I imagine being told that a problem is unsolved changes the way you approach it. You'll assume that 'obvious' things have been tried before. Without that psychological barrier you can try out ideas that are obvious to you that might not have occurred to anyone yet. Telling someone that a problem is unsolved implies they won't be able to solve it unless they're better than all the people who've approached it before in some way. That isn't necessarily true; "better" doesn't really apply at the level of people attempting these problems.

relevant:

> When asked, "How could you possibly have done the first interactive graphics program, the first non-procedural programming language, the first object oriented software system, all in one year?" Ivan [0] replied: "Well, I didn't know it was hard."

[0] http://en.wikipedia.org/wiki/Ivan_Sutherland

Or to quote Beyer's Grace Hopper and the invention of the information age:

>Common sense would dictate that the most experienced programmers should have been assigned to these difficult tasks, but, as Hopper glibly explained, young people did not know that they were supposed to fail.

They're not hard. They're things we'd expect a solid CS student grok in one year.

He just happened to be the first to grok them. Question is how he came to face those problems without any apparent precedent.

Confidence is quite important in mathematics. You would usually go further if you are confident than if you are not. That said, most unsolved problems in mathematics require more knowledge to state than these simple problems.

I think for most people, not knowing a problem is unsolved will lead them to try out many more approaches than if they knew. The problem is that most of the approaches will be approaches that have already been tried before and the rest will be useless. This does nothing for the solving of the problem but greatly aids your own understanding.

There's something to that, but for an approach to be worth trying you don't have to expect it to work: just that you'll learn something about the problem.

I think it's a nice story, but for the most part unsolved problems are solved by mathematicians who are aware of their difficulty.

> A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.

I love fun stories like that. And I love that it shows this guy is crazy brilliant yet humble enough to shrug off that success and just assume he had to figure out something else for his thesis. At least that's my interpretation.

    faithInHumanity++;

A good down to earth mathematician will always look ahead and try to solve more problems, do more math, etc. It's not surprising that he wanted to create new math despite already doing so.