In August, mathematicians discovered an exotic, record-breaking elliptic curve, unlocking major questions about these fundamental equations. Considered crucial in various studies and cryptography, elliptic curves continue to mystify mathematicians with unanswered queries regarding their patterns of “rational points.” Noam Elkies & Zev Klagsbrun recently shattered an 18-year-old record by finding a curve with the most complex rational point pattern. This breakthrough hints at the infinite possibilities and challenges within elliptic curves. Through their innovative approach and painstaking computational methods, Elkies and Klagsbrun continue to push the boundaries of mathematical exploration, showcasing the uncharted territory awaiting discovery in the world of elliptic curves.
https://www.quantamagazine.org/new-elliptic-curve-breaks-18-year-old-record-20241111/