How the hell did we create vectors?

Sometimes, during Math or Physics classes, you might have asked yourself this question, for angry moments or for pure passion on these structures. How come? Such an abstract thing!

We've seen on previous posts that Italy and France gave us brilliant mathematicians. One of them, the French Gilles de Roberval (1602–1675), during his works on Cycloid, started to work wit it's tangents. To trace the tangents, Roberval created a primitive structure that later would become a vector.

Vectors are also related to complex numbers, the same that Bombelli studied near 1540. The idea, however, is old, since Greece we have the concept of vectors (check Heron of Alexandria or even Aristotle's studies). But only in century XIX they became formalized and popular as mathematical instruments, specially due to William Rowan Hamilton (1805–1865 ) and Hermann Grassmann (1809–1877) works.

Hamilton is the author of the concept of quaternions, a very interesting structure. It has two parts — a tridimensional vectorial component plus an unidimensional scalar component. There are few practical applications for them, however. Maxwell was one of the few ones to try to apply this concept into his equations, but gave up on the idea since quaternions had almost zero acceptance on Academy. Maybe we will find a good place to apply quaternions. The great mathematician Nikolai Lobachevsky (1792–1856 ) used to say that sooner or earlier we will reach good applications for almost all mathematical structures. History point: Hamilton was a depressed figure. He passed away due to alcoholism.

Hamilton and Grassmann gave the basis to spread the idea of vectors, but it was Josiah Gibbs (1839–1903) who spread the final formal concept concept of Vectorial Algebra and Calculus with his papers and works.

Personal point: the first time I was showed the concept of Vector, in High School, I was… disgusted and annoyed. Vector concept is pretty abstract and hard to explain. But yes, it's possible to humanize the explanation with arrows and some History☺.

Did you like this post? Take a look here, I've been publishing several other about Math History.