Around 2,400 years ago the Athenians were blighted by a plague and thought they should appease their gods. They asked the Oracle of Delos how they might do so and were told to double the volume of their altar to Apollo.
The stonemasons set to work doubling its size. But when finished, they realised they had created an altar eight times as large – rather than twice the volume. Thus was born math’s famed Delian problem.
The stonemasons’ difficulty was that the original altar was cube-shaped. And in the ensuing centuries mathematicians have struggled to figure out how to double a cube’s volume. Like the Greeks the problem-solver must make do with only an unmarked straight edge and a compass (recall the thing you used at school to draw a circle) to aid their calculations.
Incredibly, a problem that eluded the greatest mathematical minds of the past two millennia may have been solved by a farmer from Fengdu County in Chongqing.
After 35 years of research, the self-taught mathematician says he’s 70% confident that he’s likewise solved two more of the great unsolved geometric questions (circle squaring and angle trisection).
Li Yaming recently posted his results on the internet asking the academic community to verify his findings. Suspecting a hoax, the Chongqing Economic Times tracked him down. They found a 62 year-old in possession of 11 plastic bags, containing thousands of pages of geometry and calculus. “These are my life’s work,” he told the reporter.
Li says he has been obsessed with maths since his early teens but was forced by economic circumstance to leave school at 16 and become a farmer. He undertook a course of self-study but couldn’t afford paper or pens. So he obtained old newspapers from the local government and wrote on scraps. When his pens ran out he would go to a nearby school. “The local students regarded him as a madman,” writes the newspaper, “and would give him a pen to show sympathy.”
Li’s mathematical obsession led to quarrels with his wife. “This cannot make money, how could I not blame him?” she still complains. His eldest daughter adds: “We just hope some experts can come and check out my father’s work so that we can live a normal life.”
Li says failing eyesight means he doesn’t think he’ll be able to carry on with research too much longer. But he says he cares little about money or fame: “I just want to crack the eternal problems of geometry.”
If a self-taught farmer has solved all three Greek problems, it could offer another argument for those who believe the Chinese have superior mathematical skills.
But has he really done it? The experts may soon pour cold water on his efforts. For example, Descartes proved that the Delian problem was impossible in 1637, declaring it was only soluble using a Neusis construction that allowed the use of a marked ruler. After 35 years of toil, it would be best not to mention it to Li. And especially to his wife.
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