FEM can offer money but you are competing against engineers who that's what they've done for years.
If you interviewed software engineers and data scientists right now I bet a third of them once were physical scientists/mathematicians who mostly regret their degrees or the fact they can't find survivable work using them.
Would mathematicians truly be regretting their degrees, if they decide to work in software? I read that mathematics one of the best degrees for a career in software engineering, as computer science is very closely related to mathematics (to the point where studies of algorithms are largely the same for mathematics and computer science students).
It is also possible that aptitude for math is related to aptitude in software engineering.
However: The mathematics content of 90%+ of mathematics degrees awarded is fully irrelevant to 95%+ of software development tasks. And when that 5% task needs that some kind special mathematical insight, the people who want that task done are going to get the top professional they can find for it. Maybe the prospective math student is going to be that professional, but I don't recommend planning a career for it.
I am not saying there isn't work where some math is useful but the most commonly used applied stuff ... say, linear algebra ... is typically covered in a respectable engineering program; degree in mathematics would be superfluous. Proving theoretical properties of Hilbert spaces or measurable sets or bifurcations of dynamic systems or advances in differentiable topology or fascinating behavior of cellular automata or whatever is going to be gigantic waste of your time if you won't use it later in your career or you don't find it intrinsic motivation in itself.
In my case, I was in basic science which hit a crisis near 2008 when the NIH was flat funded. This caused a come to Jesus moment, where suddenly all basic science labs were rebranded as translational medicine. My department was absolutely gutted, down from 15 or so PIs to maybe 8ish in the span of a year. Our field was bioenergetics which at the time was pretty competitive, and easy to link to diseases/metabolic disorders. We didn't work with pharma, some labs received contracts for small work. NIH was by far the biggest funder, followed by DARPA and other smaller health organizations.
Lack of professional integrity is a very real problem.
Over the past two years I wrote fairly frequently about some of the nonsensical / pseudo-scientific COVID papers that got published, especially the quality problems in epidemiology. Epidemiology isn't bioscience (actually that's one of the problems with it - total lack of biology), but it's adjacent. After that I got contacted by a former research software engineer who worked with top epidemiology teams in the UK. I also got contacted by a member of the SAGE committee.
Both of them told me some absolutely mind-blowing stories of ethical malpractice. I wasn't totally surprised because it was obvious that those sorts of things must have been going on behind the scenes just from reading their model source code, reports, watching their behavior etc. The RSE had become so disgusted at what he'd seen that he actually left the country and switched from working at Oxford to some US university I'd never heard of, switching fields along the way too. Quite the downgrade in prestige but after years of trying to help epidemiologists he concluded the entire field was utterly morally corrupt and he wanted nothing to do with it.
Here are some of the more memorable things I was told by those two scientists:
- The RSE at one point found a bug in a FORTRAN model being used to model malaria outbreaks. It had been used as the basis for hundreds of papers but at critical points was using pointer values as variables instead of dereferencing them. Obviously, a typical pointer has a very different value to most organic things (some FFI bug). He reported this bug to the authors and got a reply back within 30 minutes saying they'd checked the papers (all of them) and it didn't affect the results. This claim was very obviously a lie: not only could they not possibly have checked even one paper in 30 minutes but he already knew fixing the bug did indeed change results! They didn't care and he was shocked that his "colleagues" would bullshit him so directly, especially as they must have known that he would know.
- Same guy flagged code quality issues to some of the scientists and proposed introducing some rules designed to improve quality. He was dismissed with the words: "oh <name>, we're scientists, we don't write bugs".
- The SAGE member told me about some of the internal discussions they had. Criticisms of the methodological validity and accuracies of their models were dismissed with reasoning like this: "that person reads the Spectator so it doesn't matter what they think". Relatedly, he made clear that the supposedly scientific SAGE predictions were sometimes being altered to reduce criticism of the group by left wing media and journalists. The changes were presented as "the science changed" but that wasn't what was going on behind the scenes.
- Malaria research is (supposedly) being badly distorted by the Gates Foundation. Gates only cares about eradication which leads to lots of problems. There are some smaller ones, like many researchers don't genuinely believe that's possible but lie on their grant applications to make mitigation efforts sound like eradication efforts. And then there were unethical experiments on entire populations where e.g. whole areas are blanketed in anti-malarial drugs. If it works, great, you eradicated malaria in that area. If it doesn't you just selected for drug-resistant mosquitos and now the drugs that were being used only to treat the serious cases don't work for anyone. He told me this has actually happened more than once.
- The RSE told me they'd at one point tried to recruit an RSE working with climatologists to help them with their modelling (a belief that climatologists are more rigorous than they are seems to be common in epidemiology). The RSE they interviewed refused to take the job. His reason was he was quitting academia entirely, as he was so disturbed by the practices he'd seen.
A few years ago if you'd told me that a whole research field could be unethical I'd have thought you were crazy because, well, that's a whole lot of people being painted by a very broad brush. Now I've seen it for myself and heard from other former insiders, it's easy to see what happens - the honest ones discover what's happening and leave. Because academia hardly ever penalizes intellectual dishonesty, the pool of people who remain are the ones who are OK with it and have learned that it works / has no consequences. Things steadily become more and more toxic.
What I can and will say (and is on record) is that reproducibility was not a concern from the Imperial College virology dept.
BINGO! that field is notoriously horrible and interacts extremely badly with a 'when not discovered here, not important' syndrome. Biology is brutal toward bio-physicists, mathematicians as well as people who code who they are forced to work with rather than seek out to help them.
I still hold up as an example nonsense discussions around p-values in bio vs actual work going on in statistics in maths departments. It shows how far detached they've become.
Not to criticize too strongly, but given the above, combined with it's reproducabilty crisis, and existential problem of being in the back-pocket of big-pharma, I seriously doubt the professional integrity of a lot of people in the field.
Move toward mathematics, physics and chemistry. There is (some) serious money and a good atmosphere around areas such as finite-element modelling, or wolphram like tools as an example. There is a lack of direct funding for decent posts but you get recognised and paid the equivalent as a peer, I know from working with some of these people. It's not to say it's 100% always without friction, but no job is I'd argue.