# Peano's Axioms: their real origin

It is well-known that Guiseppe Peano formalized the axioms that, to some extent, motivated mathematical induction. These are known as Peano's axioms. However, these axioms are often called trivial as they are quite obvious, whether stated formally or not. Was Peano really the first one to come up with this set of axioms? Is there proof that he was the first one to make such a complete formalization of the natural numbers?

## 1 Answer

A summary from Wikipedia

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.1 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 (Latin: Arithmetices principia, nova methodo exposita).

• Oops, didn't notice it $-$ thanks! – Ahaan S. Rungta Dec 29 '14 at 15:52