Peano and arithmetics
Osnova sekce
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Giuseppe Peano published in 1889 a small book where he set out to put arithemetics (and by extension real analysis and more) onto formal ground by providing both a convenient formalism and axioms. His work became the source of modern axiomatization and also of notation, but it had some defects: most notably, he lacked the rules for the underlying logic for derivation of proofs. The axiomatization of logic (first-order logic, second-order logic, etc) had to wait for 30 years.
We will read the original small book of Peano. The text is preceded by a careful commentary and explanations by Jean van Heijenoort, and is a part of a well prepared book which collects similar articles and papers (I recommend it for reading):
Jean van Heijenoort, From Frege to Godel: A source book in mathematical logic, 1879-1931, Harvard University Press, 1967.