His work include a counterexample to the general Vitushkin's conjecture[4] and with Mark Melnikov and Joan Verdera he introduced new techniques to understand the geometric structure of removable sets for complex analytic functions[5] which together with other works in the field eventually led to the solution of Painlevé's problem by Xavier Tolsa.

[6][7] His book Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability[8] is now a widely cited[9] and a standard textbook in this field.

[10] Mattila has been the leading figure on creating the geometric measure theory school in Finland and the Mathematics Genealogy Project cites he has supervised so far 15 PhD students in the field.

He obtained his PhD from the University of Helsinki under the supervision of Jussi Väisälä in 1973.

[12] Mattila was the director of the Academy of Finland funded Centre of Excellence of Geometric Analysis and Mathematical Physics from 2002 to 2007 and currently part of the Centre of Excellence in Analysis and Dynamics Research in the University of Helsinki.