That was a wrong and conceited idea, and more to the truth is that quantum mechanics and the physics of the atom is the ultimate foundation of all knowledge and wisdom. For even math itself comes out of and is derivative of atomic knowledge. In the uncollapsed wavefunction they are the exact irrational numbers of pi and e. Physics has already proved that any dimension other than 3rd dimension is wrong, and yet math can go on and on with fake ideas and fob them off, because math is highly academic and highly institutional and highly conservative and does not have the tests and desire to change that a physics experiment insists and urges and demands change. Math can keep a fakery like Kempe's 4 color mapping or like Appel and Haken's 4 color mapping or like Wiles and Taylor FLT going for decades, even centuries past when they should be chit-canned.
Math moves at a snails pace compared to physics.
The 4th dimension and higher are like an optical illusion, and young math people are brainwashed into thinking that always another perpendicular gives a new and higher dimension which can be formed even though our minds stop at visualizing with the 3rd dimension. This is a sad reflection that math rarely listens to physics, and people in math go on teaching and believing this conservative trash season after season because noone places pressure on the math house like a physics experiment places pressure on the fake ideas within the house of physics. Math people need to pay attention to physics much more than they presently do. I claim the correct definition and understanding of 'dimension' will come from Quantum Physics. Let me point out a nice thing about the history of math and physics.