Maths is not experimental. This roundabout, handwavy, vague way to deal with things causes more harm than good, in my opinion. Try to understand a proper mathematical proof instead.
Mathematics: An Experimental Science - https://www.math.upenn.edu/~wilf/website/Mathematics_AnExper... (PDF)
> A computer is used by a pure mathematician in much the same way that a telescope is used by a theoretical astronomer. It shows us "what’s out there."
> From such explorations there can grow understanding, and conjectures, and roads to proofs, and phenomena that would not have been imaginable in the pre-computer era. This role of computation within pure mathematics seems destined only to expand over the near future and to be imbued into our students along with Euclid’s axioms and other staples of mathematical education.
Also:
Turtle Geometry: The Computer as a Medium for Exploring Mathematics - https://mitpress.mit.edu/books/turtle-geometry
That was an amazing read. It certainly made me rethink my position. Thanks!
I am with Arnold on that.
> Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French mathematical education, and then later on that of other countries as well.
I majored in math in undergrad, and one of the required courses was about communicating mathematical ideas. One of my bigger projects in that course was to explain the Monty Hall problem so it could be understood by the general public, and I got a good grade by putting together a lesson plan that included this type of simulation.
Instead they would think of adjusting the axioms and work out a useful probability theory.
For example, most children check 1+2 experimentally before accepting the theory.
So, clearly, understanding the proof isn't required. It is a great deal more work than many other methods of understanding the problem, so why prescribe it as the best way?
You might be comfortable with it, but not everyone has the time nor inclination to become mathy enough to live life through your lens.