Seventeen Equations that Changed the World

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Important work by mathematicians Vladimir Arnold and Stephen Smale helped with the realization that chaos is a consequence of differential equations. 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 .

The distinction is not clear-cut, because sometimes the same equation can be used in both ways, but it’s a useful guideline. In Victorian times, Michael Faraday was demonstrating connections between magnetism and electricity to audiences at the Royal Institution in London. The equation in the graphic, log(ab) = log(a) + log(b), shows one of the most useful applications of logarithms: they turn multiplication into addition.But Newton’s Law isn’t a mathematical theorem; it’s true for physical reasons, it fits observations.

A 2013 book by mathematician and science author Ian Stewart looked at 17 mathematical equations that shaped our understanding of the world. 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. P. Snow's much-quoted complaint that educated people felt (perhaps still feel) quite comfortable not being able to explain the concepts of mass, or acceleration - the scientific equivalent of being able to read - and indeed have little more understanding of these concepts than their Neolithic ancestors. The reviewer, a mathematician, said that Stewart was "generally successful in getting the essential points across in a nontechnical way without too much distortion.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. It is a neat idea but I wish there had been some coherence to why these equations were chosen, over other ones or why it has to be 17 instead of the top 10 or the top 20? He chose these towns because they lay on the same line of longitude and were exactly one degree of arc apart.