Mathematics is the gate and key of the sciences … . Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy. — Roger Bacon 1220-1292
How little we have progressed in 800 years. I can start with an example. Some of my first University students, “engineering students”, wanted numbers to ‘plug in’ to equations or they couldn’t understand the concept. At least that is what they said. I would submit that if you didn’t understand the abstract representation, you couldn’t really understand the concrete. It became clear that getting an answer, getting a grade for getting that answer was their goal.
So why is it that x = 3 is OK or better yet 2+2 = 4 is OK, but A + B = C is just too abstract of a construct? Or, I don’t understand A + B = C unless you give me values for A and B? While these are the most simple constructs of math, it seems to cause confusion.
This is not a lament on the poor state of math education, it is an observation that otherwise intelligent students fear and therefore don’t try to understand the value of math.
A math professor at the University of California addressed the following question, “Despite all this timeless beauty, many people dread mathematics. They say that they “hate math”. But if it is so beautiful as I claim, then why do people hate it?” Professor Edward Frenkel responded, “Imagine that you had to take an art class in which you were taught only to paint a fence or a wall but were never shown the paintings of the great masters. Would that make you an art lover?”
It isn’t enough to simply learn the tools of math, one must learn enjoy these tools and appreciate the power they provide. Math is at the heart of everything from music to space exploration. It is the language of the arts and sciences.