In the video you quoted, Mikhael Gromov said nothing about Algebras containing relations that are not computations.

The statement:

All traditional descriptions of mathematics, in my view, are greatly faulty

includes the description of Algebras as a particular case.

Interesting. From my perspective it is a valid relation in the English algebra and is neither computable nor uncomputable but something else. Now it is true that you can measure the relation (e.g., for validity) but this is very different from whether or not it is a computation.

So at least from my perspective, Mathematics contains more than just computation and I'd suggest rewording your definition. No big deal though.

In your undergraduate mathematics studies, did you take the course series in group theory, rings and fields, and then algebras? It is from that viewpoint that I state there are algebras which contain relations that are neither computable nor uncomputable, but instead fall in other categories. As an example, I cited human languages. In fact, beyond those courses there is the discipline of abstract linguistics which you might find related to your quest to define Mathematics.

In the video you quoted, Mikhael Gromov said nothing about Algebras containing relations that are not computations.

In your statements on the matter, you conflate non-computation with uncomputable. But the latter term refers to questions that can't be answered. A transitive relation such as the sentence I provided is neither a question nor a computation.

Your statements regarding the need to restate "I am going to the store" as "The store is my destination" reveal that you don't fully grasp what an algebra is, nor why every language is an algebra. Instead it seems you have misunderstood the statement to mean that a language can be used to make mathematical statements - a very different idea.

There are many different concepts concerning the definition of Mathematics. Here is one often assumed by children whose arithmetic instruction is solely by rote:

According to the above-mentioned framework, the sentence "I am going to the store" is an expression, not a mathematical object. To transform it into a mathematical object, it is necessary to make some abstraction. For example, to say "I am going to x", where x is an arbitrary place. Now, the mathematical object "I am going to x" can be represented by the following set of expressions:

"I am going to the store", "I am going to the zoo", "I am going to the mountain," etc.

Any transformation of the mathematical object "I am going to x" should transform all its instantiation. For example, the transformation from "I am going to x" to "x is my destiny" is defined by the family of transformations of expressions (computations)

from "I am going to the store" to "the store is my destiny." from "I am going to the zoo" to "the zoo is my destiny." from "I am going to the mountain" to "the mountain is my destiny." etc.

Sure, the subgroups of A that are not related to computation are an abstraction of the computational notion of subgroup. My claim "mathematics is an abstraction of computation" does not mean that "mathematics is just computation". Mathematics is obtained from computation by ignoring some features. In this case, you are ignoring a feature known as computability.

By considering the premises:

1. Every language is an algebra
2. There are several languages with subgroups unrelated to computation

to derive the conclusion

L. Not every algebra is entirely for computation

you have shown an example of the claim

Mathematics is just the result of abstraction in a computation

because an algebra that is unrelated to computation is an abstraction from an algebra that is related to computation, indeed, you have the computational concept of algebra, and you make abstraction by ignoring the property of being computational.

The definition

"Mathematics is the language of measurement" -- Steven Krashen

involves a computation, since the act of measuring is a (concurrent) computation: the transmission of information from one system to another. To overcome the computational foundations of mathematics, it is important to develop a foundation of mathematics that does not involve computation of any kind. Then computation should be derived from such a hypothetical system without using computation in this derivation process. I do not know such an approach; maybe another person knows.