I frequently see younger math students, and even those in other fields, wishing they had a burning passion for their work, one that allowed them to:
“work on problem sets for hours straight”
“solve open questions in their sleep”
“see the world in a mathematical context”
The last desire will honestly arise for most people who study math long enough — you can only “see the world in math” once you know enough math to properly fill it… most of the time. However, there is a steep misunderstanding of mathematical passion that I want to clarify, from my own experiences at least.
I’m a person who is passionate to the point of obsession; I think about math 24/7. It has benefits and drawbacks, no better than someone who completely lacks passion and forces themselves to work regardless.
I can work on problem sets for hours on end… when my interests properly align. If i’m caught up in another question that came up from a lecture or seminar talk, my brain will remain occupied, and I’ll neglect the work I actually have to do. Sometimes, even if I get myself to work on the required questions, a new one will arise mid-proving… and I’m gone.
Passion is, at times, an enemy to discipline. If I don’t sleep properly, it will effectively take over, and then I’ll terribly behind.
Also, the ability to make creative connections does not imply the ability to make good connections. I am able to “see mathematical structures” in many things, but that doesn’t necessarily mean that they lend well to theory that people are already thinking about, or have some larger application in an interdisciplinary context.
Also, some of these connections are deceiving… and just plain incorrect. I must constantly filter my mind. As I learn more math, this becomes easier, but the tendency to form new questions also becomes more intense.
Math does often enter my dreams, yet I still caution against desiring this phenomenon. Thinking about math constantly is wonderful, when I have people to share it with, but even then, constantly thinking about anything will eventually burn our brains out.
I end each week in a near spaced-out state because I’ve completely expended my mental energy, only to be hit with more ideas the second it gets a little rest.
Furthermore, if you don’t have people to share these ideas with, and people that will fact-check you when you’re still learning, it’s easy to slip into believing you’re going crazy.
Our mind has a finite capacity for knowledge and abstract pondering. We can collapse ideas into one-another as we learn more, and as we draw the right connections, but this takes time.
Passion gives you the power to push through hard moments — it saved my life quite honestly, but obsession can effectively destroy it if not properly managed. We ought to aim for subtle curiosity, then discipline and passion… but obsession should never be the goal of a young mathematician.
