What is it like being a Mathematics major?
What are common misconceptions about MAT majors?
What kind of internships and international experiences have majors had?
How will Mathematics majors save the world?
Why would anyone want to date a Mathematics major?
Mathematics is the study of the abstract. We all have notions of number or shape—just add two to four or imagine the deformation of a sphere to a point -- but mathematicians seek to understand these concepts at a deeper level. What numbers can be expressed as the sum of two squares? Of four? What is the order of the number of primes from 0 to n? Can a surface that looks locally 7-dimensional and has constant negative curvature be deformed into something more manageable? How can you transmit information over a channel with a fixed error rate with minimal redundancy? Our tools are the definition, theorem, and proof—and reams of paper.
You should study mathematics to learn how to think rigorously. Hiring managers at major companies will seek out math majors because of the depth of thought a math major is capable of. In fact, working math graduates are the most highly paid of any group of Princeton graduates (except computer science majors).
That said, your average math major probably makes for boring conversation at a cocktail party. Consider this dialogue:
English major: So, what kind of math are you studying?
Math major: Combinatorics.
English major: What is that?
Math major: It is the study of counting.
English major: Really? Like, how many numbers lie between 1 and 100? That's easy; the answer is 100!
Math major: No, like, given 
and a family A of distinct subsets of 
all of which are of size r, then the number of sets in A is at most 
.
English major: Oh.
Math major: You know, you can see that the theorem is really about uniform hypergraphs. That one is the Erdos-Ko-Rado theorem.
English major: Well, it was nice to meet you.
Math major: But wait, there's more...
In reality, there is plenty a math major can add to a conversation. Take the previous one, for instance. The math major could have mentioned Peter Pereira's "Fugue," a poem constructed using a Markov model built from several of ee cummings's poems. In a discussion with an art major, she could have also talked about how mathematicians can test the authenticity of paintings. There is more to mathematics than many believe.
What is it like being a Mathematics major?
When most juniors sweat their JPs, those in the math department need only take a seminar. Though they may still write a JP, it is not required. Students in seminars need only present one or two lectures on a topic of their choice—it has to address part of the curriculum of the seminar—and write a final paper summarizing their lectures.
The average math thesis is far shorter than the average history thesis. Math is dense stuff: a 30 page thesis, if it is mostly technical, is more than sufficient in length. Majors have even written introductory textbooks.
Math majors are known for their camaraderie. As a student in the department, you will face some very daunting problem sets. Most of the time, you will not be able to solve every problem on your own. Fear not! Great friendships come from slaving with your peers at the blackboards in the Fine Hall common room—perhaps the ugliest and dingiest (though the most charming) part of the Princeton campus.
Professors, while they may seem aloof, are generally very accessible. If you show up for tea in the common room at 3:30 on a weekday afternoon, you are bound to run into someone you know. If not, just help yourself to the free coffee, tea, and cookies. And if you're there at 3:30am, you'll probably meet someone else you know, too (and you will find the same free coffee and tea).
What are common misconceptions about MAT majors?
One huge misconception is that History majors don't have any practical training. I encourage you to check out our "What can you learn from it?" section again, and ask consulting firms, law schools, grad schools, law firms, business schools, government agencies, teachers, NGO's and the like if that isn't useful. Another is that we deal in hypotheticals. Asking "what if?" is really, really, really hard to do, and rarely helpful. Perhaps the most insidious misconception is that we spend all of our time in the library. This is totally unfair. Our research is mostly in books, so we have to spend time in a library, just like every humanities major and a lot of social sciences major. And at least we aren't stuck in labs all day. But quite frankly, this is college—where did you expect to do your work?
What kind of internships and international experiences have majors had?
Many majors have participated in National Science Foundation sponsored REUs, or research experiences for undergraduates. These give students the chance to work on math research problems in small teams, usually no larger than 4 students. There are REUs at scores of universities across the country, and each sponsors projects in different fields of math. Equally many focus on pure math as applied math.
Princeton math majors have also taken internships with the National Security Agency. The Director's Summer Program and the Mathematics Summer Employment Program both take math majors to work on problems of national importance in cryptology and communications technology.
Our smartest majors have been snatched up by quantitative hedge funds. Several have gone overseas to study math in Eastern Europe.
How will Mathematics majors save the world?
Mathematics is in nearly everything you use. When you take a picture on your digital camera, your image is compressed using the Fourier transform—a way of breaking up a function into coefficient functions of sinusoids. When you make a call on your cell phone, the algebra of error correcting codes comes into play, allowing you to discern the voice on the other end of the call. Math is used to model everything from nuclear explosions to blood flow in the heart. Math majors may not be easily visible in government or in international affairs, but math is used to drive policy decisions: the NSA is the largest employer of mathematicians in the world.
Why would anyone want to date a Mathematics major?
Math isn't easy; you need to be passionate about it to study it. If you date someone who can maintain that level of commitment, think about how rewarding your relationship could be.
On a more serious note, math majors also have great pickup lines: "Baby, you're sweeter than 3.14159265..."
