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elliptic curve expertsQuanta Magazine
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83% Informative
Elliptic curves, which date back to at least ancient Greece , are central to many areas of study.
They have a rich underlying structure that mathematicians have used to develop powerful techniques and theories.
But mathematicians still can’t answer some of the most basic questions about them.
They often try to characterize elliptic curves by studying special “rational points” that live on them.
Mathematicians have been using these surfaces to find higher-rank elliptic curves since the 1950s .
In 2006 , a prominent number theorist found an elliptic curve that he could show had a rank of at least 28 — beating the previous record of 24 .
Mathematician Zev Klagsbrun was an undergraduate student at Queens College in New York when Elkies announced his discovery in 2006 .
Elkies’ record stood for nearly two decades .
The discovery of a rank 29 curve expands the frontier of this uncharted realm of elliptic curves.
The researchers hope to find an infinite pile of curves guaranteed to have a rank of at least 22 .
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