What kind of mathematical "discoveries" have enabled mankind to build modern computers?
After studying the very thrilling Examples of mathematical discoveries which had been saved as a mystery I got here to think of something: maximum math discoveries appear to had been made centuries ago, and with Pascal and Leibniz we already had machines that would add and multiply (a few don't forget them as the first computer systems). Of direction modern computer systems needed energy and electric signals that can be transformed to at least one's and zero's, but those we've since the 19th century. First computer systems were also built with transistors, however we've the ones since the 1940's.
current computers are, at their center, not so extraordinary from the primary computer systems that followed the Von Neumann structure (with its arithmetic-logic unit). this is: they understand how move information from one place to any other, the way to upload and a way to multiply, in addition to perform logical operations (and, or, xor, now not), and from that they get all of the other operations (some can substract, divide and do some different stuff, however it is all very primitive in that sense). Of path, current computers paintings at a miles better level than their predecessors: while inside the beginning programming needed to be accomplished the use of commands composed of zero's and 1's or, in the event that they were lucky, the usage of meeting language, now we have high stage programming languages that (to say it kind of) enclose a group of these single commands into one high stage command.
And when I see pretty graphics in video-games, programs like photoshop, 3D rendering, CAD programs and such, I always think of all the calculus stuff I learned and how it must be applied to achieve those wonderful results.
And this is where my question arises: all of this mathematical knowledge has been available to us for way longer than computers existed. So, are there any modern mathematical discoveries that enabled the giant leap we took from the first computers we had in the 40's to what we have now? Or maybe old math started being applied in a different way at some point in time?