Question: Is there such a thing as an Applied Maths profession?

In my engineering experience we were often at a loss as to which mathematical approach to take, and there seemed no obvious way to find out except by an informed empirical approach, haphazard and inefficient. The mathematicians and professors we consulted seemed inward-looking, although each had their deep specialities which they were naturally keen to fit to the problem, sadly with poor results when we tried it. What we needed was an Applied Maths guy, with a wide, perhaps shallow, education who could point us in the right direction, using experience, intuition, insider knowledge, a contacts network and good luck. The advice we could get came mostly from fellow engineer CTOs, whose maths speciality had been crucial for success. However, if our product research stepped outside their experience, there seemed no-one to turn to.

Real-world engineering problem-solving presents maths challenges in a wide-ranging, uncontrolled manner. The engineer needs an index to the world of maths, hoping for a handful of potentially useful approaches to try. However, the taxonomy of maths is apparently not organised by application. It does not say, 'If you have mostly straight lines, then use this (high-school) stuff; but if it's photogrammetric construction, you'll need post-grad spherical geometry at least. There is no user interface.

The maths profession teaches and studies maths, but does not seem to provide a service that outsiders could use to access a few potentially fertile approaches. This makes applying maths inefficient - one either gets lucky, maybe having studied the right thing, or is in for a long haul. Hiring a mathematician is the obvious path to take, but which speciality do we advertise for?

My intuition is that something analogous to the electronic industry's Application Engineer is needed. Without these guys being deployed by each chip and component maker, supported by endless application notes 'Use this chip to measure infra-red', working engineers would never have found chips etc to solve their problems.

So, who is out there, actually promoting maths 'components' as solutions to users' questions, on your behalf, so that stuff gets applied in the real world?

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    $\begingroup$ It's not generally its own title in industry. Sometimes it is; for example, I see jobs titled "mathematician" that sound like they are doing cutting edge cryptography work. But otherwise, "applied mathematicians" outside academia are almost always called scientists, analysts, researchers, etc. $\endgroup$
    – Ian
    Feb 19, 2022 at 3:07
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    $\begingroup$ I am also unsure whether your question is a good fit for this site. I'd like to be able to suggest somewhere else where you might get a good answer, but it's difficult. Computational Science Stack Exchange perhaps or another of the SX sites with a more applied focus, but check first whether or not your question is on topic there. Certainly, applied mathematicians work in industry. Also, some applied mathematicians work as consultants, either from within academia or outside of it. $\endgroup$
    – J W
    Feb 19, 2022 at 6:35
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    $\begingroup$ Have you looked up SIAM (Society for Industrial and Applied Mathematics)? $\endgroup$
    – J W
    Feb 19, 2022 at 12:35
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    $\begingroup$ Also, The Princeton Companion to Applied Mathematics could help with the big picture. $\endgroup$
    – J W
    Feb 19, 2022 at 12:38
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    $\begingroup$ 1) I think this is a great question but not necessarily appropriate for this or another SX site because it seems "discussion"-oriented rather than objectively answerable -- you might try Reddit. 2) The answer to "who has the perspective on applicability of more advanced maths to real-world problems" is physicists. $\endgroup$
    – Steve
    Feb 19, 2022 at 12:40

2 Answers 2


I don't think there is any existing service for connection mathematical generalists with people in need of applied mathematical assistance in the way you suggest. Might be a good start up in and of itself!

For your immediate problem I would suggest formulating a "minimum viable problem": strip away all of the non-essentials and formulate the easiest version of the mathematical problem you are trying to solve.

Post this problem to math.stackexchange. If you get interesting or insightful replies, you could reach out to those people to do some consulting work for you.

  • $\begingroup$ The start-up idea has been ruminating away since I posted last night! (I will upvote you when I get logged-on to SX properly again) $\endgroup$
    – OookLout
    Feb 19, 2022 at 14:32

There is a field called applied math (degrees given). Sometimes it is just a "concentration" of a relevant math degree, more often undergrad.* But even here, it just means the kids took a few more applied courses and a few less pure. [But both pure and applied math are big topics, and kids have limited slots in their schedules, so it's not like either one covers the waterfront.] And that they (more) try to get a job in industry. But they don't turn into consulting mathematicians.

