The journal was established by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences. The journal was printed and distributed by Springer from 2006 to 2016. Since 2017, Acta Mathematica has been published electronically and in print by International Press. Its electronic version is open access without publishing fees.
The journal's "most famous episode" (according to Villani) concerns Henri Poincaré, who won a prize offered in 1887 by Oscar II of Sweden for the best mathematical work concerning the stability of the Solar System by purporting to prove the stability of a special case of the three-body problem. This episode was rediscovered in the 1990s by Daniel Goroff, in his preface to the English translation of "Les méthodes nouvelles de la mécanique céleste" by June Barrow-Green and K.G. Andersson. The prized or lauded paper was to be published in Acta Mathematica, but after the issue containing the paper was printed, Poincaré found an error that invalidated his proof. He paid more than the prize money to destroy the print run and reprint the issue without his paper, and instead published a corrected paper a year later in the same journal that demonstrated that the system could be unstable. This paper later became one of the foundational works of chaos theory.