Bertrand Russell and Alfred North Whitehead published the first volume of
Principia Mathematica, (commonly abbreviated as
PM)
one of the most important works on the foundations of mathematics; the second and third volumes were published in 1912 and 1913. This monumental (both in size, scope and complexity) was attempt to derive all mathematical truths from a fixed set of rules and axioms in symbolic logic. Cited by
The Modern Library as #23 of the hundred most important non-fiction works of the century, it's also referred to as 'the most important scientific or mathematical work, which no one has read." (Largely due to it's scope and the need to master a symbolic logic syntactical language invented by Russell and Whitehead.)
As an example, it takes until page 379 of volume I, for Prop. 54.43 to be proven. This is a proof that -- given the limited number of axioms and relational rules posited in
PM:
"1 + 1 = 2".
Here it is:
This proof is actually completed in the section on cardinal arithmetic in volume II page 86, accompanied by the comment, "The above proposition is occasionally useful." :)
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