“I look at a piano, I see a bunch of keys, three pedals, and a box of wood. But Beethoven, Mozart, they saw it, they could just play.”
When it comes to advanced math and science, says Will Hunting, the character played by Matt Damon in the 1997 Oscar-winning drama “Good Will Hunting,” “I could always just play.”
His character, a janitor with an innate mathematical prowess, could see the solutions that eluded MIT students.
Today, in China, a real-life Will Hunting is generating excitement and awe. Yu Jianchun, a Chinese package delivery worker without a college degree, has developed a new method to identify Carmichael numbers that reflects a creative look at a problem that has long stumped mathematicians.
His solution inspired praise from academics around the globe, and, if verified, could represent an exciting discovery for the field of Carmichael numbers, William Banks, a mathematician at the University of Missouri who works with Carmichael numbers told CNN.
Yu, a migrant worker from the mountainous Henan province, visited local universities in each new city he found work, seeking confirmation of his formulas. He had been emailing prominent Chinese mathematicians with the newly-developed Carmichael formulas for eight years to no avail, until Cai Tianxin, a math professor at Zhejiang University, invited him to present his solutions to four math problems at a public seminar. Professor Cai also plans to publish Yu’s theory in a book on Carmichael numbers.
“It was a very imaginative solution. He has never received any systematic training in number theory nor taken advanced math classes,” Cai told CNN. “All he has is an instinct and an extreme sensitivity to numbers.”
Yu told CNN he was “overwhelmed with joy” to discover a solution completely different from the classic algorithm for identifying the “pseudoprimes.” Carmichael numbers pass Fermat’s test for prime numbers, even though they don't meet the criteria for prime numbers, since they're divisible by more than 1 and themselves, making it more complicated to identify true prime numbers. R. D. Carmichael discovered 15 examples in 1910 and theorized that there were infinitely many.
As mathematicians discover increasingly large prime numbers, they're focused on sorting them out from the numbers that appear to be prime at first examination. Carmichael numbers, which begin 561, 1105, 1729, 2465, etc., also play an important role for computer science and information security.
"I made my discoveries through intuition," Yu told China Topix. "I would write down what I thought when inspirations struck about the Carmichael. I have hard work and make a hard living, but I insist on my studies."
Yu likely won't have to limit mathematics to his free time any longer.
After his findings made the news, Yu became a local celebrity and Silk Road Holding Group, a company based in Huzhou, offered to employ him in a statistics-related position.
The job would "give him better development for a career and also more time for furthering his interest and talent in mathematics,” Ling Lanfang, president of the group, told China Daily.
Yu says he hasn’t seen "Good Will Hunting," but his study of math may have familiarized him with another real-life math genius mentioned in the film, Srinivasa Ramanujan.
In the movie, therapist Sean Maguire, played by Robin Williams, compares Will with the self-taught Mr. Ramanujan, who made extraordinary contributions to number theory and infinite series despite having almost no formal training in pure mathematics.
Born in South India, Ramanujan was a college dropout from a poor family who filled notebooks of mathematical discoveries that he mailed off to prominent math scholars in India and England. He was dismissed repeatedly as a hoax.
Just as Yu’s scattershot method of reaching out to academics eventually connected him with Cai, Ramanujan found a mentor in Cambridge University mathematician G. H. Hardy, who recognized his genius and invited him to England
Ramanujan arrived at his answers "by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account," Hardy described. "I have never met his equal."