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Nov 24, 2016 11:21 AM EST

Math Equations Are Beautiful, Here's Why

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When you say math is beautiful, a lot of people will disagree with raised eyebrows. How can you find beauty in a sea of numbers and the seemingly endless formulas? Yet Nobel laureate Paul Dirac proved otherwise when he described beauty in many ways using the quantum theory and gravity.

Math is beautiful not in how its symbols appear but in the power and elegance of its formula and arguments. Perhaps, no one can explain this beauty much better than Oxford mathematician Vicky Neale who compared math with music.

She said that when you listen to Mozart, you become enthralled by the beauty of his music. However, you don't print a page of that music and hang it on your wall. It's the same way with math - it's not about how it looks but about the underlying process.

Sir Michael Atiyah, an honorary professor of mathematics at Edinburgh University, agrees with her. He said that the brain responds to the beauty of math the same way it responds to the beauty of arts and music. Brain scans of mathematicians who perceives a certain formula beautiful has brain activity in the same emotional region when people appreciate art and music.

When you ask them what is the most beautiful equation in math, they will agree that it is the simple and short formula made by Swiss mathematician, Leonhard Euler: eiπ+1 = 0. The next one is Einsten's equation E=mc2.

What makes these two beautiful is the simplicity and compactness of the formula but packed with depth to those who truly understand them. In Euler's formula, circles, imaginary numbers, and exponentials converge while Einsten's marries the ideas of mass and energy, concepts that had seemed impossible to converge before Einstein put it in that simple equation.

The power of an equation to connect what seems to be unrelated realms often happens but we're not being taught that. For example, Euclid proved an ancient puzzle about the reality of infinite prime numbers by thinking about a universe where "the number of primes was not infinite." Then he began to ask what will happen if all those prime number will be multiplied all the way to the end. The answer is 1, which provides the answer. He then arrived at the conclusion that 1 is either a prime number itself making the original list incomplete.

As Hannah Fry, a lecturer in the mathematics of cities at UCL, said that "behind beautiful processes lies beautiful mathematics."

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