Was reading a linear algebra textbook that noted that the algebra of vectors displaced the algebra of quaternions as the language of physics and I am curious why that would be the case. Is there a good book or article that goes into detail on that? Hopefully one that can be understood by someone who is not much of a mathematician.
Additionally any good history of math book that goes over the development of math in the early modern era to the 1900s.
There's an excellent book on that, actually. Crowe's A History of Vector Analysis.
To give a short recap of the history; vector calculus was developed first by Hermann Grassmann, who was one of those people who gets frequently described as being too far ahead of his time. His work simply didn't get much attention - to the extent that he largely abandoned mathematics in favor of linguistics. Hamilton on the other hand got attention and fame rather quickly for the quaternions (1843) and they were adopted by Maxwell (1864) and others for use in physics.
The drawback of quaternions is that they're four-dimensional, which is frequently one too many, needlessly complicating some things. They also turned out to be difficult to generalize to other numbers of dimensions (other than the pre-existing complex numbers and octonions). This lead to JW Gibbs (most famous for his work in chemical thermodynamics) to later (1870s) take up work on vector calculus, where he rediscovered Grassmann's work and promoted it. Oliver Heaviside reformulated Maxwell's equations in vector form and promoted their use in electromagnetic theory (which you could say was the 'killer app' for vector calculus, in today's terminology). The debate between advocates of the two raged for the following decades but by 1900 (according to Crowe's count) there were many more "vector" publications than "quaternion" ones. In the first decade of the 1900s many textbooks were published, and by 1910 quaternions were decidedly on their way out. In short, it was the battle between a better idea and an ingrained one. Which is not to say quaternions don't have certain merits and arne't more useful in some contexts. (they even get some use in computer graphics these days, even if it's vector-dominated)
In terms of the greater history of mathematics, the physicists' choice of representation of vectors is rather unimportant, so general math history books don't normally go into this in detail. In the broader perspective, the great and important thing about quaternions wasn't that they were useful in physics, but rather that it was the first non-commutative algebra; which got people thinking about number systems and mathematical operations in a new way. (and according to some historians, drive the more conservative mathematician Charles Dodgson to parody that thinking in Alice in Wonderland) While the physicists were debating vectors vs quaternions in the late 19th century, the mathematicians were being rocked by Cantor's set theory and so on.