Stage 0: Poincare, the prophet, told people that there exists a
tunnel which would go from this side of the mountain to the other side of
Stage 1: Poincare announced that he found a mistake and that
the tunnel he found could not go through
the mountain but maintained his belief that there still exists such
a tunnel yet to be found. This conjectured tunnel was then named
"Tunnel of Poincare".
Stage 2: Many pioneers went out trying to find such a tunnel but failed.
However, some of them (Stallings, Zeeman, Smale, Freedman)
did find similar tunnels in other mountains.
Stage 3: Perelman, the monk, told people that he had found Tunnel
of Poincare in the mountain that Poincare himself failed, and that
he laid out 30 trail marks at various places in the tunnel so that other
people could go through by themselves.
Stage 4: Cao and Zhu were teamed up as an expedition to explore the
feasibility of Perelman's tunnel. They were able to go through indeed and
they laid out more than 300 trail marks along the tunnel which eases
the pass greatly.
Stage 5: Yau, the king, announced that the ultimate discovery of Poincare Tunnel
was finally made by Cao and Zhu, and emphasized
the importance of the "Perelman Method" (called by Cao-Zhu
"Hamilton and Perelman's Ricci flow theory").
Stage 6: Celebration.