The Greeks actually also invented steam engines. But they didn't know what to do with them. So instead it was just a fancy art piece that spins super fast.
They also invented a lot of other stuff: door bells that sound like birds chirping, automatic doors, clocks which tracked the year, etc.
That's pretty much where manufacturers are today when it comes to implementing automation. The technology exists in many manufacturing areas, but if workers can do it more cheaply they're not investing in it.
French mathematician Pierre de Fermat wrote a "little theorem" in 1640 that is now the basis of modern computer cryptography.
The Fast Inverse Square Root is an algorithm that estimates 1/sqrt(x), a very important calculation in computer graphics. Early computers struggled when calculating this value but a programmer solved this mathematical problem...while programming Quake 3. His solution to the problem wasn't discovered until the source code for the game was released.
The fast inverse square root algorithm was known from the 80’s, and was used in at least one game I’m aware of before Quake 3. Also, it wasn’t important in the long run - the same year Quake 3 was released, the rsqrtss instruction was introduced by Intel, which made this algorithm obsolete (as it was faster and more accurate).