It's the oldest and the simplest of all questions regarding the nature of mathematical truths. History gives no universally accepted answer to it.

Proponents of social-constructivist philosophy argue, for instance, that the equation 2 + 2 = 4 is only a convention our grade school teachers bullied us into accepting as a law of nature, and that mathematical objects are social entities in the same way as monetary systems or political institutions.

Attempting here to replace a post that got lost in the server migration.

This old question should have been settled long ago. Plato was just plain wrong. The world of forms (ideas, software, numbers, information) does not exist. Only substantial things (matter and consciousness) can have existence.

Saint Augustine and St. Thomas Aquinas were both Platonists who had extensive influence on Church doctrine. The philosophical errors they propagated are still around to confuse people today.

Mathematical ideas (like addition of numbers) find expression because they are useful. They are therefore embodied in human practice and text books.

I think the biggest danger of computers is that we confuse the speed of processing with the speed of thought.

Computers don't think.

They put out something like surface impressions (illusions), and the faster they can do that the better. But are we getting fooled into thinking that speed is a valuable thing in terms of processing ideas? And really, the most valuable thing in terms of processing ideas, and most people’s experience will bear this out, I think the most valuable thing is ripening.

An idea has to ripen. Just making connections is trivial.

It can be interesting, but when an idea really takes root in my gut so I stay awake nights, it's different.

As Shakespeare said "ripeness is all."

Some scholars have argued that the brain may build its mathematical understanding with language and that the structure may still stand after the scaffolding is removed.

However, no matter how helpful language may be to mathmaticians (perhaps as a mneumonic devise) it is not necessary for calculation. Also, they are processed in different parts of the brain.