I’ve learned about plenty of mathematical concepts while having no idea who discovered them or under what circumstances. Why are quaternions the exception?
But for quaternions, it was easy: I actually cited the Brougham Bridge inscription. One cannot, of course, check the bridge out of the engineering library to check the citation, but clearly this was the original “publication” of quaternion multiplication.
My advisor finally got the point.
You'd think, but I had a professor in physics who learned German just so he could read Boltzmann's original works.
it is now..but it’s still good to know for reviewing the older work.
reading the masters, is never a waste.
https://en.m.wikipedia.org/wiki/List_of_things_named_after_L...
I don't necessarily think the story accomplishes this -- your question is but one piece of evidence that it doesn't -- but I think for those who spend a good amount of time with these kinds of algebra questions, it comes to take on that role, and that's why I think it's repeated.
(Teaser -- if you want to know more about these kinds of questions, Google for "real division algebras". There are not very many, and they way they are organized is not, I think, something one would expect.)
What does that mean? My understanding was that Hamilton was searching for a way to make the manipulation of points in space easier, such as rotation, and noticed that the imaginary part of the complex numbers could be manipulated in the way he wanted. He then created a rather artificial tool in the form of the quaternions that allowed this.
Anyway, it's pretty easy to make up some multiplication on 3D vectors, like multiplying their components. However, in general, it won't play nicely with such arbitrary 2D slices. As it turns out, this slicing property is equivalent to having multiplication play nicely with vector norms:
|ab| = |a| |b|.
The discovery of complex numbers and quaternions probably played a big part in getting people to question what math is, leading to Hilbert's program to study Foundations etc. Hamilton's story is a nice, rare single instance we can point to, symbolizing this discovery.
- quaternions maybe have a more interesting backstory than other constructs. Not everything was carved into stone.
- quaternions never really became part of mainstream mathematical education. This makes them more niche and strange, and worth telling a story about. It's not as interesting to tell a story about something commonplace.
His life should be a movie. :-)
Most introductions to Galois theory that I've read have mentioned his duel.
Does a proof exist that these are the only three of such objects?