## Comment Re:"developed an artificial intelligence(AI) progr (Score 1) 153

The *only* thing the 1950s needed to obtain recent results in convolutional neural networks, was the planar process of 1959 and a suitably accelerated coefficient of Moore's law. We can get there by applying the inverse Hackermann function.

When planning a project, increase the amount of time that you estimate it will take by doubling the number and going up to the next time unit.

Dividing 18 by 2 and shifting to a lower unit gives us a doubling time of nine weeks. Probably we're recognizing cats by 1967. Before the modern API was half fleshed out.

Seriously, have you looked at the sophistication of mathematics in the 1950s?

The discovery came when Ono and fellow mathematician Andrew Granville were leafing through Ramanujan's manuscripts, kept at the Wren Library at Trinity College, Cambridge. "We were sitting right next to the librarian's desk, flipping page by page through the Ramanujan box," recalls Ono. "We came across this one page which had on it the two representations of 1729 [as the sum of cubes]. We started laughing immediately."

... What the equation in Ramanujan's manuscript illustrates is that Ramanujan had found a whole family (in fact an infinite family) of positive whole number triples x, y and z that very nearly, but not quite, satisfy Fermat's famous equation for n=3.

... Ono and Trebat-Leder found that Ramanujan had also delved into the theory of elliptic curves. He did not anticipate the path taken by Wiles, but instead discovered an object that is more complicated than elliptic curves. When objects of this kind were rediscovered around forty years later they were adorned with the name of

K3 surfaces— in honour of the mathematicians Ernst Kummer, Erich Kahler and Kunihiko Kodaira, and the mountain K2, which is as difficult to climb as K3 surfaces are difficult to handle mathematically.... His work amounts to one box, kept at Trinity College, and three notebooks, kept at the University of Madras. That's not a lot. It's crazy that we are still figuring out what he had in mind. When is it going to end?"

The book is not even closed yet on the mathematics of the 1920s.