Dear Domenico Oricchio,
Wow. I'm glad I finally got around to reading your essay. By far the most unconventional of the essays I've read so far. I love that you presented it in reverse order. I thought it was very appropriate that you did so, and my reason for thinking that is alluded to in my essay, Doctors of the Ring - The Power of Merlin the Mathematician to Transform Chaos into Consciousness. You'll see that I also went the unconventional, artistic route.
It may be in bad taste to ask an artist why he painted the way he did, so rather than asking, I'll tell you why I think it is so appropriate.
Our perception of physical reality is a reflection and so we try to make sense of it in reverse. And I mean reflection in the literal sense of the word. Mass and its position in space are only relatively constant - relative to their own rest frame - and the only way that we can perceive of them is through interactions with motion (for example scattering light or motion of the background), which changes what we are trying to observe. As you said, "everything changes, everything is in motion, it is a long journey that will never end." Motion is a derivative (a tangent as you said). It is change (the only constant is change). But motion is perceived as change in position with respect to something else. The "something else" is also motion, but we artificially standardize it to give it a constant denomination, which we call "time". So this single tangent dimension of motion is represented mathematically as a "conformal projection" onto a two-dimensional plane of space and time. Spacetime is the mirror in which we view our reflection. Every time we look in the mirror, we see our own eyes looking back at us so we tend to believe what we see. We think that the physical manifestation is real when in fact, it is only a trick "my beautiful friend conscience." And it's a tragedy because most scientists don't realize how vital it is for humanity to understand the metamorphosis called consciousness. For that, we rely on the artists. Fortunately, some scientists are also artists.
You asked if it would be possible "for some branches of mathematics, or branches of physics, express theorems in simple languages: once the results have been obtained, then the demonstration would be useful for future developments." Yes, I think it is possible. But you may be asking for too much because it is not like asking a surgeon to explain the synthesis of the scalpel. It is more like asking a magician to reveal the secrets of his tricks, and there are jobs, reputations and careers at stake. Nevertheless, I have been trying to demystify and explain spacetime in a simple way and explain how the simplicity can quickly become complicated by skillful manipulation of the math symbols. I invite you to read my Space-Time-Motion model and The Unity of Space and Time (both can be downloaded at http://vixra.org/author/theodore_j_st_john). If you decide to read them, please let me know what you think (email to email@example.com).
Ted St. John