First off, I have no interest in being a mathematician. Math was always and continues to be quite difficult for me.
So, as an outsider to advanced math, it blows my mind that there are people who’s entire job title is mathematician. How does that work? What does a mathematician do?
You get picked up as a pet project by the Financial Engineering Professor at your college who teaches you a lot of statistical wizardry and sthochastic calculus and grooms you to become his newest and greatest quant he can brag to his Wallstreet buddies about. They have already seen your projects with the professor, the interview is pomp.
You make 2M your first year and are making well over 10M by your fifth year. You work 80+ hours a week, making some other people very, very rich. After a decade you are very burnt out and wondered why you ever wanted to do this in the first place. You quit your ridiculously high paying job at your hedge or whatever fund and move to upstate NY to get your teaching credentials and then go teach maths to high school students who will ask “when will this ever be useful” and you smile in your quietude over the whifs of the coffee in your thermos as the students finish the pop quiz of the day.
That’s what mathematicians do in my experience.
Finance, there’s a whole lot of arcane statistics underlying risk management.
Tech, the bleeding edge of computer science is really just applied math.
I thought applied math was just buying a silly amount of apples…
No, that is appled math.
Sauce?
No, whole.
I’m pretty sure your job title isn’t “Mathematician” though. You’re a “risk analyst” or “quantitative analyst” or something. You’re also not doing pure math, you’re using somewhat advanced applied mathematical processes to model financial information. Just like how a rocket engineer isn’t a physicist but may have a background in physics.
So the 6’ 4" guy in finance is just a tall math whiz?
Mathematician here (algebraic topology). Pure maths is pretty much an internship in academia. Applied math is anything between basically physics to actuary and finance. Since pure math is highly academic, though, there is no predefined job path following a degree, which is why the question is as interesting as it is hard to answer.
In academia, we do weird and wonderful things that only a few peers in the world probably will see and understand, due to the highly specialized fields of study. In industry, anecdotally, we do surprisingly little math and are mostly sought for analytical skills and proficiency in problem solving.
Sadly, most people that hire us outside of academia do not know much math themselves. I believe there are lots of real problems that could benefit from having a mathematician working on them, but there is just too little understanding of mathematics to identify the need.
An actual mathematician has arrived!
So, it seems from this whole thread that math for math’s sake is not a money-making endeavor, but being the guy who runs the numbers for a company or institution is where the money comes from.
Is there a lot of stigma in pure math circles against people who move on to do applied mathematics?
Speaking from a pure maths’ perspective here: Frankly, a little bit. I think at the university research level, the academically inclined professors might be a bit tired to be sidelined with the applied ones, especially when the latter are applauded for their industrial cooperation (read research investments) and appliances (read private ownership over publicly funded research). My study mates and I joked about applied math being dirty, but in reality it is more the absence of creativity and rigor that is the problem with applied math in my opinion.
To me, math is all about answering cool questions, sometimes posing even cooler questions in the process. Maybe an appropriate analogy would be whether an artist judges those that make commercials. Exploratory work can take a life of their own that is usually not possible when the format of the answer is predefined. That being said, I do not really judge, I only think that the different expressions are (usually) quite distinct in direction and content. I did not do math for money, though I rely on my mathematical skills for income.
This is such a neat window into a whole different world for me, thank you for writing all this out!
It does sound very much like artists and the whole conversation of who’s selling out and who is being true to the art.
It seems to me that we definitely need both types in this world, ones like you who are curious and just want to explode the edges of what we understand for the sake of discovery, and ones who are willing to apply their mathematic knowledge to narrowly defined problems.
My son has a math degree and does computer programming.
Years ago one of my old military bosses had a math degree, he did stuff for national security. Secret secret stuff. I assumed it was all codes and decoding.
Agencies like the NSA really like mathematicians so there is use for them in cryptography
- Teaching
- Research jobs
- Tech
- Wall Street shit
- Accounting
- Loss protection such as fraud prevention or forensic accountiing
- Sell dime bags outside your local convenience store
- stripping
- painting houses
- carpentry
- day laborer’s
- pouring concrete.
You work somewhere that can afford to pay you. Physics labs helping research. Universities doing theoretical work. Or you teach.
Those are pretty much it.
Im an electrician so dont expect more insight from me
I am not a mathematician, but sometimes I get accused of being one; so given that no real mathematician have answered, I guess I can give it a shot.
Mathematician are in charge of building mathematical tools that are used by physicists, computer scientists, and many other subjects, including artist.
Why is math useful: mathematics are used in social science, physics, computer science and many other subject. Take a simple example from computer science: everyone is very excited about quantum computing, but what questions can be answered faster by a quantum computer than a classical computer? This is both a computer science question and also a math question. Many mathematicians are working on problem like these.
What is the difference between mathematican, computer scientists, physicist, and so on: although people from other subject also use advanced mathematical tools and work on similar questions as mathematicians (I guess why I was accused of being a mathematician), the difference is in their approach. Typically, for non-mathematicians (like me), proofs and math tools are means to an end. We often want to prove a very concrete problem (like are two reasonable ways to define the meaning of a program are equivalent), and usually we prefer the proof the takes the least amount of effort to get to the conclusion. Whereas mathematician often makes connection between different approaches, generalize, and just explore things that they feel is interesting. The mathematical approach often is slower but also gives deeper understandings: although it is common for many of their insights to be lost through time, it is also quite often for these exploration leading to important breakthrough in other fields.
What is the life of a mathematician like: like every other academic: teaching, research, writing grant to feed yourself, and sometimes traveling to discuss ideas and start new projects. I imagine OP is most interested in is mathematical research. I feel the most apt analogy is the creation of art: for an artist, they usually have a emotion trying to express, either something they see or feel. Then they do a couple sketch, see what detail/style works in expressing their ideas and what doesn’t, then paint the painting. For mathematicians, they often have a question in mind, then they try some examples to see what steps closer to their goal and what leads to dead ends. Through these excersices they gain a intuition of what conditions are important for the desired conclusions, then they paint the full painting by finishing the proof.
These proofs can be exceptionally time consuming: even for computer scientists, they can easily take couple researcher a year of work to do a proof. Most of the sketches will be thrown away, either because they are too convoluted or because they don’t lead to the correct conclusion. Usually, a proof by computer scientists like me can easily take 20-30 pages to explain properly, if not more; and the proof that were thrown away can double that quantity. I can only imagine proofs for mathematicians will be even more energy consuming.
