So now the Emperor walked under his high canopy in the midst of the procession, through the streets of his capital; and all the people standing by, and those at the windows, cried out, "Oh! How beautiful are our Emperor's new clothes! What a magnificent train there is to the mantle; and how gracefully the scarf hangs!" in short, no one would allow that he could not see these much-admired clothes; because, in doing so, he would have declared himself either a simpleton or unfit for his office. Certainly, none of the Emperor's various suits, had ever made so great an impression, as these invisible ones.
"But the Emperor has nothing at all on!" said a little child.
"Listen to the voice of innocence!" exclaimed his father; and what the child had said was whispered from one to another.
"But he has nothing at all on!" at last cried out all the people. The Emperor was vexed, for he knew that the people were right; but he thought the procession must go on now! And the lords of the bedchamber took greater pains than ever, to appear holding up a train, although, in reality, there was no train to hold.
You're misunderstanding my comment. The OP was amazed by people who can manipulate symbols on paper. Von Neumann would have been considered an incredibly POTENT wizard. He actually impacted the world.
His work was incredibly APPLIED. Which is precisely why he is remembered and lauded.
Can anyone here not involved in theoretical math name 5 Fields Medalists? Take out Terry Tao or Andrew Wiles or Gigori Perelman and can you name any Pure Mathematicians from the last century at all?
You see that https:// part of the URL in your browser? The 's' started out as pure mathematical research into elliptic curve cryptography based on algebraic geometry and number theory, a solution looking for a problem if there ever was one. When the problem eventually came along, the solution was obvious thanks to pure math.
I wouldn't be the least bit surprised if work done on the behavior of vectors in high-dimensional space by Hong and her colleagues someday becomes relevant to practical neural-net R&D. You never know what you might need in the future, but it will suck if engineers have to stop and figure this stuff out from first principles when they do need it.
von Neumann did a lot of theoretical work, e.g. https://www.academia.edu/download/38046446/Ohta_15_von_Neuma... where he was hanging out intellectually with McCullough and Pitts. He not only wouldn't be surprised at the ANN renaissance under way now, he'd ask us what took so long. He even cited M&P in his EDVAC report. Way ahead of his time, envisioning how hardware that wouldn't be practical for another 80 years might work.
> pure mathematical research into elliptic curve cryptography based on algebraic geometry and number theory, a solution looking for a problem if there ever was one.
This is ahistorical. Elliptic curves had been around for a long time, but elliptic curve cryptography was applied from its birth in 1985. Also the reasons elliptic curves had been studied for so long (Mordell-Weil Theorem, Falting's Theorem, Sato-Tate, etc) didn't really have much to do with the reason it was proposed, which was that its group probably wasn't vulnerable to the same kinds of attacks as DH.
> When the problem eventually came along, the solution was obvious thanks to pure math.
Also ahistorical. ECC wasn't proposed until almost a decade after DHKE (possibly only that early because it was hot at the time thanks to Lenstra (https://www.math.uwaterloo.ca/~ajmeneze/publications/ecc.pdf)) and it took decades to get in common use. Doesn't seem all that obvious.
