Do we use math in research jobs?

[Mapler]

I am a mechanical engineer and now in my last semester of electrical engineering and will most probably proceed with graduate studies/research in power systems, signal processing or electromagnetism and planning on having a career in research or as a prof.

Moreover, I'm much into mathematics and enjoy using them to solve problems and model systems.

Do research careers involve heavy math at the same level we study in graduate school? And which of the above mentioned branches uses more math?

 

[anorlunda]

Some do. Some don't. Sorry to be flippant, but what other answer could there be?

If you can make your question more specific, we can give a better quality answer.

By the way, I moved this thread to Career Guidance, since that seems to be what you are asking about.

 

[zoki85]

Do research careers involve heavy math at the same level we study in graduate school? And which of the above mentioned branches uses more math?

The research careers in STEM usually involve heavier math than studied in graduate school.
The second question is too general to be simply answered.

 

[astrotemp]

It really depends for research careers... I'm doing my PhD now in a theoretical area of astrophysics (black holes, simulations, theory) and did my undergrad in math, and honestly most of the math I do each day is basic. Note that I did all of my "graduate coursework" in undergrad, and the postdocs and professors use the exact same theory I do.

We do use some higher end stuff and there's plenty you can only find in research papers, but it's not typically that difficult, it just uses language and relies on a history you're not taught in school. And you don't do the complicated stuff that often - I only have to code up the GRMHD equations once and then they're done, and all the changes I make to those will be simple power laws.

If I were to plot the frequency with which I used each area of mathematics in daily work, the winner by far would be basic trigonometry. The higher level stuff is definitely needed for the occasional hard theory you have to work with, but you use basic math skills way more often.

The real difficulty isn't in knowing hard math. That's actually a trivially easy thing to achieve, you just have to stick your nose in a book and study. The hard part in research is using all levels of mathematical knowledge to do proper research and discover new things. You can't just know random math-y things, you have to know what maths is most appropriate and how you can tweak/approximate things. For a lot of things, you don't want anything more complicated than a power law.

 

[Auto-Didact]

It really depends for research careers... I'm doing my PhD now in a theoretical area of astrophysics (black holes, simulations, theory) and did my undergrad in math, and honestly most of the math I do each day is basic. Note that I did all of my "graduate coursework" in undergrad, and the postdocs and professors use the exact same theory I do.

We do use some higher end stuff and there's plenty you can only find in research papers, but it's not typically that difficult, it just uses language and relies on a history you're not taught in school. And you don't do the complicated stuff that often - I only have to code up the GRMHD equations once and then they're done, and all the changes I make to those will be simple power laws.

If I were to plot the frequency with which I used each area of mathematics in daily work, the winner by far would be basic trigonometry. The higher level stuff is definitely needed for the occasional hard theory you have to work with, but you use basic math skills way more often.

The real difficulty isn't in knowing hard math. That's actually a trivially easy thing to achieve, you just have to stick your nose in a book and study. The hard part in research is using all levels of mathematical knowledge to do proper research and discover new things. You can't just know random math-y things, you have to know what maths is most appropriate and how you can tweak/approximate things. For a lot of things, you don't want anything more complicated than a power law.

This seems to be quite an accurate representation for almost all typical research, i.e. intradisciplinary research.

Myself, I mostly do atypical research, i.e. interdisciplinary research, specifically in dynamical systems theory in three interlocking ways, namely:
- theoretical research utilizing mathematical physics and applied mathematics methods in order to discover new methods or theory,
- experimental research utilizing statistical physics, numerical analysis, machine learning and computational methods in order to fit models to empirical data
- applied research through direct mathematical modelling of naturally occurring dynamical systems (i.e. physical, financial, sociological, political, physiological, etc systems).

Having a very broad knowledge base of different fields in mathematics helps enormously, especially when these fields show up unexpectedly in another completely unrelated context. This reoccurrence of a piece of mathematics is something which happens way more frequently than is often realized by researchers who didn't start off in (theoretical) physics; for example, Riemannian geometry learned for GR rearing its head in machine learning.

To illustrate some of this better using the Riemannian geometry example: in the actual practice of machine learning, researchers unfamiliar with Riemannian geometry seem to take a completely different attitude w.r.t. it showing up in their work than researchers who are already familiar with it. This difference in attitude is not merely trivial in that they try to learn it properly (NB: they usually don't because it isn't strictly necessary).

This difference in attitude has real consequences both for the direction and results of their research by giving those unfamiliar less methodological broadness by being able to tweak the methodology less than those intimately familiar, typically leading to research that is easier to understand and reproduce but overall less ambitious and/or generalizable.

On the other hand, a researcher who is familiar with Riemannian geometry - or more generally has more mathematical broadness as a researcher - can take advantage of this and more easily produce groundbreaking results in this field, simply by quickly regurgitating old knowledge already learned in a different context and so end up completely changing the perspective of the field.

 

[jasonRF]

I am an electrical engineering PhD that has been doing R&D work in industry for a couple of decades. I have worked with a lot of signal processing and electromagnetic experts as well.

