What is the difference between Emil Artin's Geometric Algebra and David Hestenes Geometric Algebra? Emil Artin wrote a book on Geometric Algebra. Is this the same as the geometric algebra of David Hestenes?Please correct me if I'm wrong on this, I think David Hestenes geometric algebra is just clifford algebra. Did David change anything from Clifford' original geometric algebra or is he just trying to make it more well known; it seems to be very useful. Anyway, I am just curious if the textbook Geometric Algebra by Artin is also just clifford algebra or geometric algebra? I don't really know the difference between the two. Thank you.
 A: No, Artin's Geometric Algebra is not about what David Hesetenes is talking about.
Artin's book is a much more general course on the connection between algebra and geometry via groups.  It does have a section on Clifford algebras, of which "Hestenes geometric algebras" are a special case.
So far, I've gotten a lot more use out of my copy of Artin's Geometric Algebra than out of any of the "Hestenes geometric algebra" material I've read.
I think Hestenes' principal effect has been to raise the profile of using Clifford algebras practically. I don't think I've ever seen anything about truly new results coming out of the program, but indeed since he raised the profile I think people have been taking a closer look at the Hestenes school perspective.
At one of the spectrum, I have seen some things to the effect that phrasing things with geometric algebra can make some things clearer or more memorable.
On the other end of the spectrum, I have seen people say that geometric algebra and the associated geometric calculus is just "for people uncomfortable with basic manifold theory." The whole situation reminds me a little bit of the quaternion/vector-algebra war.
Just remember not to get caught up in hype, because there is a bit of that. Personally, I someday plan to sit down and weigh these things on their virtues, but for now I'm still brushing up my manifold theory :)
