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That would depend on how much mathematics is in one's "standard sense."

Hello Doc!!! It's good to see you again!

Not to quibble overmuch, but I think Bohr was using the word "visualizable" in its "standard sense": What is "visualizable" is what comes into our consciousness by means of the "inputs" of sensory perception. His point is that this sort of thing is what shapes the categories of human thought that inevitably translates into such conceptions as the physical laws. In other words, our immediate perceptions of space and time condition how we think.

Now mathematics does not work thataway. It has nothing to do with sensory perception, or the "visualizations" we can describe based on sensory perception. It seems to me that mathematics is extraordinarily "non-visual": It allows us to formulate conceptions about things that are "unseen." If i might put it that way.

Not visualization is involved here, but conceptualization. Which tells you that "material inputs to the brain via the eyes as stimulated by external phenomena" is not the whole story of how the mind works. Mathematics is unimpeachable evidence of this.

Anyhoot, I just love what Eugene Wigner had to say on this point:

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research.

And I hope so, too, dear Doc, with all my heart.

Thanks so much for writing T. -- it's good to hear from you.

It has nothing to do with sensory perception, or the "visualizations" we can describe based on sensory perception. It seems to me that mathematics is extraordinarily "non-visual": It allows us to formulate conceptions about things that are "unseen." If i might put it that way.

One may describe many things mathematically. Some people visualize these; others may not. I tend to visualize most mathematical items. Certainly things in vector spaces or arithmetic have a visual component.

..."material inputs to the brain via the eyes as stimulated by external phenomena" is not the whole story of how the mind works.

You, and your words: Gems. Many thanks for sharing your insights with me. Our Lord of Grace and Truth continue His blessing to thee in Christ Jesus His Son and keep you blessing others continually as you do here!