In the early 1980s Douglas Lenat wrote EURISKO, a program Eliezer called "[maybe] the most sophisticated self-improving AI ever built". The program reportedly had some high-profile successes in various domains, like becoming world champion at a certain wargame or designing good integrated circuits.
Despite requests Lenat never released the source code. You can download an introductory paper: "Why AM and EURISKO appear to work" [PDF]. Honestly, reading it leaves a programmer still mystified about the internal workings of the AI: for example, what does the main loop look like? Researchers supposedly answered such questions in a more detailed publication, "EURISKO: A program that learns new heuristics and domain concepts." Artificial Intelligence (21): pp. 61-98. I couldn't find that paper available for download anywhere, and being in Russia I found it quite tricky to get a paper version. Maybe you Americans will have better luck with your local library? And to the best of my knowledge no one ever succeeded in (or even seriously tried) confirming Lenat's EURISKO results.
Today in 2009 this state of affairs looks laughable. A 30-year-old pivotal breakthrough in a large and important field... that never even got reproduced. What if it was a gigantic case of Clever Hans? How do you know? You're supposed to be a scientist, little one.
So my proposal to the LessWrong community: let's reimplement EURISKO!
We have some competent programmers here, don't we? We have open source tools and languages that weren't around in 1980. We can build an open source implementation available for all to play. In my book this counts as solid progress in the AI field.
Hell, I'd do it on my own if I had the goddamn paper.
Update: RichardKennaway has put Lenat's detailed papers up online, see the comments.
From what I remember of the papers, it was pretty clear (though perhaps not stated explicitly) that AM "happened across" many interesting factoids about math, but it was Lenat's intervention that declared them important and worth further study. I think your second paragraph implies this, but I wanted it to be explicit.
A reasonable interpretation of AM's success was that Lenat was able to recognize many important mathematical truths in AM's meanderings. Lenat never claimed any new discoveries on behalf of AM.
Yeah, that was basically what I meant. My hypothesis was that if you gave AM to someone with good mathematical aptitude but little prior knowledge, they would discover a lot more interesting mathematical statements than they would have without AM's help, by analogy to Lenat discovering more interesting logical consequences of the wargaming rules with EURISKO's help than any of the experienced players discovered themselves.