# Prime Challenge: a massively important math problem

While it doesn’t have the same cache as this year’s discovery of a Franklin ship, another mystery from the 1800s may be on the cusp of being solved in Yellowknife that would send shockwaves around the world.

Considered the most important mathematical challenge of the century, Donald Mackay says he believes he is close to proving the Riemann Hypothesis.

If you’ve never heard of the Riemann (pronounced Ree-man) Hypothesis, you are likely; a) not a math geek, b) not working in secured financial encryption or software coding, and c) not alone. But if you are obsessed with it, like the 36-year-old mechanical-engineer-turned music producer who moved here from Halifax, you can think of little else. In fact, the lanky Mackay – who bears more than a passing resemblance to Shaggy of Scooby-Doo with his green sweater and untrimmed beard – spends much of his day in meditation in Old Town, clearing his mind for what he calls “the great white whale” of mathematics; how prime numbers are distributed.

Were he to discover a prime pattern, Mackay could literally bring the world’s banking systems, and other forms of security, to its knees, since the algorithms that protect those online infrastructures now rely on unorganized prime numbers. Think Y2K, only this time for real.

Prime numbers, in case you forget, have no natural divisors other than one and the number itself. (For example 2, 3, 5, and 7 are prime numbers, since no two numbers multiplied together can equal 2, 3, 5, or 7, other than 1X2, 1X3, 1X5 or 1X7).

If Mackay could decipher how they are distributed, he’d also earn \$1 million from the Clay Mathematics Institute, a privately-funded charitable organization in Boston that has deemed the Riemann Hypothesis one of its seven Millennial Prize Problems. While money and high-stakes hacking don’t seem to be his motivation – he says he just really loves math – Mackay acknowledges that new insights on the Riemann Hypothesis would “probably be worth billions, considering their far-reaching implications.”

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The problem dates back to 300 BC when Euclid determined prime numbers are infinite, but could not find their pattern.

Then in 1895, German mathematician Bernhard Riemann produced calculations that pointed to an underlying order to all primes. Even though no one has since been able to prove or disprove his hypothesis, a guy named Albert Einstein found Riemann’s calculations useful when he was working on a little something called the theory of relativity.

Donald Mackay contemplates math, music and spaces between. | photo Pat Kane

So what makes Mackay believe he can crack the code for a problem that’s vexed so many brilliant minds for so long?

“I’m bringing music concepts and harmonics into the world of math,” he says. “While mathematicians have been investigating the prime number theorem for centuries, I believe they are, ironically, limited by the tools of their trade. No one is turning to music for the answers.”

Mackay says his training in applied mathematics combined with his love for music as a composer and sound engineer – he ran the Spaces Between Sound Studio in Halifax for almost a decade, recording such artists as Jenn Grant and Amelia Curran after graduating from mechanical engineering at the University of Waterloo – puts him in a unique position to hunt for hints and patterns which would escape both a pure mathematician and a musician.

“Prime numbers are a form of vibration, but we treat them as statements of linear logic,” he says.

There’s always been a relationship between length (math) and corresponding sounds – the length of strings on a guitar or in a piano for example – which have been turned into the western musical scale. And Mackay says there’s evidence the human ear links sound to prime numbers. The cochlea, the key part of the inner ear responsible for hearing, decodes 20,000 frequencies of sound into nerve impulses. Its spiral, snail-like shape is in interval lengths that appear to follow the prime number distribution.

For the past four years Mackay has been conceptualizing these links in a multi-visual, multi-dimensional project he calls Axiomatic Art. Using AutoCAD, a computer software program familiar to engineers and architects, his graphs, sketches, math equations, songs and diagrams create a fascinating, albeit mind-boggling, journey through space, number theory, physics and sound.

Some of Mackay’s penciled calculations.

The Canada Council has awarded him an inter-arts grant to continue working on the project. Having lived in Yellowknife on a co-op placement as an engineering student, he was familiar with what he calls the “resonating expansiveness” its natural setting has to offer an artist, or a mathematician. So he’s tucked away in a historic Old Town shack at least until May, trying to find the “spaces between” that will solve the age-old mystery of prime numbers.

He’s fond of quoting Charles Darwin when describing the limitations and nature of such work: “A mathematician is a blind man in a dark room looking for a black cat which isn’t there.”

“I’ve basically got a couple golden keys and I’m just hunting my way down to try them in the lock,” adds Mackay. “I feel like something’s getting close, and that makes me

really nervous.”

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