Moshe Klein wrote:

Hi Doron:

In the book "The man who loved only numbers" about Poul Erdos it's written that Gödel tried to understand Leibeniz" so it is very clear to me today more the ever, that Leibeniz was right when he wrote that the fundamental problem in the human race is using a wrong language.

What do you think about that, one day before your Travel?

Let me give some analogy:

30 years ago scientists had to kill any living creature, in order to examine it under an electronic microscope.

Today we can examine living creatures without killing them first.

Standard Math has to kill any living insight in order to examine it under the rigorous mathematical microscope, because it has no ability to deal with redundancy and uncertainty as first-order properties of the examined insight.

The result is that standard Math can deal only with trivial problems, which mostly based on black XOR white state of mind, which is a very trivial way of thinking when compared to colorful realm.

Standard Math can deal only with dead flock of birds, but in order to deal with a living flock of birds we need a paradigm-shift in the language of Mathematics and its standard logical reasoning.

It is a very trivial thing to through a dead bird in the air, and then calculate its ballistic path, according to Newtonian calc.

But in order to deal with a living bird thrown in the air, we need a deeper and finer language that does not kill first in order to define its trivial ballistic path.

When a language is tuned to kill first, the first victim is the cognition that uses it, and we can clearly see how most of professional mathematicians around our planet have lost their ability to think freely, without the continuous control of the agreed terms of their community.

Real Mathematics, first of all has to educate its users to develop their natural abstract skills, in such a way that it is not depends on any specific school of thought.

By this educational process, any student and any teacher, learn together and develop together abstract skills through a real-time dialog, which is the heart of the mathematical education.

Gödel's incompleteness theorems clearly show us that any axiomatic system is actually an open framework, which can be deeply changed when deeper insights of its fundamental concepts are invented/discovered by its speakers.

Strictly speaking, rigorous definitions must not kill insights in order to define them, and the best way to do it, is to accept redundancy and uncertainty as welcome first-order properties of the language of Mathematics and its logical reasoning.

Monadic Mathematics is the first mathematical framework that uses redundancy and uncertainty as its first-order properties, as can be shown here:

http://www.geocities.com/complementarytheory/TAP.pdf