[FOM] mathematical understanding

[Regien Stomphorst]

Hello,
I am a new member of this mailing list. The reason I subscribed is that I am
interested in 'Mathematical Understanding'.
I would like to compare Mathematical Understanding with Scientific
Understanding. Because of my background education I have abundant
information (literature) about Scientific Understanding. However, I lack
contacts and information about 'Mathematical Understanding'.

The way I see the distinction between scientific understanding and
mathematical understanding is as follows:
Mathematics seeks to prove new theorems within its own domain. Propositions
are proved within the mathematical (axiomatic) framework. Physical theories
need experimental verification. Any physical theory described in
mathematical terms needs a direct relation to experimental conditions. Any
mathematician will develop a familiarity with the behaviour of the equations
(s)he deals with. This familiarity is mathematical in nature. To explain
phenomena, physical theories are used. These theories can be formulated in
abstract mathematical equations. To understand the relation between the
theories and phenomena mathematical understanding is not enough. It should
be supplemented with scientific understanding.

More specifically, I would like to know when do mathematicians understand
their subject matter? Do they agree on when something is understood and on
what is understood?

I would be grateful if there is anyone who can enhance my understanding (!)
of Mathematical Understanding?
Best regards,
Regien