MathPages

An older legendary story with the same premise:

"Wren, Hooke, and Halley had discussed the problem at a coffee house following a meeting of the Royal Society in January of 1684, and Wren had offered a cash prize to whoever could provide a derivation of the shape of planetary orbits under the assumption of an inverse-square central force of attraction toward the (presumed stationary) sun. Hooke had claimed to have a proof that the paths were ellipses, but never provided it. Against this background, Halley paid a visit to Newton, who later told Abraham De Moivre about the fateful meeting. According to De Moivre:

In 1684 Dr Halley came to visit him at Cambridge. After they had been some time together, the Dr asked him what he thought the curve would be that would be described by the planets supposing the force of attraction towards the sun to be reciprocal to the square of their distance from it. Sir Isaac replied immediately that it would be an ellipse. The Doctor, struck with joy and amazement, asked him how he knew it. Why, saith he, I have calculated it. Whereupon Dr Halley asked him for his calculation without any farther delay. Sir Isaac looked among his papers but could not find it, but he promised him to renew it and then to send it him…"

http://www.mathpages.com/home/kmath658/kmath658.htm

Here's a quote that I think you may find interesting, as it seems to be along the lines of what you are saying:

"A meta-mathematical proof of the consistency of arithmetic is not excluded by...Goedel's analysis. In point of fact, meta-mathematical proofs of the consistency of arithmetic have been constructed, notably by Gerhard Gentzen, a member of the Hilbert school, in 1936. But such proofs are in a sense pointless if, as can be demonstrated, they employ rules of inference whose own consistency is as much open to doubt as is the formal consistency of arithmetic itself. Thus, Gentzen used the so-called "principle of transfinite mathematical induction" in his proof. But the principle in effect stipulates that a formula is derivable from an infinite class of premises. Its use therefore requires the employment of nonfinitistic meta - mathematical notions, and so raises once more the question which Hilbert's original program was intended to resolve." -Ernest Nagel and James Newman

Taken from https://www.mathpages.com/home/kmath347/kmath347.htm

Awesome.

Some concepts in math are so much easier to grasp with an interactive visual. I once made an entire game around matrix multiplication -- such that players didn't even know they learned how to do this.

And sometimes, visualizations can help cause discoveries. A lot of progress in theoretical physics came about because physicists 'guessed' what nature's equations should look like...and then got shocked when they discovered they were right.

Take James Clerk Maxwell, for instance:

"He had achieved his greatest success by relying on just one empirical fact known to every school boy. Yet now he tried to do without any empirical facts, by pure thinking. He believed in the power of reason to guess the laws according to which God has built the world."

http://www.mathpages.com/home/kmath103/kmath103.htm

I think your watch is slow and you think mine is slow in the following sense. For each of many events, I record their time t and position x while you, moving relative to me at constant velocity, observe a different time T and position X. Between two events with the same X-value, such as ticks of your pocket watch, the difference in t-times is larger than the difference in T-times by a factor gamma. Conversely, between two events with the same x-position, such as ticks of my pocket watch, the difference in T-times is larger than the difference in t-times by that same factor gamma.

There is no contradiction because events with identical x-positions do not have identical X-positions.

If you already know what a partial derivative is, see the first paragraph of this: http://mathpages.com/rr/s4-07/4-07.htm

If you took out the bits of relativity that were developed by others, you'd be left with not very much. Relativity without the Lorentz transform... I'm not even sure how one would resolve that. As I said, the vast majority of the insight was just taking what the math was already saying seriously. Einstein put it into a final form, and this is important and valid work, but it's not like he invented all the mathematical tools from scratch.

Either you've misinterpreted Adam Frank's work, or it isn't excellent.

I'll counter-cite Reflections on Relativity, which contains a lot of deep analysis of the mathematical history of relativity both before and after Einstein: https://mathpages.com/rr/rrtoc.htm which makes it quite clear both what he did, and did not do.

Getting a patent is an expensive business. Patentability of methods of manipulating numbers is variable around the world, but in most places its not going to work. You might have managed it in the US a few years ago, but not now. Seriously applying for a patent is not cheap. The odds are that you will spend a lot of money for no return.

Getting priority for something on your CV is another matter. As others have mentioned, write up a paper and submit to arxiv.org.

Incidentally, are you aware of this: http://www.mathpages.com/home/kmath505/kmath505.htm

The last couple of paragraphs describe a geometric construction giving an approximation that is good enough for many purposes, and would also be the right starting point for any iterative algorithm.