Tag Archives: Beautiful Patterns

An Infinite Series of Beautiful Patterns

You’ve probably heard this story, but it bears repeating: In 1918, when Cambridge mathematician G. H. Hardy visited his protégé, Srinivasa Ramanujan, at Putney, they boarded cab number 1729. Habitually given to looking for distinguishing patterns in numbers, Hardy felt compelled to remark to Ramanujan that he found 1,729 rather dull. Promptly disagreeing, Ramanujan responded with the number’s exceptional characteristics: 1,729 is the smallest number that can be written as the sum of two cubes in two different ways (123 + 13 and 103 + 93).

When New Yorker reporter Charles Bethea asked Emory mathematics professor Ken Ono what was unique about the number 73—which represented the record number of wins that the Golden State Warriors were poised to notch for the 2016 NBA season—Ono’s response was equally inspired. “I like the number,” he told Bethea. “It is the sixth emirp.” Emirp is prime spelt backwards and emirps, Ono explained, are prime numbers that are also primes when written backwards. So 73 as well as 37 are prime numbers.

The creativity behind discovering patterns in numbers and equations was brought up at a panel discussion at Stanford on the making of the film, The Man Who Knew Infinity, based on Ramanujan’s life. Ono was a panelist at the event and he used the word “artistry” to describe Ramanujan’s work. Others on the panel—Princeton professor of mathematics Manjul Bhargava and the director of the film, Matthew Brown—seemed completely at ease with this idea of Ramanujan’s work being an expressive art form.

Indeed, when Ramanujan’s process of discovery is examined and compared to other great artists, so many parallels can be found.

Leonardo da Vinci, the artist who gave us The Last Supper and Mona Lisa, was known to be obsessively driven to observe, record, analyze and sketch. His art form was decidedly scientific in its approach. His paintings are breathtaking observations of nature and the puissant energy of movement and stillness.

So also Beethoven, Bach, and Indian artist and mandolin maestro U. Srinivas. These musicians explicated the purpose and vitality of sound through a rigorous investigative process.

Ramanajun’s three legendary notebooks contain between 3,000 to 4,000 mathematical discoveries. He had in abundance what is essential for any artist: keen insight, and a talent for persistence.

Ramanujan was engrossed in the explorations of equations just as an artist would. To the exclusion of things and people around him. In a 1987 BBC documentary on Ramanujan, his wife Janakiammal says, “All I can tell you is that day and night he worked on sums. He didn’t do anything else. He wasn’t interested in anything else. Just sums. He wouldn’t stop work even to eat. We had to make rice balls for him and place them in the palm of his hand. Isn’t that extraordinary?”

There’s a particular and startling beauty in finding patterns, whether in numbers, words, behavior, music or in natural formations around us. And to questions about that beauty, Hungarian mathematician Paul Erdos is famously known to have said, “it is like asking why is Beethoven’s ‘Ninth Symphony’ beautiful? If you don’t see why, someone can’t tell you.”

Perhaps the point is not to question whether Ramanujan was an artist or a scientist. For it is only in the intersection of the two that extraordinary works of genius are produced. Without analytical bearing, poetry is a mere collection of words set to meter. Without recognizing the exquisite skill it takes and the knowledge it exposes, math is a mere tedious process of proofs and calculations.

A work of art must radiate an uncommon perception. A work of science must uncover hidden truths. And each requires a particular skill and rare imagination. Ramanujan’s equations and theories advanced our knowledge of how we relate to the world around us. He drew exceptional patterns with ordinary numbers and gave infinite color to our world. He was an uncommon artist in the pursuit of truth.