I'm doubtful in the majority, but I happen to regard numbers as abstract (as opposed to concrete). Concepts or abstractions (something entirely different) may be a property of the mind, but not only do I find a distinction between concepts and what concepts are concepts of, I distinguish between abstract objects and mental abstractions.
Although I agree that numbers are real (genuine), my intended meaning by regarding numbers as real is to deny that they are imaginary. If people never came to be, numerals, like words, would not be, but the referents to which they refer are not held by the same constraints. The referent to the numeral three is the number three, and since I regard it as an abstract object, I regard it as an existent that is neither concrete nor mental.
Of course thay are imaginary. They doesnt exist anywhere except in our imagination.
They are useful, but why shouldnt imaginary objects be useful?
I would say that our brain hardcodes ”gruoping” (the unconcious mental festure of grouping features into objects and creating sets). Numbers 1-3 has some hardwired brain representation. Then the brain has some other more complex hardwiring (pattern recognition etc) but rest of math is not just abstract but also imaginary.
Numbers exist but they are not a product of mind. They are not in the imagination. They do not exist anywhere, but again, they exist. They are not concrete. They are abstract. But, they are not an abstraction. The latter is a product of the mind, but the former is not.
Not to make an analogy but on a completely different topic (that is a stretch at most to tie together), what in physics other than particles physically exist? For instance, consider a rock vs a rock rolling (oh say, down a hill). We can examine the number of atoms in the rock. Now, how many atoms are before us should the rock begin to roll? I'd suggest they are the same.
Now, if we have a rolling ball (or rock, whatever) with x number of atoms and we remove the rolling from the equation, we are left with the same physical substance, a ball not rolling with the same number of atoms before us. Notice that it doesn't work the other way around. If we start out with a rolling ball and remove not the rolling but just the ball, we are not left with anything.
Back to the question, what in physics is in fact physical? We have particles, and we have particles in motion, but count the particles whether moving or not. The count stays the same. Speed, momentum, time, anything not composed of physical substance is what, apart of physics as we know it, but the atom count or particle count or subatomic particle count is zero. Yet, we don't deny these things exist.
To say of something that it exists need not be constrained merely to objects composed of matter. Such a perspective need not invoke fears of including truly nonexistent things.
Numbers are (again) abstract, not an abstraction. However, the complexity involves levels of abstractness. For instance, the number three is the class of all triples. We can't find any actual three's composed of physical substance, but like the ball that can roll, there are objects in nature that have a correlation of triples. A group of three trees, for instance, or a planet with three moons orbiting it.
It requires a mind capable of abstraction to KNOW (or believe) what is true of the world, but we ought not lose sight of the fact that what abstractly exists independent of us does not require abstraction. There are three big holes in a chunk rock whether we know it or not.