“Mathematicians need at least 29 independent points to characterize them.”
Noam Elkies set the rank record of 28 in 2006. He broke it himself with Zev Klagsbrun. They sliced a K3 surface to get curves guaranteed rank 17 and searched the pile with Klagsbrun’s faster method. The record moved by one, and the question of whether rank has a ceiling is as open as it was.