I agree that mathematicians want understanding, but that's true of all scientists. Physicists or biologists, economists, or sociologists, psychologists or historians want to understand, but they want to understand different things, with different methods. If you want to explain what defines mathematics as a scientific discipline, you need to explain what it is that mathematicians want to understand, and with which methods. But maybe that's not what you want to do?
The Greeks said it was turtles all the way down. Modern mathematicians say it's elephants. Vive les pachyderms.
I agree that mathematicians want understanding, but that's true of all scientists. Physicists or biologists, economists, or sociologists, psychologists or historians want to understand, but they want to understand different things, with different methods. If you want to explain what defines mathematics as a scientific discipline, you need to explain what it is that mathematicians want to understand, and with which methods. But maybe that's not what you want to do?