IMHO, this statement never hold for Maths : since all math reasoning is just the construction of a logical and symbolic proof based on a set of existing theorems and the underlying axioms, it requires the student to :
1. be familiar to the logical reasoning : what «implies» or even «for any x» means.
2. know the relevant set of theorem and axioms used in the demonstration.
You could probably illustrate what a mathematical result implies in some real-life example, but you won't be «explaining» it.
Quantum physics is a really good example of this, because it's not that difficult to understand if you look at it with the mathematical PoV : it's basically linear algebra in infinite dimension, you have vectors (in the space of «functions of |R³») and linear applications on these vectors (with all properties of such applications, like eigenvalues and eigenvectors), etc. But if you try to «explain» it in simple terms, you're going to distort the reality to fit in the macroscopic-scaled human representation of the world and you'll probably say things that won't be true.
1. be familiar to the logical reasoning : what «implies» or even «for any x» means. 2. know the relevant set of theorem and axioms used in the demonstration.
You could probably illustrate what a mathematical result implies in some real-life example, but you won't be «explaining» it.
Quantum physics is a really good example of this, because it's not that difficult to understand if you look at it with the mathematical PoV : it's basically linear algebra in infinite dimension, you have vectors (in the space of «functions of |R³») and linear applications on these vectors (with all properties of such applications, like eigenvalues and eigenvectors), etc. But if you try to «explain» it in simple terms, you're going to distort the reality to fit in the macroscopic-scaled human representation of the world and you'll probably say things that won't be true.