The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us. This is the story of the ascent of humanity, told in 17 equations. Equations in pure mathematics are generally of the first kind: they reveal deep and beautiful patterns and regularities. They are valid because, given our basic assumptions about the logical structure of mathematics, there is no alternative. Pythagoras’s Theorem, which is an equation expressed in the language of geometry, is an example. If you accept Euclid’s basic assumptions about geometry, then Pythagoras’s Theorem is true. History:The genesis of Einstein's equation was an experiment by Albert Michelson and Edward Morley that proved light did not move in a Newtonian manner in comparison to changing frames of reference. Einstein followed up on this insight with his famous papers on special relativity (1905) and general relativity (1915).

In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. Equations are the lifeblood of mathematics, science, and technology. Without them, our world would not exist in its present form. 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.A good example of the second kind of equation is Newton’s law of gravity. “It tells us how the attractive force between two bodies depends on their masses,” Stewart writes, “and how far apart they are. Solving the resulting equations tells us how the planets orbit the Sun, or how to design a trajectory for a space probe.” This isn’t a mathematical theorem but rather it’s true for physical reasons in that it fits the observations. So understanding right-angled triangles is the key because “they prove that there is a useful relation between the shape of a triangle and the lengths of its sides.”

The course of human history has been redirected, time and time again, by an equation. Equations have hidden powers. They reveal the innermost secrets of nature. This is not the traditional way for historians to organise the rise and fall of civilisations. Kings and queens and wars and natural disasters abound in the history books, but equations are thin on the ground. This is unfair. In Victorian times, Michael Faraday was demonstrating connections between magnetism and electricity to audiences at the Royal Institution in London. Allegedly, Prime Minister William Gladstone asked whether anything of practical consequence would come from it. It is said (on the basis of very little actual evidence, but why ruin a nice story?) that Faraday replied: ‘Yes, Sir. One day you will tax it.’ If he did say that, he was right. James Clerk Maxwell transformed early experimental observations and empirical laws about magnetism and electricity into a system of equations for electromagnetism. Among the many consequences were radio, radar, and television.Importance:Fundamental to the development of topology, which extends geometry to any continuous surface.