Derek Thompson of The Atlantic discusses a history of invention.
The world’s most famous inventors are household names. As we all know, Thomas Edison invented the light bulb, Alexander Graham Bell invented the phone, and Eli Whitney invented the cotton gin.
Except they didn’t. The ideas didn’t spring, Athena-like, fully formed from their brains. In fact, they didn’t spring fully formed from anybody’s brains. That is the myth of the lonely inventor and the eureka moment.
“Simultaneous invention and incremental improvement are the way innovation works, even for radical inventions,” Mark A. Lemley writes in his fascinating paper The Myth of the Sole Inventor. Lemley’s paper concentrates on the history and problems of patents. But he also chronicles the history of the 19th and 20th century’s most famous inventors — with an emphasis on how their inventions were really neither theirs, nor inventions.
The definition of addition of natural numbers was in effect created by Hermann Grassmann in 1861 and in effect self published.
Then Dedekind gave his version of the Grassmann approach in 1888.
Peano was a refinement and in many ways step backward from Dedekind’s book.
The Kalmar definition is disputed by Leonard Blackburn as being valid without doing the recursion theorem of Dedekind first anyhow.
Various innovations on proving the recursion theorem before order were done in the 20th century.
Doing order starting from the front end of the natural numbers was first done by David Groisser.
The pitch line addition approach was developed in 2012 in the course of writing a pre-Algebra book to teach the commutative and associative laws of addition. This also created the geometry of addition. It also led to a large number of easy induction proofs that don’t have quadratic or higher algebraic formulas.