Stevo Todorčević
In order  to establish this partition relation, Todorčević discovered an entirely new mathematical object called rho functions.  Sierpinski in 1933 coloured the edges of the complete graph  whose vertices are the elements of the smallest uncountable cardinal number. He coloured the edges of  with 2 colours in such a way that each colour appears on some edge of any uncountable subgraph of . Galvin and Shelah in 1980s had increased the number of colours from 2 to 3. Improving 3 to 4 seemed beyond any available methods. Todorčević used  his newly discovered rho functions to increase  the colours  not just to 4, but all the way up to the smallest uncountable cardinal, which is the maximum conceivable number. This was one of the results for which he was invited to the Berlin ICM.