Building a supercomputer that would solve unsolved mathematical problems

[Eddy Street]

What if we built a supercomputer and fed it all the mathematical knowledge we have today and allowed it to use this knowledge to prove things like the Goldblach conjecture or the Reimann hypothesis? The computer would go through its database and create a solution or a number of distinct solutions which mathematicians would later try to decipher. This computer could also be used to make new connections and create new theorems or new entirely mathematics. What do you think of this?

[mathematic]

Computers are intrinsically extremely dumb. They can calculate very fast, but can only do things that programmers (people) tell them. For example: the four color problem was solved because someone was able to break down the problem into a finite number of cases and told the computer how to analyze each case.

[Strange]

There are computer programs to prove theorems and to generate new theorems. The trouble is, nearly all the theorems the generated are of no real significance. For example: http://theorymine.co.uk/

 

IS MY THEOREM INTERESTING?

TheoryMine applies a series of filters to remove uninteresting theorems before it generates them. On the other hand, don't expect your theorem to earn you the Fields Medal! (the Nobel Prize of Mathematics).

 

 

p.s. Sorry, mathematic, I accidentally down-voted your answer (and there doesn't seem to be any way to undo it)...

[Sato]

I think an analog to this would be asking if we could have used Kim Peek to solve all these unsolved mathematical problems like the Goldbach conjecture or Reimann hypothesis. Human intellectual prowess is distinct because of our ability to manage and understand abstractions and our [mathematical] ability to quantitatively understand the world around us and derive abstract ideas and concepts from it; having them, we're able to observe, tinker with, and analyze these abstractions. This, I believe is significantly more important than memory and processing speed, which is encapsulated in my reference to Kim Peek. He retained immediate recall to ~98% of the information he absorbed word-for-word and could read extremely fast (I think ~800 WPM with each eye, as his split them between pages). He could also likely do arithmetic with very large numbers very fast and numerical table look ups. But, he was disabled in terms of comprehension and mathematical ability; I think his tested I.Q. was an 88 if I recall correctly. Computers are not much different than Kim if you're looking at the potential to solve the problems you posed, but I think that A.I. developments will be able to create a simulated ability to work on such problems. I have worked with genetic algorithms and ANN's before (albeit just via a MOOC) and can see how certain things can be managed with them (such as via brute-force), but I am not seeing how others can.

 

 

Edit:

Strange: There is no way to undo it, but don't worry as it has been pushed back up to a 0.

Edited August 7, 2013 by Sato

[HalfWit]

Solving a hard math problem is nothing like starting from axioms and blindly trying to reach the desired theorem. Look at Wiles's proof of FLT. He spent seven years attacking the problem with new ideas from the field of advanced algebraic number theory. The idea in math is to have an insight. Computers don't have insights; or at the very least, we have not yet figured out how to create a machine that has insights. We might do so in the future, but how would we even approach the problem? It's very difficult.

 

Contrast math with chess; a discipline in which it was once thought that human players using insight could always defeat a "look-ahead" computer program. But it turns out that chess programs can use brute-force algorithms to defeat the best human players in the world. In the field of chess-related artificial intelligence, brute-force algorithms have handily won out over insight or gestalt algorithms.

 

But math genuinely is different. Advanced math is about finding a new perspective, building a new conceptual structure, or even using new foundational principles. You can't just bang together axioms and hope a valuable theorem will drop out. Because the definition of "valuable" is a subjective, esthetic value judgment made by human mathematicians.

Edited August 16, 2013 by HalfWit

[Thorham]

Computers are intrinsically extremely dumb. They can calculate very fast, but can only do things that programmers (people) tell them.

So are brains, they can only do things for which they are wired up. A brain without connections between the neurons can't do anything more than a computer without software.

Edited August 20, 2013 by Thorham