# Angela Moore ’12 The Million Dollar Question: The Beal Conjecture

It’s literally a million dollar question. Anyone who can solve The Beal Conjecture, a number theory based on Pierre de Fermat’s 1637 “Last Theorem,” will be awarded a million dollar prize, funded by D. Andrew Beal, a prominent banker and mathematics enthusiast.

Angela Moore ’12, another mathematics enthusiast and lifelong lover of puzzles, heard about the conjecture in 2013 and decided to try her hand at what’s become known as the “unsolvable math problem.” Her foray into the problem led her to California, where she presented her idea at a conference for mathematicians.

“In 2013, a lot of people were talking about the Beal’s Conjecture and I knew enough math to understand it and thought it would be an interesting way to pass the time,” Moore said.

For most people, solving a complex mathematics theorem doesn’t sound like an ideal way to pass the time, but for Moore it was a fun challenge. “I’ve always liked puzzles and games — I’m a huge chess player,” she explained. Working on this problem involved a lot of trial and error as well as playing around with different concepts, which Moore said was similar to how she solves puzzles.

The Beal’s Conjecture states if Ax + By = Cz, where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor. After several months of working on the problem, Moore devised a counterexample that challenges what’s commonly accepted about the integer zero.

“The more I played around with it and tested out different options, the more I thought, ‘too bad you can’t use zero in the equation, because it’s not a positive integer,’” Moore said.

That thought led Moore to look at the history of the commonly understood neutral number. “In some mathematical cases,” Moore said, “zero is positive, so taking that into account, it might be able to disprove Beal’s theory.” From there, Moore devised a counterexample to Beal’s Conjecture, which states that “positive zero” might be different than “neutral zero” and may even be a positive integer in certain instances.  She then submitted it to the 19th Annual CMC3 Recreational Math Conference held in Lake Tahoe, Calif., where it was accepted for presentation and publication in their refereed conference proceedings.  Prior to acceptance, her paper was posted on arXiv, a Cornell University “pre-print” server.

Not a bad result, for a recreational math lover. Surprisingly, Moore didn’t major in mathematics while at Fairfield, although she has always excelled at the courses she took. Instead, she majored in sociology and anthropology and minored in philosophy.  She was also inducted into Fairfield University’s chapter of Phi Sigma Tau – the International Honor Society in Philosophy.

Currently the New Haven, Conn., native works at Yale University in the Human Research Protection Program. She’s also pursuing an entrepreneurial project, a comic series titled Truth, 30% Off, geared toward children that addresses social development issues like peer pressure and problems with body image.

As for her side hobby, following Moore’s presentation at the conference, she will submit it to the Beal’s Conjecture Committee (which requires all submissions to be published in a refereed mathematics publication). It may take up to two years for a decision to be made, particularly since Moore is challenging the concept of zero. “My submission uses a philosophical approach that will require debate,” Moore said. “It’s an intense conversation.”

When he offered the prize money in the 1980s, Beal said he wanted to inspire young people to become interested in mathematics, which Moore wholeheartedly agrees with. “A lot of people are afraid of math. There needs to be more ways to make it fun, interesting and applicable to teenagers,” she said. “The more games and puzzles that can be incorporated into teaching it, the better.”

Puzzles and games are what led Moore to work on a problem that could eventually change the concept of zero, after all. And while her counterexample may or may not win the prize, the journey has been a good one. Moore said, “I’ve had so many different hobbies and not all turn out well, of course, but if I’m interested, I’ll try it out. The worst-case scenario is that you’ll fail, but you’ll learn from that experience.”