## Thursday, March 01, 2018

### Equations That Changed the World

A few years ago, mathematician Ian Stewart published a book titled 17 Equations That Changed The World. It's an interesting list:

I would go beyond these 17 and add:
• 1+1=2, which some unknown someone realized long ago was profound and incredibly useful. The logical proof of this assertion, though, didn't come until Bertrand Russell and Alfred North Whitehead three-volume Principia Mathematica. It's a crazy book -- the text looks almost alien or elvish, and it took them several hundred pages of work before they could prove that 1+1=2. Russel said his work on this book "had actually damaged his brain." Here's an interesting discussion of the Principia Mathematica from NPR in 2010.
• Newton's second law of motion, F=ma (really, F=dp/dt, the time rate of change of momentum).
• Planck's Law of radiation (probably).
• The Lagrangian of quantum electrodynamics, because it changed how quantum physics was done ever afterward.
• Einstein's equations of general relativity, because they changed our view and understanding of the universe, and for their sheer elegance and sophistication.
You?

CJ said...

This one ties three familiar numbers together: https://www.math.toronto.edu/mathnet/questionCorner/qc_hlimgs1/image142.gif
..
May not have changed the world, but is simply elegant.

Thomas said...

sqrt(2)<> p/q

David Appell said...

Thanks, CJ. If you write this equation as exp(i*pi)+1=0, it ties five important numbers together....

David in Cal said...

Mean (aka Arithmetic Mean, Average) = The sum of all of the numbers in a list divided by the number of items in that list.

Also, the variance and standard deviation
(sorry, I don't know an easy way to paste the formulas here)

@whut said...

I would replace the Black-Scholes equation with the Fokker-Planck equation.

The former is a recasting of the latter so it can be used in economics.

The latter is primarily responsible for semiconductor electrical transport modeling.