After a day of conference talks, but before drinks arrive, game theorists have been known to debate whether what is known as Zermelo’s theorem was actually proved by Zermelo. Eran Shmaya (who is always fun to talk to with or without drinks) decided to go and look at the paper (recently translated) and all but strips Zermelo of his theorem.
So, Zermelo clearly did not set out to prove his eponymous theorem. But was he aware of it ? I guess the answer depends on what you mean by being aware of a mathematical statement (were you aware of the fact that any even number greater than 2 can be written as a sum of a prime number and an even number before you read this sentence ?). But I do believe that some of the logical implications in Zermelo’s paper only make sense if you already assume his theorem.
Cheap Talk 
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December 10, 2009 at 4:55 pm
RL
“were you aware of the fact that any even number greater than 2 can be written as a sum of a prime number and an even number before you read this sentence”
How can this be? all prime numbers greater than 2 are odd. An odd number plus an even number is odd. So how can any even number be written as a prime plus an even number?
December 10, 2009 at 6:51 pm
K
Let n be an even number. Then n – 2 is even. But now we know that (n – 2) + 2 = n. Hence n is the sum of an even number ( in this case n-2 ) and a prime ( 2 ).