The usually solitary, hermetic world of mathematics has begun to buzz – thanks to an unassuming Chinese-born mathematician with a reputation for solving the unsolvable.
Sixty-seven-year-old Yitang Zhang may have taken a key step towards understanding the most important unsolved problem in mathematics, a problem that has vexed academics for more than a century.
More than 20 years ago, Zhang, now a professor at the University of California, Santa Barbara, began to tackle a conjecture related to the Riemann hypothesis, a formula for the distribution of prime numbers.
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On Saturday, a 111-page manuscript that seems to have been written by Zhang, began to circulate in the research community. The article showed a proof related to the Riemann hypothesis.
The paper, “Discrete mean estimates and the Landau-Siegel zero”, has neither been peer reviewed nor confirmed by Zhang himself, but if verified, it could be a historic breakthrough for number theory and mathematics in general, according to experts.
First proposed by German mathematician Bernhard Riemann in 1859, the Riemann hypothesis concerns the location of solutions to the so-called Riemann zeta function, which has crucial implications for the distribution of prime numbers.
The problem has become so formidable that the Clay Mathematics Institute, a US non-profit foundation dedicated to increasing mathematical awareness, has offered a US$1 million prize to anyone who can solve it.
“The Riemann hypothesis is rightly regarded as the jewel in the crown in mathematics,” a researcher from the Academy of Mathematics and Systems Science in Beijing said on Monday.
The problem, which first surfaced in the study of prime numbers, was later found to have major implications beyond number theory, for instance in nuclear and quantum physics, said the researcher, who asked to remain anonymous.
One of those implications would be that if the Riemann hypothesis is correct, then another famous conjecture might die.
While the Landau-Siegel conjecture – named after mathematicians Edmund Landau and Carl Siegel – concerns the possible existence of zero points of a type of L-functions in number theory, the existence of Landau-Siegel zero points would be potential counterexamples to the Riemann hypothesis, the researcher said.
“What Zhang has done is to give a very strong lower bound on the L-functions – very close to the original theorem stated by Siegel, but not yet to rule out the zero points completely as stated in the original Landau-Siegel conjecture,” the researcher said.
The paper would mark “a very significant step forward” if proven true after strict scrutiny by the mathematics community. “We will know the outcome probably in a few months’ time,” he said.
Zhang will present his work on Tuesday, when he is set to give an online talk organised by Peking University. It will be the first time he has met the public since rumours of his work began in mid-October.
If Zhang’s paper holds up to scrutiny, it could be the mathematician’s second landmark contribution to the understanding of prime numbers.
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In 2013, the then obscure 57-year-old lecturer from the University of New Hampshire shocked the academic world with his work on the so-called twin-prime conjecture.
The conjecture proposed that there were an infinite number of pairs of primes that differ by 2. Zhang used a unique approach to prove this true with twin primes that differ by less than 70 million – an approach that can be used to eventually reduce the difference down to 2 – the ultimate goal.
Born in Shanghai in 1955, Zhang taught himself high school maths at age 11, but because of the Cultural Revolution, he could not attend high school. After working in the fields and at a factory for several years, Zhang was admitted to Peking University and obtained his master’s degree in mathematics in 1984.
Zhang then moved to the United States to obtain a PhD in mathematics. But after graduating from Purdue University in 1991, he had trouble finding an academic position. To make ends meet, Zhang is said to have worked as an accountant, a restaurant manager, and even as a Chinese food delivery person, while at one point having to live in his car.
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After he began teaching pre-algebra and calculus at the University of New Hampshire in 1999, Zhang seemed to have published only one paper before his 2013 breakthrough.
“If someone asks me why I can succeed, I will first tell them to persevere. If you really love math, stick to it and never give up,” Zhang said during a talk at Soochow University in Suzhou in 2019.
“Be bold enough to challenge the big problems and do not lose heart in the face of setbacks.”
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