Anthropic’s AI steals mathematicians’ record for most complicated curve
A search for the most complex elliptic curves has taken mathematicians years. Claude beat the record in days
Anthropic's artificial intelligence, Claude, has broken a longstanding record in the field of mathematics. Mathematicians have spent years searching for the most complicated elliptic curves, but Claude quickly achieved a feat that took them decades. Elliptic curves are essentially curves and lines, with the complexity determined by their rank—a higher rank means more complex patterns and more distributed points along the curve.
The current record, held by mathematicians Levent Alpöge and Ava Howell, features an elliptic curve with a rank of at least 31, achieved in just a few days. This breakthrough comes after an 18-year period where progress was minimal, as mathematicians strived to surpass the previous record of rank 30. The underlying elliptic curves of the equations may appear simple, but they have intrigued mathematicians for centuries.
The distribution of rational points on these curves, which are values of x and y that can be expressed as fractions and satisfy the equation, is of particular interest. The rank of an elliptic curve signifies the number of independent families of rational points, with higher ranks indicating more complex patterns. The possibility of finding elliptic curves with infinitely high degrees remains an open question in number theory.
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