Math without notation

Question

Are there any researchers that try to develop learning materials to teach the core mathematics knowledge without using notation (and instead just plain English -- preferably without images)?

Answer 1

You'll notice throughout the development of mathematics, and dependent branches such as physics, the use of mathematical notation increases more so as the field becomes more advanced. For instance, Isaac Newton's Principia is a renowned book on the early development of physics and mathematics, and yet you will find it hard to find someone who has actually read (and understood) the text itself.

The question is, why is this so? Consider this passage:

''If a body $A$ should, at its place $A$ where a force is impressed upon it, have a motion by which, when uniformly continued, it would describe the straight line $Aa$, but shall by the impressed force be deflected from this line into another one $Ab$ and, when it ought to be located at the place $a$, be found at the place $b$, then because of the body, free of the impressed force, would have occupied the place $a$ and is thrust out from this place by the force and transferred therefrom to the place $b$, the translation of the body from the place $a$ to the place $b$ will, in the meaning of this Law, be proportional to this force and directed to the same goal towards which this force is impressed. Whence, if the same body deprived of all motion and impressed by the same force with the same direction, could in the same time be transported from the place $A$ to the place $B$, the two straight lines $AB$ and $ab$ will be ...''

and so on and so forth. This is Newton's explanation of his second law, expressed conicsely today as $$\mathbf{F}=m\mathbf{a}.$$

Newton's Principia was written as to be coherent to a wider audience, but of course we can see that, as this passage is representative of the entire structure of the text, it is extremely tedious and often terribly complicated. Writing out a mathematical idea was terribly difficult to do without mathematical notation, and if it wasn't for the geometric drawings of Newton's, a whole explanation would be impossible.

It was obvious to people that mathematics needed to become symbolic so as to have more concise works, remove ambiguity, and save heaps of time writing.