Page "Peano axioms" Paragraph 1

The need for formalism in arithmetic was not well appreciated until the work of Hermann Grassmann, who showed in the 1860s that many facts in arithmetic could be derived from more basic facts about the successor operation and induction.

In 1881, Charles Sanders Peirce provided an axiomatization of natural-number arithmetic.

In 1888, Richard Dedekind proposed a collection of axioms about the numbers, and in 1889 Peano published a more precisely formulated version of them as a collection of axioms in his book, The principles of arithmetic presented by a new method ().