Experimental Blog #98

Summary of "The Great Equations - Breakthroughs in Science from Pythagoras to Heisenberg" by Robert P. Crease

The "great equations" in this book refer to 10 single or groups of several equations in the history of mathematics.

The first equation is the well known Pythagorean Theorem from around the 6th century BCE, but it apparently had been known for over 1000 years in Babylonia, and it was also apparently independently known in ancient India and ancient China. There are over 500 proofs for this theorem.
The second and third equations were formulated by Isaac Newton. They are: Newton's Second Law of Motion, that is, motive force equals mass times acceleration, and Newton's Law of Universal Gravitation. The work of several other people of Newton's time contributed to one or both of these equations.
The fourth equation was derived by Leonhard Euler in the 1740s, and it has been called the "Gold Standard for Mathematical Beauty". It involves rational numbers, irrational constants, and an imaginary number in an almost "mystical" relationship.
The fifth equation is the Second Law of Thermodynamics; that is, entropy, or disorder, is "forever" increasing in the universe. Robert Crease lists 12 contributors from the 19th century who contributed to this most simple equation.

Number 6 are the equations of James Clerk Maxwell that describe the relationships between electricity and magnetism. These equations were reformulated into a more understandable form by Oliver Heaviside in 1884.

Equations number 7 and 8 are Albert Einstein's: the equation for "Special Relativity", which attempts to solve{apparently successfully} contradictions between the physics of Isaac Newton and the physics of James Clerk Maxwell, and is about the conversion of mass and energy; and the equation for "General Relativity", which describes the curvature of space and time by mass. Several other scientists had achieved some progress on the equation for "Special Relativity", and Einstein's famous equation is derived, in part, from the Pythagorean Theorem. The equation for "General Relativity" is based, in part, on non-Euclidian geometry.

Equation #9, derived in 1926, is called "{Erwin} Schrodinger's Equation" and it is the "basic equation of Quantum Theory." It appears to be a long and very difficult equation, and it attempts to achieve a "compromise" between the wave and particle theories in physics.
Number 10, derived in 1927, is the "{Werner} Heisenberg Uncertainty Principle". It appears to be a simple equation, but, similar to equation #9, it has had many "critics" or "inputters".