WATERLOO — James Moore says it took him just a few weeks and a handful of chalk to solve several famous math problems that have puzzled some of the world's greatest minds for hundreds of years.

But Moore, a self-described green energy consultant, said the professional math establishment refuses to acknowledge his supposed discovery.

This week, Moore rented the University of Waterloo's Humanities Theatre and unveiled his "historic breakthrough" to a sparse crowd.

The Cambridge-raised man said his work has been "vetted to death" by unnamed "professors on campus" and an overseas software company that he declined to identify. At the end of his presentation, he directed people to his website, where he was selling self-published copies of his findings at $27.05 a piece.

Moore, 48, suggested his work on the Twin Prime Conjecture and the Strong and Weak Goldbach Conjectures is like discovering the "Holy Grail" for prime numbers, which are numbers that are only divisible by one and themselves.

He claimed his discovery also solves several of the coveted Millennium Prize Problems, work that comes with $1-million prizes.

"I think solutions come when the time is right and, right now, the world needs it. It's here and now," he said. "We have slayed some of the toughest dragons in mathematics."

But at least one local math expert expressed extreme skepticism that Moore has done what he claims, and suggested he's just trying to sell books.

"The chances of a nonmathematician making any progress on such a thing, it's essentially zero," said Jeffery Shallit, a computer science professor at the University of Waterloo.

If there was really a breakthrough of the kind Moore claims, even by an unknown layperson, the math world would likely have heard about it, Shallit added. Moore's explanation of his work suggested a fundamental misunderstanding of the basic challenges of prime numbers, Shallit said.

Typically, major mathematical advances are posted on publicly-accessible archives and eventually published after a thorough vetting process. Moore isn't listed as the author of any papers on MathSciNet, an online database that reviews all noteworthy math publications, he said.

"I've never heard of him, he's never published anything … and he's going about this in a very strange way," Shallit said.

Moore said he's not surprised by the skepticism.

"If you come up with the solution to something that has been questioned by great mathematicians for hundreds, if not thousands, of years, the first thing that pops into these guys' heads is, 'Sure. It's not possible,' " he said.

He called his discovery a historical moment that promised to change digital banking security forever by making financial transactions hacker-proof.

Moore bills himself as one of the world's "leading experts on prime numbers," and says his education as an engineer at the University of Waterloo trained him to solve complicated problems.

Moore also says he's a regular guest lecturer at Waterloo's faculty of engineering, although he's not licensed with the Professional Engineers of Ontario. Moore says he doesn't need a licence because his work is focused only on research and development.

The solutions to the prime number problems were hiding in plain sight, Moore said. He showed the small crowd a long string of equations that illustrated basic patterns of prime numbers, but it wasn't entirely clear what was groundbreaking.

"In the past, mathematics have been very complicated in trying to solve this. It started out complicated and it got more complicated after that," he said. "One of the reasons I found it was because I wasn't trained like that. I came at it from a much more simplistic standpoint."

On Monday, he presented himself as an inventor and a math prodigy, claiming he was so advanced in his class in Grade 6 that he was separated from the rest of the students and made to do math in a room by himself.

Moore said he solved the prime number problems after borrowing two books from a library branch in Cambridge.

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"I just took chalk to chalkboard and, within a few weeks, there we were," he said.

Moore says he's the chief executive officer of a one-person company called Halcyon Systems Inc. that he says "specializes in research and development of next generation green technologies." He said he couldn't talk about any of the company's projects.

He also said he used to work for the City of Kitchener retrofitting buildings for energy efficiency. In 2004, Moore appeared at a public forum in Kitchener asking for a $60-million investment in a green energy fund that would go toward local projects.