To: Nootropic,
I'm almost 60 years old, so I have had plenty of time to familiarize myself with all those particular branches of mathematics... and then some. How about you?
I never said, or even implied that "the way mathematics has been done is a sham". Those are your words, not mine.
Mathematics must adapt to and be consistent with new discoveries if it is to remain both both vital and dynamic. Therefore, new discoveries must be disseminated rather than "swept under a rug" for fear of change.
Courage is required!
Most importantly however, new discoveries must be studied so that all of their consequences and ramifications are properly, which is to say logically, interpreted.
Initially, there may be disagreements with regards to various possible interpretations, (such as the disagreement between Newton and Liebnitz on the subject of limits) but in the end, the truth will prevail, and mathematics will grow, thrive and flourish rather than stagnate.
Your fear that my equation would "reduce mathematics to trivial statements" is without foundation. My equation happens to be true, and the truth can never render the robust and sublime body of knowledge called mathematics "trivial".
Now, let's muster up all of our courage and ask ourselves the following questions:
Given the true equation:
if our variables are to represent non-negative integers, then:
(1) Which term has the better defined variables?
(2) Keeping in mind that unity is not an actual common factor but a "trivial" or "degenerate" common factor, which term is more suitable for representing actual common factors?
(3) Keeping in mind that what we do to one side of an identity, we must also do to the other, can we "cross out" the cancelled T's the way we were taught in school?
(4) What occurs at T=1 and what does it imply?
When answering these questions, please remember that the above equation is absolutely new to mathematics ( I discovered it only a decade ago) so there is, as of yet, no "general consensus" on what it actually means.
It's proper interpretation is perhaps the greatest challenge that the mathematical community has ever faced! Try answering those four simple questions and see for yourself!
Don.
