Isn't it terrifying that AI can become smarter than any Mathematician?

[SSequence]

Can AI be trained to prove only interesting theorems? If yes, can it be trained to explain us why they are interesting? As a specific example, I have in mind the Godel incompleteness theorems.

Well, for one, many/most of the theorems of (ordinary) computation theory [say in literature etc.] should, in principle, be provable in sufficiently powerful axiomatic systems.

I suspect that if one tries to look for results of negative nature (no program can do this etc.) then probably this can serve as the most basic "filter" as a starting point (for results similar to what you mentioned).

===========================

Of course the question of "interesting" in general is well much more broad than this. As with most other questions of this type [including the one in OP], one can take two different viewpoints (mechanical/aesthetic or theoretical/practical distinction depending on question).

Here we have:
(i) purely mechanical [mechanical isn't the best word here, but I don't know of an alternative] viewpoint
(ii) aesthetic viewpoint on this.

(i) If we take a mechanical viewpoint we can say that nothing is really interesting or non-interesting. It is just that based on several factors (our lifespans, information processing speed, physical limitations on movements etc.) we only take those statements to be interesting which feel "short"/"elegant" enough to us.

(ii) The aesthetic viewpoint would not accept (i).

 

[BWV]

Rumor is most of the mentors and science advisors here are bots, part of some secret program at Google

 

[jaketodd]

Here we have:
(i) purely mechanical [mechanical isn't the best word here, but I don't know of an alternative] viewpoint
(ii) aesthetic viewpoint on this.

(i) If we take a mechanical viewpoint we can say that nothing is really interesting or non-interesting. It is just that based on several factors (our lifespans, information processing speed, physical limitations on movements etc.) we only take those statements to be interesting which feel "short"/"elegant" enough to us.

(ii) The aesthetic viewpoint would not accept (i).

Before letting machines take over too much, it's important to realize that our knowledge and understanding and feelings are not completely understood. So a computer "thinking" may not be thinking as we think. I firmly believe that we are a lot more than our incomplete understanding of ourselves and the world. So just because computers can be made to think and make decisions, doesn't mean they are anywhere near what you and I are.

 

[jaketodd]

Rumor is most of the mentors and science advisors here are bots, part of some secret program at Google

Do you have a link? Thanks

 

[Ralph Dratman]

in actual history, when computers enter a new field, they have always helped people do their existing jobs. Actually replacing people is rare, as far as I can see. At worst, I suspect mathematicians will be enabled to spend more time asking challenging questions and combining new answers with existing mathematics to ask even more new questions. That doesn't sound so bad to me.

 

[mfb]

Do you have a link? Thanks

My algorithms are 99.7% confident that the following is a link, and 72.3% confident that the linked post is related to the topic:

https://www.physicsforums.com/threads/most-likes-page.912736/page-9#post-6151556

It's somewhat of a running gag in many internet forums.

in actual history, when computers enter a new field, they have always helped people do their existing jobs. Actually replacing people is rare, as far as I can see.

People no longer route phone calls by hand. All the big mail sorting in first world countries is done by machines today (well, most of the time at least...). "Type this properly with the typewriter" jobs are largely gone and many reasons to write, send and deliver physical mail disappeared due to computers. Some subways are driven by a computer - no train conductor jobs in them. In the near future the demand for truck and taxi drivers will go down notably and that's a big employment sector. At the same time many new jobs appeared that didn't exist without computers, of course.