It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering".

[7] Norman Steenrod characterized Lefschetz' impact as editor as follows: "The importance to American mathematicians of a first-class journal is that it sets high standards for them to aim at.

In this somewhat indirect manner, Lefschetz profoundly affected the development of mathematics in the United States.

"[7] Princeton University continued to publish the Annals on its own until 1933, when the Institute for Advanced Study took joint editorial control.

Issues from before 2003 were transferred to the non-free JSTOR archive, and articles are not freely available until 5 years after publication.