives valued at one quadrillion dollars per year" by 2007. However, perhaps someone could teach a mathematics course with this as a supplementary text, with the necessary "translation" being performed by the teacher. They encode information about the real world; they express properties of the universe that could in principle have been very different. However, equations have a reputation for being scary: Stephen Hawking’s publishers told him that every equation would halve the sales of A Brief History of Time. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day.

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. For certain values of k, the map shows chaotic behavior: if we start at some particular initial value of x, the process will evolve one way, but if we start at another initial value, even one very very close to the first value, the process will evolve a completely different way. And it takes an exceptional mathematician to be able to communicate that enthusiasm without boring the pants off you. He gives a fascinating explanation of how Newton's laws, when extended to three-body problems, are still used by NASA to calculate the best route from Earth to Mars and have laid the basis for chaos theory. There was no overarching theme other than each one is important, nor did I feel was there any attempt to flow from equation to equation.He used the Second Law of Thermodynamics as an example, as it is a very fundamental physical law that should be familiar to everyone. James Clerk Maxwell transformed early experimental observations and empirical laws about magnetism and electricity into a system of equations for electromagnetism. They are valid because, given our basic assumptions about the logical structure of mathematics, there is no alternative.

Importance: Fundamental to the development of topology, which extends geometry to any continuous surface. Fortunately, you don’t need to be a rocket scientist to appreciate the poetry and beauty of a good, significant equation. Euler's formula states that, as long as your polyhedron is somewhat well behaved, if you add the vertices and faces together, and subtract the edges, you will always get 2. The populist banker bashing this chapter represented made me seriously question the accuracy of the detail in the other chapters. History: Imaginary numbers were originally posited by famed gambler/mathematician Girolamo Cardano, then expanded by Rafael Bombelli and John Wallis.Mathematicians can expand our idea of what numbers are by introducing the square roots of negative numbers. But his publishers had a point too: equations are formal and austere, they look complicated, and even those of us who love equations can be put off if we are bombarded with them.

I certainly hadn't appreciated the importance of Newton's development of calculus, which Stewart breezily points out led to "most of mathematical physics". 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.His book takes a look at the most pivotal equations of all time, and puts them in a human, rather than technical context. The Navier-Stokes equations describes the behavior of flowing fluids — water moving through a pipe, milk being mixed into coffee, air flow over an airplane wing, or smoke rising from a cigarette. Stewart adopts an interesting approach of explaining the circumstances around the discovery of each equation, zooming into the maths a little, zooming out to explain the wider relevance of the equation, and finishing by talking about its applications in the modern world. Although I’ve gotten many ideas for my YouTube channel from the book, I wouldn’t recommend this book to anyone but a core popular education reader.