Saturday, July 06, 2019

The future of A.I.

I notice some tech execs making casual claims about A.I as if strong A.I is a reality, but to my knowledge that goal remains as elusive as ever. For instance:

Shor: Computer proofs really haven't undermined the concept of traditional mathematical proofs, at least not yet (although in 1993, some mathematicians were certainly afraid that they would). There are at least two reasons mathematicians look for proofs:

a) to ensure that the things they claim are actually true,

b) to gain more understanding into mathematics.

Computer proofs are generally satisfactory for the first reason above, but very few of them, if any, provide us any real understanding. There are certainly lots of computer-aided proofs now, where computers have helped in performing long calculations without error, or with elaborate case analyses.  But coming up with most mathematical proofs requires actual understanding of the underlying mathematics, and computers don't have that today. So computers can help mathematicians who understand the underlying mathematics by performing infeasibly long calculations and case analyses, but although they have been very useful for these purposes, most of the time they cannot come up with proofs by themselves.

It's possible that sometime far in the future, mathematics will be dominated by incomprehensible computer proofs. This might lead to “The End of Mathematics,” or at least of mathematics as carried out by human mathematicians. But we're nowhere near that point.

1 comment:

  1. Is this like lawrence Krause' claim that computers will ne sentient in 30 years?

    I know Max Tegmark ia teaching that conscience us just mathematics inside microtubules.

    Sounds like the tower of babel to me.