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We pursue unification in physics, so why not in math?

http://faculty.luther.edu/~macdonal/ http://geometry.mrao.cam.ac.uk/2015/10/geometric-algebra-201...

If you read the original bookshelf as a matrix look at row 3 column 3. I recognized at least 5 books on geometric algebra and geometric calculus. This is the way geometry will be done in the future.

adam930on ‘No-drill’ techniques can treat tooth decay just as well, study finds

http://www.credentis.com/en/innovation/

This is what everyone here seems to be after. A toothpaste with this technology came out this July. But it's only sold in Switzerland.

For background: http://www.futurepundit.com/archives/008256.html

adam930on Parallels Between Math and Software Engineering

Yes, in fact there already is such a formalism: http://faculty.luther.edu/~macdonal/

From the first page:

"Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas, including linear algebra, multivariable calculus, real analysis, complex analysis, and euclidean, noneuclidean, and projective geometry. They provide a unified mathematical language for physics (classical and quantum mechanics, electrodynamics, relativity), the geometrical aspects of computer science (e.g., graphics, robotics, computer vision), and engineering."

adam930on A naturalist account of the reasonable effectiveness of mathematics in physics [pdf]

The essay by David Hestenes is a worthwile read. Especially the comments where Geometric Algebra is discussed.

adam930on Reforming the Mathematical Language of Physics (2002) [pdf]

I'm sure you will like it. Macdonald is an excellent teacher.

Years ago (2009) I sent an e-mail to David Hestenes asking him if he was planning on writing an introductory textbook on geometric algebra. He said it was in the planning stages.

From what I understood later, it seems he is attempting to write a 100% purely geometric algebra book unlike macdonald who reserved it for the second part of laga.

adam930on Reforming the Mathematical Language of Physics (2002) [pdf]

There are two very good introductory textbooks on the subject by the same author:

http://faculty.luther.edu/~macdonal/laga/ http://faculty.luther.edu/~macdonal/vagc/index.html