Do the numbers exist?

The question is to understand how it can be potentially
The number three either exists at the moment (Platonists and their army you) or does not exist (the others).
If it exists, then so do the numbers nine and ten, and all the numbers (which of them does not exist? Does it only rise from nothingness to existence at the moment of thinking about it?), it is a concrete infinity. How could it not?

Every number exists actually, not potentially. But it can be said about all numbers that there is no largest number that exists, or that the number of existing numbers is as large as you like.

I can't understand and it seems this is not the place.
If you wrote about this somewhere else and can give me a reference, please do. If not, then too bad.

As far as I remember, I haven't written about it, and I don't see what there is to write about. What's not clear here? Even if all numbers are existing entities, it is still possible to say instead of “there are infinitely many existing numbers” (which is apparently a concrete and not potential statement), the potential statement: “there are as many objects as you want”.

I don't know how to explain further what I don't understand. I feel like an idiot. It just seems like a contradiction to me to say that 'all' numbers are real numbers but still not 'saying' that there are infinite numbers. I don't understand why the concrete statement (which creates problems with the view that there is no concrete infinity) is incorrect.

I didn't say it was wrong. What I said was that if you oppose the existence of a concrete infinity and assume that it cannot exist (as I also tend to think), then even in the Platonic assumption there is no need to assume it. There too you can express everything in a potential way.

It is impossible to say that the world of ideas works in decimal or any other form.

You could also say that the idea of number exists and the divisions are with us (or that every division exists as an idea). There are lots of forms, but I also answered assuming that every number in itself exists, and I still don't think there's a problem.

How can one decide or think that the numbers “exist” and how can one think otherwise? I don't see what could convince me or make me lean to one side. What am I missing here?

How can you decide whether parallel lines meet or not? There is intuition. The same is true here. It is not a decision based on arguments. But read about Platonism. That is not the issue here.

If it's just direct intuition, then why is there a correlation between practicing mathematics and Platonism as written above: "Most mathematicians are Platonists, and so am I."

Because someone who works in the field has a more well-founded intuition. He encounters this material every day and knows it well.

But most people in the world encounter numbers all the time, why is it that from a Platonist perspective numbers are less obvious to the intuitive eye than a host of monstrous mathematical constructions? Why isn't it like saying that a truck driver encounters and knows gravity better than a person who works in front of a computer (and truck drivers would have a more common and well-founded opinion on whether gravity is an object or not)

They don't meet but pass by. After all, it's not like someone who lives with a partner knows them and meets them occasionally.
But I have no arguments about it. If you don't agree, then no. Each person has their own impressions.

Nikanor, to your question about the correlation, it may be something psychological that makes it more fun for them to think they are dealing with something objective and not just human concepts.