Undergrad Visualisation in math and physics

[trees and plants]

Hello. Do physicists and mathematicians visualise math formulas or specialised math or physics words?

Words like metric space, Lindelof space, metrizable space, Gamma function, harmonic function, mathematical limits, series, power series, Laurent series, phase space, symplectic space, observator, spacelike, timelike curves,vectors, Jacobi fields, spacetime, n-sphere, n-manifold, Banach space, convex function? Or formulas like the Gauss-Codazzi equation, $m_1a_1+m_2a_2+m_3a_3=0$, $<x,y>=x_1y_1+...+x_ny_n$, the transformation law in tensor analysis , the Riemann curvature tensor, the Christoffel symbols, the Gauss map, the shape operator?

Do they visualise them like physical objects for the symbols or images from things they know for he symbols in the formulas or the words?This also helps i think in learning, memorising and understanding. When they want to make questions or when they read scientific works do they visualise to understand?Or when they try to answer scientific questions? Thank you.

 

[Mayhem]

A study showed that physicists and mathematicians tended to have a very numerical-quantitative approach to problem solving, whereas chemists, biologists, etc. were more closely aligned with spatial-visual reasoning. I can't find the link right now, but it does suggest that physicists and mathematicians use less visualization than chemists and biologists. If you read a physics/maths textbook vs. a chemistry or biology textbook, this becomes very apparent.

 

[Mark44]

On the other hand, some areas of mathematics are more easily understandable if there are some images involved. For example, geometry, trigonometry, differential and integral calculus, group theory, among others. As far as physics is concerned, just examine any textbook, and let me know if you find any with no diagrams or figures. I don't disbelieve that some study showed physicist and mathematicians had a strong numerical-quantitative approach to problem solving, but I believe that many of them also draw upon their abilities in spatial-visual reasoning.