I don't think there are consulting mathematicians, the way there are consulting statisticians. But even here, don't be surprised how much they specialize by field (e.g. health statistics). Or that a lot of what they do, does not mean knowing the biggest catalogue of fancy techniques of stats, but more about how to avoid/correct typical problems in study design or interpretation.

All that said, I think part of being a thoughtful knowledge worker or manager in the modern era is the ability to find the particular expertise you need. I mean, I don't know details of market research, law, financial modeling. But I know enough to recognize situations and access experts. And even to figure out what subfield is relevant and make sure the expert can handle the subfield. And even if I don't know the subfields, can educate myself to the extent of recognizing a situation and determining the right sort of expert needed. And then tracking him down. And paying him. Or hiring him, full time.**

For example, the problem you described here requires a projection geometry. So fine, get someone who knows that. But don't expect every math or applied math person to be skilled at it. That's like expecting every random mechE to know a very particular issue (say expansion joints/anchors in piping). They won't all know everything. You should be capable of Googling or just talking to people (telephone game) to get to the right sort of expertise. Heck, I did this before the Internet!

I think a lot of your issue is that you (sound to be) in computer code writing, not traditional engineering. And coders are even more mathematically weak than physical scientists and engineers. Engineers in construction, oil production, aerospace, chip design, etc. etc. are capable of finding help. They very often may not be very mathematical themselves (especially after graduation, in normal tasks) but they are at least aware of colleagues who are more mathematical and can advise on the correct approach, formula, etc. when they (very infrequently) deal with something mathematical.

What I've seen in structural mechanical programs (finite element modeling) and in molecular modeling (e.g. Gaussian) is that software companies hire at least part of their development resources from appropriate math (or even just mathematically astute science/engineering). That way, they don't just have a bunch of coders on staff who don't know the needed math/science for what the program does.

I do agree with your issues talking to professors. They all want to do "their stuff" and get grants to do it. It can be very unlikely to find someone who has exactly what you need, for a consulting contract. And even then, they are more used to writing papers and trying to get promoted to full professor and the like than in solving real problems for a company. It wasn't always like this, but academia and academic math/science has become very specialized as fields have advanced. And the high availability of mass research funding has allowed this to occur. Not saying there are not some outliers, but that's not the norm. And it's a common problem that companies have dealing with professors (not even wanting to hear your problem, just tell you their research). It's why some universities set up industry outreach groups or FFRDCs, because they know their regular faculty doesn't work well with industry.

Really, I think your best bet is just to hire a few smart, willing to work, wanting to get out of academia kids who can figure out the raytracing for you and learn enough of the code monkey stuff also. (And you have to give them some time, too. Don't expect manna from heaven. They have to figure it out, also.) It's not an immediate solution, but it's how you build a workforce that can take care of your needs.

[Edit: loved the comment about physicists...get some washed out of academia, but hungry one. There are many of them. Even if he/she/thing doesn't understand the projection geometry, he'll go learn it. Your "didn't want to take ODEs" computer scientist grads won't.]

Note* and Note**: That you didn't have at least a "Googled and read stuff" level of awareness of what universities offer that they call "applied math" before running to a SE with a forum question, worries me. Shows similar lack of initiative as with finding appropriate consultants/employees to fix your code/business problems.

  • $\begingroup$ Thanks for the thoughtful reply. I won't defend my shallow approach - it reflects the common experience of an innovator discovering (too late lol) that parts of a project require R&D which is either bleeding edge, neglected elsewhere, or plain esoteric. This is during the initial feasibility stage, intended to reduce uncertainties and risk early on, so no way to avoid it (other than go get a proper job). $\endgroup$
    – OookLout
    Feb 19, 2022 at 13:56
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    $\begingroup$ The photogrammetry example is historic - and we had repeated experiences with other projects. They do say, "Stick to what you know". BTW my prior Google/reading showed that there were many versions of 'Applied Math', hence my question - is there a particular term I should search on. Anyway, I think I have enough to be going on with, keep up the good work, and help your students to develop the analytic viewpoint and methodology that will help their employers. $\endgroup$
    – OookLout
    Feb 19, 2022 at 14:11

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