I have a soft question that is interesting for me in some aspects. I appreciate your answers and comments about it.
Four years ago, one of my friends in MIT, in the biology lab, had working on neuroscience and specially he worked on Deja-Vu phenomenon. When he asked me about writing a program with Matlab for simulating this phenomenon with a network of cells that they want simulate the Sinc function, I found that there are many good theorems in graph theory that can be useful for his research. When I suggested him this idea, he found it very interesting.
My question are about this event in a little bit different way. Is it possible that we publish a paper in some mathematical journals that:
1) The only new thing in the paper is relation between a real phenomena and a field of mathematics that is well known. For example, we just model the controversy with bandwidth problem, and no more things just using the theorems that proved for bandwidth problem.
2) This paper does not have new theorems as like as theorems that are common in mathematical papers. This paper just use mathematical theorems in its direction.
Also, do we have some mathematical journals that publish such a papers? And if yes, is there some evidences for this type of publication?
Maybe someone think about the Hilbert Spaces and quantum mechanic. But, in my view, this is not the case. We use Hilbert spaces to model some aspects of quantum mechanics and we get some new results and theorems in quantum mechanic. If we want to think this relation, the paper only must be contain the modeling of quantum mechanic by Hilbert spaces and no more.
Briefly, suppose we found a connection between a real phenomenon and a field of mathematics that can be acceptable or a new view point for analysis the phenomenon. For example, if we found a relation between Darwin's evolutionary theory and a game on graph, is it possible that we can publish such a results as a paper in a mathematical journal? And what kind of mathematical journal is good for this work?
Sorry me for long question.
Best Answer
Oh yes! Establishing a connection between some class of natural phenomena and a well known field of mathematics can make you famous. And you do not have to prove new theorems. The most striking recent example is Benoit Mandelbrot. According to the Google Scholar he is THE MOST cited mathematician of all (at the time I write this). And all his activity was exactly as you describe. Even before fractals, he was looking for new connections between "well known" fields of mathematics and real world. For example he was looking for "stable probability distributions" everywhere, "power laws" etc. But his greatest success was "fractals". The relevant mathematics was known for about 50 years. Well known to a very narrow circle of specialists, as it happens to most areas of pure mathematics. He invented a catchy word "fractal" and then showed by examples that "fractals are everywhere". I don't know a single new theorem that Mandelbrot proved. But his influence on mathematics and science was really enormous.
On a smaller scale we have Kramers-Kronig relations. Which is nothing else but the "well known" Spkhotski-Plemelj formula. It is not important that Kramers and Kronig discovered these known relations independently. What is important is that they proposed a physical interpretation. And there are thousands of examples like this. You can even receive a Nobel prize by establishing a new relation to the real world of some well known mathematics.