I was reading A Beautiful Mind yesterday and tripped over a lovely exchange between John Nash and John von Neumann.
It’s a great book, a great movie too. Highly recommended. I’ve also read countless books on the scientists and mathematicians of the era and always love hearing more stories about them.
Anyway, they’re both at Princeton. Nash had his great idea and rushed off to tell the great von Neumann about it.
From Chapter 10: Nash’s Rival Idea.
“Nash went to see von Neumann a few days after he passed his generals. He wanted, he had told the secretary cockily, to discuss an idea that might be of interest to Professor von Neumann.”
Then the exchange:
“He listened carefully, with his head cocked slightly to one side and his fingers tapping. Nash started to describe the proof he had in mind for an equilibrium in games of more than two players. But before he had gotten out more than a few disjointed sentences, von Neumann interrupted, jumped ahead to the vet unstated conclusion of Nash’s argument, and said abruptly, “That’s trivial, you know. That’s just a fixed point theorem.”
Both mathematical geniuses.
John von Neumann perhaps the biggest genius to have lived.
And before Nash can finish, von Neumann jumps to the end and says:
“That’s trivial, you know.”
Now, let’s oversimplify a little.
The great human computer, von Neumann, was pointed in the direction of a problem and a proof. Nash only just started to explain. Then von Neumann jumped to the solution and it was so uninteresting at that point that he commented that it was trivial.
Perhaps not the whole solution and perhaps he was pushing back on a cocky student in the hypercompetitive world of math at Princeton in the late 1940s. For example:
“Nash later rationalized von Neumann’s reaction as the naturally defensive posture of an established thinker to a younger rival’s idea, a view that may say more about what was in Nash’s mind when he approached von Neumann than about the older man. Nash was certainly conscious that he was implicitly challenging von Neumann.”
Yet, this is quite something.
I read all this and intimately relayed it to my poor ever-patient wife. And the implication for LLMs.
Take the oversimplified case as what went down. Some version of this has been described in other books about von Neumann. That his, him jumping to the solution of very complex problems. That’s why, later in his career, he was wheeled in to so many government programs.
Do we going to get something like this with LLMs, but on demand?
I already see it with truly trivial language and programming problems. That is, point it in the direction (give context) and then ask a question and jump to the solution (even if it’s hallucinated to please me, the user).
We will get von Neumann “on tap”. On demand. Ready to reason and jump to the end of any challenging topic.
I believe so. It’s why this is all so exciting.
It’s a “trivial” extrapolation of what we’ve already got :)