You apply the thoughts onto the physical world i.e. typing, measuring, hammering, drilling, and driving ... etc. You have ideas how to use and manipulate the physical objects. But the ideas are in your head, not in the world. — Corvus

Ideas are in the head, but ideas can change the world.

If ideas in the brain exist as part of the physical structure of the brain, then this would explain how an idea can change the physical world.

In the same way that an idea physically exists within the brain, numbers, being ideas, would also only exist within the brain in physical form.

Ideas are in the head, but ideas can change the world. — RussellA

I had an idea to cut down the tree in the back garden for 10 years, but it was just an idea. The tree is still standing tall. Can ideas themselves change the world?

In the same way that an idea physically exists within the brain, numbers, being ideas, would also only exist within the brain in physical form. — RussellA

Where about in the brain do you see numbers existing in physical form?

Where about in the brain do you see numbers existing in physical form? — Corvus

P1 - Numbers and colours exist somewhere otherwise we couldn't be discussing them.
P2 - We know that numbers and colours exist in the mind because we are aware of them.
P3 - We observe the colour red even though colours don't exist in the world. What exists in the world is the wavelength 700nm. We mentally project the colour red onto the world that we are observing.

C1 - Similarly, it is possible that even though we observe numbers in the world, numbers need not exist in the world, as we can mentally project numbers onto the world.
C2 - As it is possible that numbers need not exist in the world, there need be no metaphysical angst about numbers existing in the world.

P4 - A calculator can manipulate numbers within the physical structure of the calculator in a deterministic and explainable way.

C3 - There needs be no metaphysical angst about numbers existing in a calculator.

P5 - Similarly, there is no reason why the brain cannot manipulate numbers within the physical structure of the brain in a deterministic and explainable way.

C4 - Similarly, there needs be no metaphysical angst about numbers existing in the mind.
C5 - Any metaphysical angst about numbers is unnecessary.

P1 - Numbers and colours exist somewhere otherwise we couldn't be discussing them. — RussellA

The fact that we are discussing something is not the evidence for existence of something. We can discuss about the unicorn or a flying pig. Does it mean the unicorn or flying pig exist?

"Numbers and colours exist somewhere"? Somewhere is like saying nowhere.
No one would know where the somewhere is. In which country, and which city, an what street, at which number of the property does it exist? It has to be a specific location that can be verified by possibility of visiting the site in person in giving out the location of the existence to be meaningful.

I could go on pointing out the logical problems in your list, but I will just stop at the first one (to save time).

The fact that we are discussing something is not the evidence for existence of something. We can discuss about the unicorn or a flying pig. Does it mean the unicorn or flying pig exist? — Corvus

They exist in literature and in the mind as thoughts.

If either the unicorn or flying pig didn't exist somewhere, then you couldn't have written your post.
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"Numbers and colours exist somewhere"? Somewhere is like saying nowhere. — Corvus

The expression "exists somewhere" does not mean "exists nowhere".

If either the unicorn or flying pig didn't exist somewhere, then you couldn't have written your post. — RussellA

I know them in my thoughts, and that's how I could write about them. I knew them as non-existence ideas, but they don't prevent me from writing about them. They don't exist. They are known as ideas.

The expression "exists somewhere" does not mean "exists nowhere". — RussellA

It means it doesn't mean anywhere. In other words, it is a meaningless assertion.