What I see for signal processing I s that there is definitely some work that involves heavy math, but even those folks that have a track record of doing such work also spend a fair amount of time on more practical tasks such as designing and conducting tests (need to collect the data for your fancy algorithms!) leading teams and meeting with customers. Some projects have little or no heavy math required, while others depend on someone really smart coming up with a good approach - often requiring knowledge of the hardware as well as the math to develop fancy algorithms and an understanding of the numerical and computational power required to implement real-time.

The overwhelming majority of the electromagnetic work I have seen in my workplace is numerical - usually using commercial tools. I have been doing some of this recently. The main math has been constructing and finding approximate solutions to problems that I can use to validate the numerics. These problems must be simple enough to “solve” yet close enough to my problems of interest that they give me confidence my results make sense.

Jason

 

[Dr.D]

I'm at the end of a long career (50+ years) of teaching and industrial work. I can say with certainty that almost all of the work that came my way came because I was the only one around who could do the necessary math. Over the years, I used all of the math that I had learned in college, and a lot that I learned later.

If you know the math, and let it be known that you are unafraid of it and willing to use it, the work will find its way to you.

 

[Auto-Didact]

I'm at the end of a long career (50+ years) of teaching and industrial work. I can say with certainty that almost all of the work that came my way came because I was the only one around who could do the necessary math. Over the years, I used all of the math that I had learned in college, and a lot that I learned later.

If you know the math, and let it be known that you are unafraid of it and willing to use it, the work will find its way to you.

This. I have actually made many different mathematician friends solely for this reason. Then I consult them if necessary for every specialist task which requires a more delicate or rigorous approach than that my pedestrian physicist ways will allow me to stomach myself.

Also, protip for mathematicians:

 

[Dr.D]

Actually, today I do it for free most of the time simply for the fun of it.

 

[Auto-Didact]

Actually, today I do it for free most of the time simply for the fun of it.

Don't tell anyone but I do as well 🤫

 

[RUQIAN]

For my opinion, for the work of metaphysical and abstract, I think math is a must tool to make sense of the establishment of a model, but for mature research for getting conclusion, my idea is math is always used as a thinking way you ponder about events through thinking trials to finally can organize the measurements to support one or two ideas making sense for the audience to understand situation. Hope this helps.

 

[zoki85]

For my opinion, for the work of metaphysical and abstract, I think math is a must tool to make sense of the establishment of a model, but for mature research for getting conclusion, my idea is math is always used as a thinking way you ponder about events through thinking trials to finally can organize the measurements to support one or two ideas making sense for the audience to understand situation. Hope this helps.

Obviously he meant "advanced math", but forgot to put word "advanced" in the text of the title

 

[symbolipoint]

Obviously he meant "advanced math", but forgot to put word "advanced" in the text of the title

Just what is and is not "advanced", is not clear. Someone simply doing a two-point data plot to make a mixture-production decision might trigger some manager or executive to say, "do we really need this advanced mathematics here?"

 

[mpresic3]

Fear not. In both jobs I have had with DOD, I have used math extensively. Currently, I have a doctoral degree in physics and lately I have had the necessity and the opportunity to learn even more math. I have several colleagues with similar educational backgrounds (in physics) that are in the same position and we are taking a in-house class together. I know post-docs in engineering who never solved a partial differential equation in college or graduate school even from a textbook. Now they have to solve them at work in practice.

 

[Auto-Didact]

I know post-docs in engineering who never solved a partial differential equation in college or graduate school even from a textbook. Now they have to solve them at work in practice.

One word: Mathematica

 

[zoki85]

Just what is and is not "advanced", is not clear. Someone simply doing a two-point data plot to make a mixture-production decision might trigger some manager or executive to say, "do we really need this advanced mathematics here?"

Yes, but it is more clear if you read OP introductory post. Pieces of mathematics not taught or not taught enough in typical graduate school courses. Sometimes these are not more "advanced" but rather on the same level, however some never even mentioned despite importantce for particular field of research.

 

[Auto-Didact]

Yes, but it is more clear if you read OP introductory post. Pieces of mathematics not taught or not taught enough in typical graduate school courses. Sometimes these are not more "advanced" but rather on the same level, however some never even mentioned despite importantce for particular field of research.

Yes, exactly. The OP seems to be asking about the usage of both sophisticated mathematics and non-standard mathematics in practice, e.g. the daily practical application of abstruse or unconventional (at least to non-mathematicians) topics like etale cohomology, sheaf theory, K-theory, Clifford algebra or hyperfunction theory.

Many forms of sophisticated and non-standard mathematics are actually mistakenly seen as more difficult than the standard 'undergraduate curriculum' mathematics for STEM; especially non-standard mathematics tends to be not necessarily too advanced for the typical mathematics or physics senior undergraduate, but instead just merely unknown to them.

 

[wukunlin]

I am a mechanical engineer and now in my last semester of electrical engineering and will most probably proceed with graduate studies/research in power systems, signal processing or electromagnetism and planning on having a career in research or as a prof.

Moreover, I'm much into mathematics and enjoy using them to solve problems and model systems.

Do research careers involve heavy math at the same level we study in graduate school? And which of the above mentioned branches uses more math?

In my previous job (physical simulations) and current job (mocap), I have to keep looking for new mathematical techniques to solve my problems more accurately and quickly. They may not have the depth of graduate school levels (this obvious depends on the school and the discipline) but I am exposed to more variety.