For his proof of the partition relation formula_8, Todorčević earned explicit appreciations. Paul Erdös wrote, "This certainly is an unexpected and sensational result." and Jean A. Larson added, "... (it) was a wonderful shock that introduced a wide audience to the walks on ordinals and the oscillation function." Todorčević obtained this partition relation in September 1984, while lecturing on it in the Berkeley seminar, wrote up the notes of his lectures and circulated them in January 1985 and published the result later, in 1987. The walks on ordinals method Todorčević devised in May 1984 when he came up with a new proof of the existence of a Countryman line. 