Ramsey Parties
zufallstee.blogspot.com
zufallstee.blogspot.com
But, a minor correction: Frank Ramsey merely proved (in 1930) a theorem equivalent to the statement that Ramsey numbers are well-defined. The study of the values of particular Ramsey numbers seems to have been started in 1955 by Robert Greenwood and Andrew Gleason, and I believe they are the first ones to note that R(3,3)=6.
Disclaimer: Combinatorics is my field. History of mathematics is not. And corrections are welcome.