This article records tradition as it has been passed down and reported. Its sources are not yet part of the atlas's verified catalogue.
By the spring of 2006 the mathematical community largely agreed that Grigori Perelman had proved the Poincare conjecture. What it had not yet agreed on was who should get the credit, and for a few strange months that argument became public in a way pure mathematics rarely is.
In June 2006 the Asian Journal of Mathematics devoted its entire issue to a single paper, more than three hundred pages long, by Huai-Dong Cao of Lehigh University and Xi-Ping Zhu of Sun Yat-sen University, presenting what its authors called a complete proof of the Poincare and geometrization conjectures. The paper's editorial path was unusual: the journal's editorial board, thirty one mathematicians, were given three days to comment on a draft that arrived by email without the paper itself attached, and at least one board member who asked to see it was told it was not available. The journal's co-editor was Shing-Tung Yau, a Fields Medalist and Cao and Zhu's own former teacher.
At a Beijing press conference that June, the acting director of a mathematics institute Yau had founded offered a division of credit for the proof: Richard Hamilton, whose Ricci flow program the whole argument rested on, got just over fifty percent; Perelman got about twenty five percent; and Yau, Cao and Zhu together got about thirty percent, a total that runs past one hundred by design or by accident depending on who is asked. In a lecture the same month, Yau said that in Perelman's own papers many key ideas were sketched or outlined rather than spelled out, with complete details often missing, and praised Cao and Zhu's paper as completely solving the puzzle.
Other mathematicians did not see it that way. John Morgan, then chair of Columbia University's mathematics department and himself a co-author of one of the independent expositions of Perelman's proof, said flatly that Perelman had already done it and that his proof was complete and correct, and that he did not see that Cao and Zhu had contributed anything different. Perelman, asked about the Cao-Zhu paper directly, was equally blunt: it was not clear to him what new contribution they had made, he said, and it appeared that Zhu had not quite understood the argument and had reworked it rather than clarified it.
None of this changed the outcome. The Clay Mathematics Institute's own account of the episode, written after the dust settled, credits Perelman alone with resolving the conjecture, and the Fields Medal committee had in fact already reached that same conclusion at the end of May, before the Beijing press conference ever took place. But the dispute is on the record, named participants and all, a reminder that even a proof everyone eventually accepts can pass through a genuinely contested moment on its way to being settled.