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If I recall correctly, Euler has the most pages of published math. Erdős has the most papers (some of them not more than a handful of sentences).

Erdős has a huge amount of credits in the papers of others (hence Erdős number) because he would just travel all over the country helping people get unstuck on their work.

Euler had scribes do a lot of the grunt work for him. His vision was quite bad and worsened throughout his life, going blind in his right eye rather early on and later developing cataracts in his left. He once joked "Now I will have fewer distractions" on his condition.

There’s more about the effort to publish his complete works here: https://en.m.wikipedia.org/wiki/Opera_Omnia_Leonhard_Euler