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An important period for the journal was 1928 – 1958 with Solomon Lefschetz as editor.
During this time, the annals became an increasingly well-known and respected journal.
Its rise, in turn, stimulated American mathematics.
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.

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