The 38-year-old was among four Fields Medal recipients at the International Congress of Mathematicians held in Seoul, and the first Austrian among the 56 winners since the prize was established in 1936.
Hairer was awarded for his outstanding contribution to the theory of stochastic partial differential equations - the branch of mathematics dealing with random processes like crystal growth and the spread of water in a napkin.
He told the Austrian Press Agency that he was very happy as the prize was "the highest honour one could receive as a mathematician".
One fellow mathematician compared Hairer’s 180-page treatise to the Lord of the Rings trilogy because it “created a whole world”.
Hairer is also the creator of an award-winning sound-editing program called Amadeus, a popular tool among deejays, music producers and gaming companies.
The other three Fields Medal winners on Wednesday were Artur Avila of the National Centre for Scientific Research in France and Brazil's National Institute for Pure and Applied Mathematics; Manjul Bhargava of Princeton University and Iranian mathematician Maryam Mirzakhani of Stanford University in California - who became the first woman to be awarded the Fields Medal.
The prizes are awarded every four years to between two and four mathematicians under the age of 40. Wednesday's prizes were presented by South Korean President Park Geun-hye.