I am currently reading this book by Stony Brook U. Philosophy Dept. Chairman Robert P. Crease. Great read, so far. I'm also reading about 8 other books, and it's arguable if I'll completely finish all of them.
This one, I will. I give it my strongest recommendation. it's not for everyone, just everyone from 14-80, or better.
The Great Equations: Breakthroughs in Science from Pythagoras to Heisenberg
This post ends with one positive review by Robert Yu "Pinger" of Astoria, NY. I disagree with a few of Pinger's points, but he nails what I've read of it so far pretty well. Indeed, many will argue Crease leaves out a few really important equations (like the Quadratic Equation), but that wasn't the point of the book, to be Mr. Super-complete. These are 10 damn good equations, and the stories of how they came about, are beautifully told.
The Great Equations summarizes what the author feels are the ten greatest equations in the history of human intelligence, and who could argue with him? During the time reading it, I thought about Planck's resolution of the Blackbody Catastrophe, Dirac's QED eq, leading to anti-matter (actually Dirac was trying to unify Quantum Mechanics with Special Relativity, but 'stumbled' onto anti-matter),or Hubble's expanding universe (Einstein had postulated this much earlier, but recanted causing him to state that it was the greatest blunder of his life), but guess top 13 would be unlucky. Listed, not by import, but chronologically as follows:
1-Phythagoras's Theorem (~700 BC), which states that the sum of the squares of the lengths of the two sides whose vertex is a right angle, equals the square of the third side. This is not just some schoolchild postulate, but is the basis of ancient civilization. Structures and ideas were constructed on the basis of this deep insightful concept. But there is proof that in Asia, and South America, a similar theorem was proposed, evidenced by the level of their intellectual progress.
2-Newton's Second Law of Motion (1666), which states that any force produced by, or imposed upon a body, results from the product of its mass and its change in motion. This is the pillar upon which all explainations of motion and forces on any bodies, stand to this very day. Galileo was on the brink of this idea, but the concept of 'change in motion' was still too abstract then, plus he was having serious troubles with the Catholic Church. Sir Isaac was the first the understand this concept, and led him to discover differential calculus as an afterthought.
3-Newton's Universal Gravitation Law (1666). The main word here is Universal, implying that it is valid, not only on in merry ole England, or even the Earth, but anywhere in the heavenly skies. Remembering that we are not far removed from the medieval period, and to demonstrate this degree of dogmatic farsightness was nothing short of revolutionary.
4-Euler's Equation (1740's).(not Euler's eq for fluid dynamics, which is just a fluid version for #2) Here Euler combines the five most fundamental numbers in all of mathematics (base of the natural log, pi, square root of -1, one, and zero) into one simple arithmetic statement. I remember asking my math teacher if this was a coincidence, and he replied 'there are no coincidences in mathematics.', meaning that there is a deep interrelationship between the values of these numbers.
5-The Second Law of Thermodynamics (1840's - 1850's) Aka the Law of Entropy, it was the culmination of the work of many,and in the author's words, worthy of a 'Shakespearean drama'. This was the period of the Industrial Revolution, and the Steam engine was all the rage. It was left to the physicist to explain what is heat, and its effects on the environment. The plot and cast is as follows: Carnot examines heat engines; Joule and Kelvin quantify heat; Clasius introduces entropy; Boltzmann and Maxwell applies statistics to describe entropy, the first time probabalistic concepts entered science, and foretold much of what was to come. It also definitively defined the direction of time. Up until then, it was assumed that time traveled with the clock hand, sunrises or birthdays, but there was no proof.
6-Maxwell's Equations (1860's). From statistical thermodynamics, Maxwell moved on to electricity and magnetism. He was deeply influenced by Faraday's lines of force and proceeded to unite the seemingly unrelated laws of Gauss, Ampere and Faraday. Along the way, he proved that light was just another electromagnetic effect. He actually proposed 12, sometimes more equations, and it took the practical ingenuity of Heaviside in 1884 to give it the familiar, symmetric, iconic (and much simpler) form we know today.
7-E=mc^2 (1905). Who in this world has not seen this? It conjures up images of wild-eyed, eccentric, white-haired madness and the atomic mushroom. Einstein, during one of his famous thought experiments, imagined to be surfing on a light wave. What would happen to the laws of physics? He concludes that the speed of light is the same for all observers, and that it is time and the three physical dimensions (space-time) that are variant. This was earth shattering at that time, but he was not yet done.
8-General Theory of Relativity (1915), so called because #7 was only a 'special' case. This showed that "space-time tells matter how to move, and matter tells space-time how to curve"; that the universe is like a trampoline-it conforms to the objects that are on it. The extension of this theory includes time travel, black holes, multiple universes, and string theory.
9-Shrodinger's Equation (1926). In the early 1920's, the new quantum mechanics was the latest hot research topic. But who really understood it. There's an expression-'if you can't explain it, then you don't understand it.' Shrodinger was an 'old-time' physicist (in his late 30's), and was comfortable with the conservative approach. Everyone knows the wave equation, which he adapted to ever growing number of quantum observations. The scientific community applauded his effort, which enabled them to 'simply' solve the 'standard' equation which fit in nicely with experimental data.
10-Heisenberg's Uncertainty Principle (1927). Although Heisenberg also shared the credit for #9, his approach was much too perplexing, utilizing obscure matrices, confounding many who tried to apply his method. But not to be forgotten, his uncertainty principle forever destroyed the notion of predictability of the universe. It was a century earlier, when Laplace declared, 'give me the mass and motions of every object in the universe, and I will predict the future.' We now know that there is a calculable probabilty, that you are not where you think you are right this second; that parallel universes can exist, that it's possible for Scotty to 'beamed us up'.