One of the classes I was assigned at UCF, was “Chemistry For Engineers“. It was a cut-class for the School of Engineering – which had no chemical engineering degree path. The faculty of the School hoped that an assistant professor in Chemistry would be the scapegoat or fall “person”, for cutting their own frosh engineering class back. At that time, and probably still, Florida Universities were forced to take on ALL the AA-graduates of the Community College systems of the state. This may have been modified, as my discussion with a DoD recruiter stationed at UCF in January, 2019 clarified (A chance meeting on my part in the American Admiral Club at Reagan National in DC, after I attended the historic opening of the 116th US Congress). He was happy with all his recruits. Not like the School of Engineering at UCF in the 1990s!
I diverge, though. The course, “Chemistry For Engineers” was an eye-opener for me. I had never understood the engineering student’s mind until then. And only partly. I began giving what I considered a typical course in Undergraduate Analytical Chemistry from the textbook. Almost 80% science. It was too much for the 330-odd students, based on their quiz grades.
So, stepping back, not wanting all those students not to have a fighting chance, I ask them. All at once, after the first quiz grades. “What do you need from me, but a passing grade?” By this point, I had – if not a rapport – a reputation for being honest. They answered, individually and all together, “we want the equation we need,” or more precisely..
“We Want the Equation To Conquer The World!”
Seemed like a tall order for a new professor of physical chemistry with a joint appointment in Physics, and an an adjunct appointment in CREOL. However, if we see teaching a course is also like taking the course, it was a mind-opening revelation.
I came back in the next class session with an idea of how they could remember that equation, and they LOVED IT! (I will not divulge that here, just yet).
The Engineering Student’s mind is geared towards analytics like nobody’s business. They are trained to seek-out that formula, utilize it to the max, and until it fails them, will find better uses for it and for purposes outside its intended realm. I truly believe engineering graduates are some of the finest mathematicians in the World.
And yet. They are not scientists, they cannot jump into a novel situation without a formula, like a scientist or more specifically, a physicist. That is where there tried and true method comes from. Use a formula, ’til it busts. This has been demonstrated to me, time and again by engineers-as-designers, engineers-as-patent-lawyers, engineers-as-entrepreneurs.
Physicists are not mathematicians. That came as a shock to many, but not all PRC Chinese students I have met. They had been trained to view physicists as the smartest mathematicians! “How else can they design and build rocketships if they are not the smartest mathematicians?,” they asked. Well to begin with engineers build and design rocketships, not physicists.
Richard Feynman’s only mathematics award in his life was early on, in 1939. Einstein was not “horrible” at math. He had his girlfriend bring him class notes from his math class at ETH in Zurich. While he did OK in math, Einstein did flunk the math section of the entrance exam to the Zurich Polytechnic when he first took it. He was NOT the smartest mathematician. He was aces on natural science and physical sciences, though.
From Newton, to Feynman, to Einstein, the greatest physicists INVENTED new math when they lacked it, to explain their physical discoveries. For Einstein, he had the idea for a ‘General Relativity’ near the same time as Special Relativity was published, in 1908 (ref.: 1949 in Schlipp, Einstein Archives Israel), but could not express it mathematically; without breaking the bond between coordinates and spacetime in his mind.
He made many errors in doing so through the 1910’s. Heisenberg corrected him more than once on whether gravitational swells or “waves” could carry energy or not! Finally, Emma Noether came to his rescue. She was the smartest mathematician of the 20th Century, and perhaps of all time. She saw the truth in the physical ideas of Einstein and melded it into the mathematics of the time.