When I was a little younger than Ahmed Mohamed is now, I invented the distance formula for Cartesian coordinates. I wanted to make a simulation of bugs that ran around and ate each other. To implement a rule like “when the predator is near the prey, it will chase the prey,” I needed to compute distances between points given their $x$- and $y$-coordinates. I knew BASIC, and I knew the Pythagorean Theorem. However many people had solved that before me, it wasn’t written down in any book that I had, so I took what I knew and figured it out.
Those few pages of PowerBASIC on MS-DOS never amounted to much by themselves, but simulating ecosystems remained an interest of mine. I returned to the general idea now and then as I learned more.
And then, hey, what’s this? It looks like a PhD thesis.
“I bet every great mathematician started by
rediscovering a bunch of ‘well known’ results.”
—Donald Knuth, Surreal Numbers