## Posts Tagged ‘**Automated theorem proving**’

## This is cool, but I’m holding out for a disease…

Hankering for a little immortality? ** New Scientist has the answer**:

While most mathematical theorems result from weeks of hard work and possibly a few broken pencils, mine comes courtesy of TheoryMine, a company selling personalised theorems as novelty gifts for £15 a pop.

Its automated theorem-proving software can churn out a theoretically infinite number of theorems for customers wishing to join the ranks of Pythagoras and Fermat. “We generate new theorems and let people name them after themselves, a friend, a loved one, or whoever they want to name it after,” explains Flaminia Cavallo, managing director of TheoryMine, based in Edinburgh, UK…

“We’re inventing totally novel theorems, and the tradition is you have the right to name these theorems,” explains Alan Bundy, professor of automated reasoning at the University of Edinburgh and another member of the TheoryMine team. “There are 10 star companies out there, and none of them have any affiliation to the International Astronomical Union.”

He’s got a point. Automated theorem proving is a well-respected mathematical field, used by manufacturers to guarantee that the algorithms in computer processors will work correctly. Bundy and his colleagues have worked in this area for a number of years, and Cavallo came up with the idea for TheoryMine during her final year of an undergraduate degree in artificial intelligence and mathematics at the University of Edinburgh, where she wrote a program to generate novel theorems for her dissertation.

From its library of mathematical knowledge, the program generates a set of mathematical axioms, then combines them in different ways to produce a series of conjectures. It then uses the library to discard a portion of these on the basis that there are already counter-examples, showing they can’t be true. Overly complex conjectures are also ignored. Then it applies a technique known as “rippling”, in which it tries out various sequences of logical statements until one of these sequences turns out to be a proof of the theorem…

“It’s a clever idea,” says Lawrence Paulson, a computational logician at the University of Cambridge and the creator of Isabelle, a theorem prover that Cavallo’s program uses. He is more interested in the theory behind the new program though, adding that “some of the technology here is quite impressive, and I would hope that it finds other applications apart from selling certificates”.

It may well do. Lucas Dixon, another TheoryMiner, is investigating the possibility of using the same techniques to elucidate the rules of algebra in quantum computing systems, which follow different mathematical rules to classical systems.

Don’t prepare your Fields medal acceptance speech just yet though, as TheoryMine’s theorems are unlikely to break drastically new ground. “We can’t say that we’ll never do that, but having looked at the things that come out, they’re not typically things that are going to change the world,” says Dixon.

Your correspondent just purchased “Eleanor’s Equation” for his daughter; reader’s can score their own mathematical monument at **TheoryMine**.

**As we search for the “rum” in theorum,”** we might wish a Buon Compleanno to Count Francesco Algarotti, the philosopher, critic, and popularizer of complex scientific ideas; he was born in Venice on this date in 1712– and wrote *Neutonianismo per le dame* (*Newtonism for Ladies*) when he was 21.

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