Aristotle may have been the first to assert that a whole is more than the sum of its parts. Mathematics textbooks are likely to say otherwise, postulating that a whole is equal to the sum of its parts.
Emily Dickinson also comments on the matter.
(1341) by Emily Dickinson
Unto the Whole -- how add?
Has "All" a further realm --
Or Utmost an Ulterior?
Oh, Subsidy of Balm!
From Poems by Emily Dickinson, Volume 3 (Hayes Barton Press, 1955).
I am unsure whether it has been my study of mathematics or a childhood full of fables and their morals -- A stitch in time saves nine, Haste makes waste, Little by little gets to the goal . . . -- that's given me the habit of testing every truth with an opposite. Perhaps haste makes wealth or the whole is less than the sum of its parts. As poet I have had this latter experience: a quartet of finely crafted lines fail to hold together into a stanza, or fourteen lines in perfect rhythm and rhyme have not summed to the the song of a sonnet.
And so it goes.