Im not at all math savvy. In fact the opposite. I was having a conversation about math with a colleague and I realized that other than teaching i have no idea what someone with a math degree or a “Mathematician” actually does? Im curious now. Whats their day like? Who employs them?
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Depends a lot on what you specialize in. Some work in math research, some work in IT, some work in financial analysis, or insurance risk calculations.
I’m an engineering researcher but in a very theorethical field so many of my colleagues studied math. We optimize differential equation systems to improve the control of industrial machines. Our work schedule is like 80% writing code to execute our math, 10% debating with each other over equations and 10% talking to “customers” about their goals and specifications.
Lots of industries and companies need to build models of complex systems: business analysts, stock traders, insurance actuaries, sports teams, engineering firms. Other people can also build such models, but mathematicians are the specialists at this. The tech giants employ lots of mathematicians to analyse human behaviour (you may have heard of big data).
Then there are the complex systems that companies themselves need. The software that banks use to keep track of and move money around are naturally incredibly complex. Again a mathematician would have useful skills here.
Sometimes mathematicians are also useful in the industry because if the way learned to reason and solve problems. Math studies require the ability to focus on one problem and find the most efficient solution for this, it requires rational thinking (als logic is also a great part of mathematics) and mathematicians are used to not being able to solve a problem on first sight but to think and riddle about it to get it done. These qualities are useful in a lot of fields, e.g. I know a lot of Managers and Consultants who a mathematicians but obviously mainly use their soft skills instead of the math part they have learned.
I have a friend that’s a mathematician. Do does research for a university but he has to go out and find his work. I.e. he gets companies to sponsor grants for him to solve a problem they might have. Turns out a big user of this sort of research is the government, more specifically the military. They are always thinking up new ideas to see if they can get x information out of y. I can’t give you any specific examples because he wasn’t allowed to share them, because military. That said, he may have gave me a couple really good examples that would make you think that there is absolutely no way that that could be done. Turns out it can be done. But he absolutely did not tell me.
Mathematician here. My regular job is as an analyst. Analyzing large data sets to identify trends, writing formulas, and yes debating the proper way to calculate metrics with my colleagues.
I do a lot of work related to Lean Six Sigma, which is optimization and problem solving. Mathematicians are excellent problem solvers! We use logical thinking and break down problems into smaller components to identify root causes.
Also, some statistics is involved with creating control charts and calculating the confidence intervals of the analyses.
A programmer once told me that as you get more and more complicated with what your code is trying to do, programming and mathematics converge.
A big part of it is that for a lot of things, making a rudimentary algorithm to solve a problem is pretty easy. But this rudimentary algorithm will require a lot of steps and computations. And each step costs money in hardware (computer parts don’t last forever), energy (electricity ain’t cheap, and time (you actually need a solution).
Mathematics can be used to improve algorithms and make things faster, easier, and cheaper. And depending on time constraints, usable.
The Alan Turing film about code breaking shows all of this. In the film Turing makes a machine and has a rudimentary calculation for breaking the enigma cod le relatively early in the story. But the algorithm is rudimentary and after computing for a week it’s still not done; and since the code changes every day this is useless. So they spend all day every day improving the algorithm to the point where the computer can perform all the calculations in minutes.
Lots of real world problems are like this. Logistics systems change in scope and what products and locations are involved constantly, so you also want your calculations done ASAP.
Mathematics and physics converge too. Optimization is a big part of optics design: everything from car headlights to the camera lens in your cell phone to the Hubble. Hubby just retired from the Optics group of Synopsis. Was a programmer on their CAD system. Used math for:
1. Ray tracing
2. The “glasses” that fixed the Hubble
3. The optical version of the scanning tunnelling microscope (how to get light out of a fiber optic cable thinner than the wavelength of light, as I understand it)
4. Detecting gravity waves
5. Periscope
6. All sorts of lenses (cell phones, flashlights, the light pipes that light up your car dashboard)
Over the years, he has regularly solved quadruple integrals (lots of calculus in optimization and Ray tracing), found math errors in PhD theses algorithms, and did a lot of code in quadruple precision.
Everyone here is talking about applied fields in industry, but there’s also plenty of research mathematicians who don’t work in any of these fields, who simply further the study of mathematics in universities or research centers.
At the core, mathematicians prove conjectures and develop theories. I know that sounds vague, but mathematics is such a massive subject that you really can’t narrow it down much further.
For reference, here’s a (far from complete) [list of unsolved problems in mathematics](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics). Here’s the [Millennium Prize problems](https://en.wikipedia.org/wiki/Millennium_Prize_Problems), which will net you a million dollars if you manage to resolve one of them. Mathematicians will explore techniques and directions of research in problems like these, making incremental progress, proving weaker versions, noticing connections with other parts of math, and occasionally having breakthroughs that result in a proof.
This may seem unmotivated and pointlessly academic, but actually as fields like physics and computer science grow, they continue to take advantage of more and more recent mathematical theories and fields. Not that the mathematicians working on new theories necessarily care about its applications, but today’s mathematics could easily be essential for tomorrow’s physics.
Other than this, research mathematicians will likely teach at least some courses, give some talks, and a few will author textbooks.
I interviewed a pure mathematician for a course in university. Very interesting gent.
He said most of what he does has no real application. He said he spent a lot of time thinking about the foil knot at the time. His average work process was to think about different problems and things that interested him for 2-3 months, then he’d lock himself in a room and write a paper on 1 or 2 days. Rinse and repeat.
But some of solution will have an application. Not ELI5 but pathway finding solutions Google maps uses has relations to geometric shapes (paths and nodes) i believe. So all that work thinking about 2000 sided shapes does make sense when you try to map out all the possible houses in a city.
I work in science R&D, and my own specialism is data. An engineer gives me a metric buttload of data, often in a stupid format (seriously, screw .wfm files) and optionally tells me what it is supposed to mean. I work out how to work things out from it, then find the person who understands the system, sit with them and work the things out, then work with them to tell the decision makers (who are not in general experts) something that is simple enough for them to understand and yet somehow complicated enough to be a reflection of what we think the reality is.
I also take in regular measurements of a zillion things from a process that isn’t supposed to be changing, and work out if it actually is changing, and warn the people in charge of it if it is.
On top of this I do what you might call *natural philosophy* – I give people advice on how to run an experiment that will be able to answer the questions they have, and I give people advice on how to keep their process from changing.
In a school-maths-lesson sense, this counts as stats, programming and discrete maths.
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