Discrete Mathematics

8 DISCRETE MATHEMATIC..._

________________________

_

Fields Medalist Steve Smale writes about this, calling it an "immense gap" in the proof that was not

filled in until

1920, more than a hundred years later.

•

In

1900, Poincare carelessly claimed a certain very simple topological characterization

of

the

3-dimensional sphere. Later, in

1904, realizing it was not so obvious, he demoted the claim to the

status

of

a "conjecture".

The

Poincare Conjecture is now one

of

the biggest open questions in math-

ematics (two Fields Medals have been given

out

for partial progress on it).

•

In

the 1940s, Paul Erdos conjectured a certain combinatorial