Wasilly Kandinsky is seen as the first purely abstract artist in the modern meaning of the term. But as the the realization of the power of the pure abstract came about through accident.
Art by 1910 had been in an abstract mode for some time, with artists like Monet and Cezanne having paved the way. Initially Kandinsky was such a painter, painting street scenes in and other subjects in an impressionistic style.
Things changed for Kandinsky rather suddenly on a day in 1910:
In his memoirs Kandinsky recalls the day in 1910 when he accidentally discovered nonrepresentational art. As he returned home at sunset he was struck as he entered his studio by an “indescribably beautiful painting, all irradiated by an interior light.” He could distinguish only “forms and colors and no meaning.” He soon realized that it was one of his own paintings turned on its side. Soon after he began working on paintings that came to be considered the first totally abstract works in modern art; they made no reference to objects of the physical world and derived their inspiration and titles from music. (html)
There is coverage of Kandinsky elsewhere on wiki. See Circles in a Circle (1923)
Kandinsky is recognized as the first abstract artist, however it was discovered independently many places. See Hilma af Klint
For more on discovered art, from the perspective of a nine year-old, see Haiku by a Robot
via On Its Side.