Since I intend to reduce fear and misunderstandings about mathematics, and since I am a mathematician, I will start with the most scary thing I know about mathematics: it has no end.
I did my graduate work at Caltech, an excellent school, if it does not drive you insane. While I was there I helped teach an introductory course with the inspiring name Math 1. One of the students in my group, a very orderly fellow who always wore a starched white shirt and carried a briefcase, would often chat with me after we had resolved whatever questions the current homework had caused him to ask. During one of these chats he asked in a puzzled voice, “What do you people do around here?”
It had just occurred to him that I and my office mates were available for about three hours a week to help him and surely we must have some other duties. The “here” to which he referred was the department of mathematics, in particular my office, which housed three graduate students at the time.
I replied, “we figure out new mathematics.” This caused him to look at me in horror which he vocalized by saying, “but I’m a physics major!”
I toyed with the idea of assuring him that this was a treatable condition, but since he actually looked upset I asked a question that I’ve been asking people my whole life: “why do you care?”
“How can I do physics if we don’t know all the mathematics yet?” he replied.
“I thought this one over for a minute and then said, “follow me.” A couple doors down the corridor from my corridor and across the hall was the reading room. It has large tables which are handy when you’re trying to track something down in five parts of three different books (a lost art, mostly, what with the interwebs and all). The tables were also quite useful for grading stacks of papers (this still happens. Way too much). I took my charge there and gestured at the floor-to-ceiling shelves that covered three walls.
“This is all new math, within the last five years.”
“ALL of it? There are hundreds of books in here.”
“Actually they are bound collections of journals, and just the ones that are close to current faculty interests. The seventh floor of the library is all math, much of it recent.”
“But physics depends on math!”
“Well, only a few bit of math are relevant to physics. Dr. Simon actually fills in the math underneath some of the stuff the physics professors make up.”
“He’s a mathematical physicist. Physicists are careless and just make up stuff that fits their observations or lets them justify an intuitive conclusion. One of the things we do is figure out if its possible to make what they did mathematically rigorous.”
At this point, the student walked off looking dyspeptic.
I hope you enjoyed this story.
Department of Mathematics and Statistics
University of Guelph, Ontario, Canada