AI: Why hasn't a robot solved one of the "unsolved mathematical questions"? Why shouldn't these "unsolved mathematical questions" be solved by "algorithmic approaches"?
Dennis
Dennis Mazur
Hi Dennis,
In general, it is not clear can everithing be expressed by means of the so called effectively calculable functions. If you take a look at the Church-Turing thesis you will see the nature of the problem... See " Non-computable functions" here for ex. : https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis#complexity-theoretic_Church%E2%80%93Turing_thesis
In my personal opnion, not everithing can be expressed in a form, calculable by a machine, so I accept the original Church-Turing thesis.
Regards,
Velina
Solving mathematical problem requires meta-mathematics and meta-mathematics needs meta-meta-mathematics ... and so on.
Machines haven't self reference, reflexion and are so far from existence ...
I have indirectly given an answer to this absolutely pertinent and fascinating question in my treatise 'Laws of Singularity'. tldr: no AI can pass the threshold of mathematical inventiveness without a) a 'body', b) an instance of 'I think', an at least formal consciousness c) the ability to compute non-digitally. See Article Laws of Singularity
I assume that the question really means ‘well known’ unsolved problems - otherwise if we take robot to include automated theorem prover the proof that every Robbins Algebra is a Boolean Algebras - a problem fist solved by an automatectheorem prover and published by (I think) by Wos, Winkler and McCune should qualify.
Aside from the issues regarding (non-)computable functions, there are no doubt questions that unbeknownst to us have no solution, as well as questions whose solution cannot be found because the number of steps required to reach it ensures that entropy will end the computation before it can be completed.
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