Dear Colleaugues & Allies ~ I just posted the final prepublication draft of an article on the nature of the Langlands Program, RH, P v. NP, and other "open" problems of pure maths, number theory, etc., and the proofs. I would deeply appreciate your feedback and suggestions. So, if you are interested, please send me a request for access to the [private] file, for review and comment. Thanks & best of luck etc. ~ M
R. 1, page 001
If by `RH´ Riemann-Hypothesis is meant, there already exist an article. Please see my research.
Dear Peter, i will read your article, because i always find something new to consider, re: RH and th many normal & unusual ways people think about it, etc. BTW, are you now beyond learning anything new about RH & the related issues (re: RH, etc.).
R. 3, page 001, posted 2023/08/23
Dear Michael,
each conversation may be good. Arguing pro or arguing re. Both may help to extend the insight or doing a better argumentation.
There is very much I agree. Sorry I didn’t read all of it word by word. Up to the definitions for proving my view was very detailed.
My first arguments may be sent at once.
• Quantity
All we do in mathematics should be on quantities. So the definition of math goes (quantities and their relations).
The things of our understanding, we may distinguish, get so by bundled properties (maybe more of them). A special property is the reason defining a set. A set contains, at least, two elements. No element, no set. The name doesn’t make the set. By the property an element gets part of the set. If `in the set´ all elements are equal among themselves. So no naturals as a set if by the second sight seeing different. A natural number, maybe `7´, and another natural number, maybe `3´, can’t result to `10´ adding them. The sum is `two naturals´. But no `2´ is inside the set – by definition. Two is the number of subsets.
If the property is `natural number´ or `apple´ …, the set is on the plural of this property, natural numbers, apples. It is the unit (like in physics) what the name represents.
A complete quantity is on this three: ABC
A := counter (by naturals), which counts the amount of measures
B := measure (to take in square-brackets), which is the defined part of the unit
C := unit, which has its special character or word to be named and distinguishes the phenomenons of our perception (see the definition Cantor did).
`1[1] natural numbers´ is the pure `one´ in mathematics.
`1[π] relations circumference by diameter´ …
• Ints / Intuitionistics
Intuitionistic theory got introduced by Brouwer. Very hard to read. I studied that topic by Conrad Kuck. A PhD-course was named `Non-monotonic learning automata´. The same title as his dissertation has. He extended this topic by four books, `Intuitionistis Set Theory I – IV´.
The learning automata is a problem solving system, a proof system. Using a Kac-Moody-Lie algebra.
This completes Hilbert’s program and restricted Goedel on monotonic proof systems (incompleteness).
All I did for reforming mathematics is by such technique in thinking.
If interested, see: www.mathe-neu.de
• Cantor and uncountable
Refuting Cantor, as you cited it, is on circular argument. My way is by a correct proof.
• Field
The expression `field´ at math stays for an algebraic construct. Set and two defined, major and minor distributive, combinations.
Refuted by my Reform.
• Zero
If a number should express how many of what ever there will be under examination, zero tells us that there is nothing.
So you didn’t do right in calculating by zero anyway. There no calculation could take place. Even if one of the partners for combination is missing.
Zero only is position if so special defined. More it is equal to empty space: 101 / 1001 …
• √-1 — imaginary unit (measure)
Unit is the wrong taken expression. If to take consistent, `i´ should be named and taken as the measure of the unit `imaginaries´.
1[i] imaginaries — (as the complete quantity has to look like)
But no imaginary is on logic! The square-root could be taken and has two results using not reformed math or is unambiguous by multi-prefix-results for multiplication (division).
So my refuting stays. There is no zero at the RH.
Further discussion is welcome. But not on learning anything by RH itself. More on proof systems / theories.
Reform goes on.
Dear Peter - I appreciate your effort & response. There is much to consider in your work. However, my definition of "maths" includes study of relations, proportion, effects, causes, and contributing factors. So, i find it hard to respond to your opinions in a brief msg. Of course, the added complications of other modern redefinitions & warring factions make a simple discussion difficult.
R. 5, page 001
Dear Michael, that's the point. You did a lot. It's hard for me to take care of all.
If you are interested we may do it by a single point, the most important:
√-1
Will you hold the old definition? Or will you go the way as I did and look behind the veil? At least you may have your own opinion on that.
But not been able to see where the results of (+1)(-1) or (-1)(+1) came from, denies half the area of reasons. Most mathematicians find it too kiddy to talk about that. Let them be limited.
There are many ways to find it obscure to stop doing the exercise for square-root only by having a negative radicand.
Transforming the coordinates makes the other areas not calculable.
Martinez (negative math) introduced the inverse rule for the prefixes of products. So no definition is complete except this of holding all the prefixes of the quantities which are to combine.
If you know they were + and – => the result is + and – , not? If you don't know the way the sources were, you have to deal with absolutes and further conditions.
Riemann took `imaginary´. Will you too?