## 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?

C Jarzbek 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 Palm 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.