Math Notation

Good notation leads mathematics. MathML has to follow that path. What I write here though, is an idea.

Differential Forms appeared last century, most applied mathematicians and engineers do not use these tools. I know I don't, just recently started to study this.

Professor Jerrold E. Marsden is studying discrete differential forms with colleagues, like Ari Stern.

I started to consider this structure many years ago, but didn't pursue it. My idea is simple, here it is:

When expressed in its simplest form, the Fundamental Theorem of Calculus, is almost tautological: The sum of the differences is equal to the total difference.

Then I started to think in more dimensions, soon I saw Stokes, Gauss, Green, and some others that had already done this many years ago.

Now I am studying V. I. Arnold's book: Mathematical Methods of Classical Mechanics. This is amazing; the structures are so natural. I believe that one can do a useful discrete version of all this.

And this leads me to notation and HTML. At least since the nineties there have been efforts to use math html. The thought occurred to me that the problem in rendering math formulas, notation, and the invention of new math are related. For instance:

Think of the wave equation; one can easily convert a second order partial differential operator into the composition of two first order ones. These factors define the best variables to describe a wave, x - ct, and x + ct. Neat. Just by keeping the right variables around one can describe complex physics, I feel that at its core, good notation is good math; and HTML is an important advance in medium agnostic expression of symbols. It is hard not to think of Donald Knuth and TeX.

More later.