What can I do with a general mathematics degree?

Many people seem to think that mathematics is just about adding large numbers, but that's not accurate. Mathematics is the study of problem solving by using logic. What careers do you think can benefit from that particular skill? That's right. All of them.

I'm guessing that by a "general mathematics degree", you're talking about getting a BA or BS with a mathematics major or minor. In my experience having "mathematics" on your graduate school application or resume is a good thing, no matter what subject or career path you plan to pursue. Admissions committees and employers alike recognize that an interest in mathematics is not common and that it's not easy to achieve good grades in mathematics.

Now I'm going to go a bit off mark and offer you some unsolicited advice.

If you get a degree that includes mathematics in some way, you will likely take a good number of mathematics courses. When taking those courses, it's important to keep in mind that what you're learning is not about how to complete your homework or pass an exam. You're learning about the thinking process of some of the most brilliant thinkers in human history. And you're going to learn it by seeing examples of how one can apply that thinking process in specific situations.

Consider the following simple example which you might see in elementary school. There's a sack containing six oranges and another sack containing nine oranges. If you combine the contents of the two sacks, how many oranges are there in total?

"Well, that's 6+9=15. Fifteen oranges. Easy!" I will show you that though it was easy to obtain the solution to this problem, the mathematics behind it is not so easy.

You probably think that the addition part of the problem was the mathematics. Addition is only a small part of the mathematics involved in this problem. The meat of the mathematics you performed is what's called abstraction. You were given a problem about specific objects---oranges---whose count you represented using an abstract notion known as integers. You interpreted the word "combine" to mean "addition", which is an operation that can be performed on integers to obtain other integers. After finding the solution to the abstract problem---6+9=15---you translated that solution to answer the original problem---fifteen oranges.

By abstracting the problem, you're now able to generalize the problem to solve all similar counting problems. Any problem that combines the same objects---oranges, apples, dollars, teaspoons, velocity of rocket ships---can be abstracted into a problem about integer addition!

But it's not as simple as you might think. Let's say that we were talking about time instead of oranges. It's 6am right now, what time will it be in 9 hours? Can you apply the same argument? To answer this problem, you have to know that time doesn't go beyond 12. After 12, you actually start counting from 1 again. Now you're not working with an infinite collection of integers. You have a limited number of integers---twelve of them.

What I did here is give you a counterexample to what you may have thought was a pretty solid rule about counting objects. That addition rule only applies when you're working with objects for which you can have an infinite supply.

Now that's some real mathematics!

What those admissions committees and employers know about mathematics is that it helps students develop a skill known as critical thinking, and that is a useful skill to have in any job. As proof, you will be able to find mathematics in almost every subject. All the sciences, surely, but also art and music, even law contains some mathematics. The LSATs are an exam that one takes to go to law school. The logic section is an enjoyable game to play for most mathematicians.

I want to add one more thing. I noticed you used the word "gifted" to describe a certain level of mathematical understanding. I dislike that word immensely, especially when it comes to talking about mathematics. It implies that one must be born with a gift to be decent in math and that just isn't true. I think that math, just like driving, is something everybody can do with practice. Some people are better at it than others. Sure. But those who are better probably had a lot more practice. Those people who are pegged as "gifted" are probably those people who happen to *want* to practice more, and so they did.

Even the world of mathematics is deeply divided in this particular debate, so you don't have to agree with me. But I've spent many years studying mathematics and met mathematicians all around the world, and this is the conclusion I've come to.

Don't be so certain about your mathematical abilities just yet.