1. andrei_novikov says:

Unfortunately, no one can describe to you what is impossible. Mathematics is a very strict science. If it is claimed that something is impossible, then it must be proved. For example, to prove that it is impossible to prove the continuum hypothesis, or that the equation x*x+1=0 cannot have real roots.

Just because something isn't described at the moment doesn't mean that you CAN't come up with a description for it. This is just an unsolved problem. If it is proved somewhere that no mathematical model can be created for something , this will be a very strong result, but it is unlikely that such a statement can actually be proved.

2. mathematics_and_mathematics says:

The old classical mathematics could not solve very simple description problems (which are correctly solved today by a very rare modern university graduate) –

1) first and second derivatives for a piecewise constant function (velocity and acceleration, physics), solution of the inverse problem by integration;

2) description of the mass distribution density, for one material point, finding the mass from this density.

The new mathematics is very successful in solving these and much more difficult similar problems by applying the theory of generalized functions, which is developed comprehensively, theoretically and practically.

THE REASON is that each new class of problems requires its own new adequate mathematical apparatus.

3. alexander_shestakov says:

It is impossible to describe mathematically those processes that we do not “see” and will never “see”, but which actually exist, “see” us and, possibly, affect us. The finer penetrates the coarser, studies the coarser, and is able to influence it. But not the other way around. To “see” the subtle, you need even more subtle tools to study this subtle. Does anyone really think that the Law that created us all will put a scalpel in our hands to pick at the Heart of this Law? While physicists and mathematicians delve into the great mysteries of Nature to predict something for a few days ahead, the Superconscious Mind of the Universe replays their entire past and future lives in a split second, like in a movie…

4. viktor_voevodov says:

I very much doubt that such processes exist. Mathematics has a lot of methods, and if something can't be described with formulas, you can always model it numerically. There are also many methods for numerical modeling. In the most unpleasant cases, you can simply describe a huge array of data.

I don't see any fundamental limitations here.

5. leonid_sakharov says:

This is not a question that is really interesting. Other interesting questions are: is it worth trying to describe everything “mathematically”? Why did light converge in a wedge on a formally logical rational method of cognition of reality? After all, there are also methods of irrational holistic cognition of the world and things-processes in it. Shouldn't we develop these methods of understanding reality first? In these questions and the answer to the question posed. No, it is not impossible, but it is better, more accurate (!) and easier to describe-to know many processes of reality by irrational methods, which, oddly enough, the human mind quite confidently owns.

6. vanya_vankov says:

For starters, what is M. (from wikipedia): Mathematics (Greek: μᾰθημᾰτικά [1] : This is the science of relations between objects about which nothing is known, except for some properties that describe them, namely, those that are used as axioms in the foundation of a particular mathematical theory[3].

Hence the strict reliable answer. It is impossible to describe those processes in which they are unknown (or absent). those properties that can be used as the basis for a particular mathematical theory.

I believe that it is impossible to describe mathematically the process of thinking of a genius who discovers something that was not known before. By the way, it probably follows that artificial intelligence will never be able to discover new natural science laws.

7. sergey_khaibulov says:

The word “process” implies a change in something over time. If there is a change in something, then this change can somehow be described by a mathematical model. Another question is how accurate and / or verifiable this model will be.
Let's take a simple example: is it possible to describe the process of snow falling mathematically? Can. For example, snow didn't fall yesterday, but it's falling today. Here is a simple model of such a process – yesterday 0, today 1. But more complicated-a graph with a minute step of snow mass per unit of the earth's surface. This can also be done. Here is even more complicated-the same graph, but by the number of snowflakes, taking into account their separately measured distribution �by size (~ mass). This can probably also be done. But it will be impossible to simulate the trajectories of each snowflake falling in a given snowfall purely technically – there are no means to control and there is no computing power to simulate.
Let's take a more complicated example: five years ago I didn't like Zoshchenko's works, but now I do. The first type of model (0 / 1) is just as easy to model, since I remember when I started liking it. But then the problems will begin – there is no conceptual framework and there is no possibility of quantitative measurements. That is, it is possible to model something, but how much it will make sense is a big question.

That is, formally, any process can be modeled mathematically, but in reality, for modeling with a reasonable degree of accuracy, and not “once, twice, many”, there may be a variety of technical and, worse, methodological problems of varying degrees of surmountability. Including those that are probably insurmountable in general.

8. alexander_vanetsev says:

A fool can describe anything mathematically. But the result will also be stupid.
Smart can't describe 2 categories of processes mathematically:

1. Processes that are not quantified. Like, for example, the emotions that Julian Avramov wrote about. But not just them.

2. Processes for which there is no complete / clear data. For example, the economy of the Pskov region or geological activity in Io. Both will probably one day be able to be described mathematically when people have substantially more data.

Just in case, let me clarify: the fool will collect statistics for the Pskov region, somehow make a model out of them, and will run around with this model like a fool with a written bag. Well, or it will estimate the probability of a new volcano appearing on Io, based on the assumptions of its left heel.
But it will not be math – it will be a fool's fantasy, written using mathematical symbols, and having zero predictive accuracy.

9. oleg says:

Do not ask elementary questions that do not require a mat. modeling-because it turns out to be a philosophy. Philosophy is not mathematics.
Just like a semi-human.
How to tell the difference between a sharp tragus(Oleg Voevodin's method, face reading)