Mathematics: The Most Misunderstood Subject

The author has rightfully directed his words at those considering becoming math majors. Consequently, he makes it clear that most basic math education is inadequate to really understand math and its practicality, but leaves as the only solution enrolling as a math student. This is a great call to action for students, but for the broader audience, it leaves me thinking the following:

My math background is clearly inadequate, and his description of mathematical reasoning sounds like something I'd like to be familiar with, so how do I get there? What's the route to the prize other than enrolling in Fordham's math program?

While the professor in question has no reason to answer this, at least on the Fordham website, I wonder what answers the HN crowd might have... thoughts?

The author does imply that great teachers have a lot to do with it. At a later age, when one is out of school or almost out of school, one obviously needs to show more personal initiative. And a lot of people here and elsewhere have asked or written about how to best self-study mathematics. However, the importance of having a teacher is often not mentioned. Even if you are very self-motivated, a teacher can make an enormous difference by showing you the cool stuff that you might miss on your own. One can be very motivated about building a house by themselves, but might have only ever seen mud bricks, and hence will try to diligently build a house out of mud bricks. A proper teacher can illuminate and guide a student through the vast world of other things out there, just like someone trained in construction can show the self-motivated builder how to build a proper house.

Now, how does one find a teacher, you ask (especially when one has left school)? A few options I can think of:

* Go back to school.

* Participate in an appropriate online community.

* Reach out to professors or even students in nearby schools.

This reminds me of "A Mathematican's Lament" by Paul Lockhart ( http://www.maa.org/devlin/LockhartsLament.pdf ). It is a great read in any case.

Another good article about mathematics education, by William P. Thurston, a Fields medalist:

http://www.math.sunysb.edu/~mustopa/thurston_edu.pdf

I'm pursuing a career as a math professor (currently an undergrad). I'm not shy about my passion for math, and this has lead to countless conversations like the ones below:

"What do you want to do with your math degree?"

"I want to go to graduate school and eventually become a math professor."

"Oh, so you want to teach!"

"No, I want to do research."

(Here they give some expression of confusion. I've had this particular conversation dozens of times)

Also

"So, what do you do in math research? Do you just sit around and solve equations all day?

I do my best to explain to these people what math is like and why I do it, but I usually don't feel like I'm getting through. I have been told by mathematicians many times, and have experienced myself, that doing mathematics requires lots and lots of frustration (I'm sure many people here, including those who don't do pure math, know what I'm talking about).

But for me the most frustrating and disheartening part of math is the fact that most people don't know what it is. It's not just that they don't understand the details, or what happens at high levels. It's certainly not just that they look at an end product (analogous to, say, a product from a startup) but don't get where it came from. It's that most people fundamentally don't understand what I do. They think of math as the capricious monotony they were put through in grade school and can't fathom why anyone would consider dedicating a life to it. Most aren't even willing to try. My love of math is a very big part of me, and it's a part that very few people understand.