# Automated Theorem Proving and Manufacturing

# Automated Theorem Proving and Manufacturing

### There have been computer-verified proofs of important mathematical theorems, but I’m not aware of any interesting discoveries that have come out of a theorem prover.

Join the DZone community and get the full member experience.

Join For FreeBuckled up and all set to kick-start your Agile transformation journey? 10 Road Signs to watch out for in your Agile journey. Brought to you in partnership with Jile.

When I first heard of automated theorem proving, I imagined computers being programmed to search for mathematical theorems interesting to a wide audience. Maybe that’s what a few of the pioneers in the area had in mind, too — but that’s not how things developed.

The biggest uses for automated theorem proving have been highly specialized applications, not mathematically interesting theorems. Computer chip manufacturers use formal methods to verify that given certain inputs their chips produce certain outputs. Compiler writers use formal methods to verify that their software does the right thing. A theorem saying your product behaves correctly is very valuable to you and your customers, but nobody else. These aren’t the kinds of theorems that anyone would cite the way they might cite the Pythagorean theorem. Nobody would ever say “And therefore, by the theorem showing that this particular pacemaker will not fall into certain error modes, I now prove this result unrelated to pacemakers.”

Automated theorem provers are important in these highly specialized applications in part because the results are of such limited interest. For every theorem of wide mathematical interest, there are a large number of mathematicians who are searching for a proof or who are willing to scrutinize a proposed proof. A theorem saying that a piece of electronics performs correctly appeals to only the tiniest audience, and yet is probably much easier (for a computer) to prove.

The term “automated theorem proving” is overloaded to mean a couple things. It’s used broadly to include any use of computing in proving theorems, and it’s used more narrowly to mean software that searches for proofs or even new theorems. Most theorem provers in the broad sense are not automated theorem provers in the more narrow sense but rather proof assistants. They verify proofs rather than discover them. (There’s some gray zone. They may search on a small scale, looking for a way to prove a minor narrow result, but not search for the entire proof to a big theorem.) There have been computer-verified proofs of important mathematical theorems, such as the Feit-Thompson theorem from group theory, but I’m not aware of any generally interesting discoveries that have come out of a theorem prover.

What does it mean by Scaling Agile? Download the whitepaper on Five dimensions of Scaling Agile in Large Enterprises. Brought to you in partnership with Jile.

Published at DZone with permission of John Cook , DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

## {{ parent.title || parent.header.title}}

## {{ parent.tldr }}

## {{ parent.linkDescription }}

{{ parent.urlSource.name }}