Yesterday, I closed a mile-stone sale and just out of curiosity, I declared today's afternoon as learning hours. What would I have done many years ago?
So, I opened a few Wolfram|Alpha windows in my browser and played around first top down asking about certain topics in mathematics.
Then, solving polynomial equations, I played around with degrees and coefficients. I remembered that in a brainteaser forum the probability-a-quadratic-function-has-two-real-roots was asked and I thought how can this be generalized to the general case of degree n (do you need to transform this into questions on probability density functions?).
However, "simulating" lower degree polynomials I "found" clustering of roots when especially playing around with, say "middle coefficients" and they also influence the number of real roots.
So, I needed to look into probability and distributions and played with examples again.
Yes, it is possible to explore and construct knowledge from computations. If you have the right engine that reports not only results but also views ....
I really should take an hour per week at least to repeat such sessions, and not wait for the next mile-stone sale.