Dear Yuri, I think that a mathematical theory can be originated either from theoretical inputs and from applicative aims. Newton's "Principia" (1687-89), considered as a Physics matter, are based on Newton's previous (1664-65) mathematical studies, which were originated from practical considerations (see J. Gleick Newton biography). My answer to your question is: mathematicians and applied scientists. Gianluca

Dear Yuri, I think that a mathematical theory can be originated either from theoretical inputs and from applicative aims. Newton's "Principia" (1687-89), considered as a Physics matter, are based on Newton's previous (1664-65) mathematical studies, which were originated from practical considerations (see J. Gleick Newton biography). My answer to your question is: mathematicians and applied scientists. Gianluca

I think that an important scientific field comes mostly from practical science and not math. However, new mathematics is often needed for its foundations.

The ideal case is when one person knows both this field and corresponding mathematical tools. Newton was such a person. But note that his calculus was not fully rigorous from the perspective of pure mathematician. Proof of the basic theorems about limits, that come in theory before differentiation, was done more than100 years later, by Cauchy and others.

P.S. I agree with Gianluca regarding Newton. But what about the other cases? Recall, for example, game theory by von Newmann.

Mathematical sciences is complimenting and mathematical ideas are being applied various other areas of science. Because many of new emerging areas in science are fostered by the explosion in capabilities for simulation, computation, and data analysis. The process of simulation-based science and engineering is inherently very mathematical the include mathematical structures that enable modeling, algorithm development, computing, model validation, uncertainty quantification, analysis, and optimization. In conclusion, much of twenty-first century research is going to be built on a mathematical science foundation, and that foundation must continue to evolve and expand.

I really like the definition that philosophy is pure thinking. Regardless of the contingent need to overcome is to solve some specific problem when a new theory is created, this is nothing but philosophy, that is, pure thought. When and if this theory overcomes the Galilean principles of reproducibility, verifiability and falsifiability then it becomes science.

When man reaches any of his limits, everything he can do is to resort to God or to Philosophy. God does not offer answers, because we are too insignificant in order to be able to reflect them. However, Philosophy is forced to offer us answers, although the answers are infinite, not yet identified, or impossible. This is also valid for the medicine as science, that must resort to God or Philosophy, when they reach the limit of their possibilities. God does not offer answers or we cannot reflect them, but the philosophical extrapolation is an answer. This is one of the reasons why the science or nonscience, whatever their nature, should always resort to Philosophy. The Unconventional/Philosophy tries to make these extrapolations known for anyone who wants to get familiar with them or who intends to surpass his own limits. This is one of the many reasons why you should not exclude Philosophy or the philosopher from your researches. The philosopher must replace the unknown from beyond any limit with extrapolations of the conventions we are. We could not understand this unknown in the absence of these conventions.

There are two ways of logical deduction: one that starts from the whole to the parts, or from the general to the particular, as is the case of the Unconventional/Philosophy and another one that starts from the parts to the whole, or from the particular to the general, as it happens in the case of sciences and nonsciences. By deduction and extrapolation, we can sustain that any whole assumes the properties of the parts, that it multiplies, under the form of a bigger whole, whereas the parts maintain all the properties of the whole, on the basis of which it divides. Sometimes the division of the whole is to be found beyond the capacity of reflection specific to any entity/universe, some other times, multiplication takes place beyond any capacity of reflection specific to the entities/universe. This does not mean that the parts lose from the properties of the whole, but only that the properties of the whole are no longer visible in the case of the parts, because of our limits and not because the limits of division or multiplication. A piece of metal divided into bigger parts remains the same metal. The atoms of that metal have the same properties as the piece of metal they were part of. It is ourselves that cannot reflect, know, relate all these properties to a system of reference, as they are too small for us and our devices. Each atom has a spirit, as long as the simultaneity of the atoms in the human body generates, creates ideas. We cannot create something from something that does not exist. However, we can reflect the existence that is to be found beyond our limits. This is the reason why, in our opinion, the extrapolation of matter/energy is still matter/energy, even if the extrapolation tends to the smallest or biggest unlimited or if we ourselves or others can reflect, compare, relate this thing to a system of reference or not. Any divided or multiplied unlimited notion is still a small or big unlimited, (notion) and we are part of this unlimited. Furthermore, let us not forget that there is no identity between the parts of the whole. There is no identity between the entities/universe of any kind as a whole, because of the internal and external space/time dimension, (transformation), which are always different.