For advice: I'm a mathematician looking for a plan B outside of academia

Learning to program is the most important thing you can do. As long as it isn't web applications everything is fine. Programming isn't really about knowing the syntax of some language or having memorized a list of algorithms, but understanding how to build an appropriate architecture for your system.

>but it seems of dubious usefulness when it comes to finding a job.

There is a very large embedded industry if you want that. Learn about basic electronics as well if you are interested. I highly recommend learning C and (C++ and/or rust) if you want to enter there.

>combinatorial optimization

Nobody in the industry would hire you for that specifically. You might find a role where it is also needed/usefull but it isn't a career path.

>blender/3D modelling

I would absolutely avoid that as a career unless it is a major passion. Maybe you are interested in computer graphics though? That could be an option. Computer graphics is a major industry, video games, professional software for artists or engineering software are some of the larger groups there.

I would focus on R&D positions at large companies or institutions. Engineering positions are more process focused ("do what you are told") and it gets worse the more regulated the industry is (e.g. aerospace).

Government: Working for a national lab is very similar to working for a research college without the coursework. There are frequent (as in weekly) technical lectures across a vast array of areas. Lots of work for someone with math+applications interests. Including work for NASA, LHC, astronomy, etc. You can literally walk up and talk to them after the lecture ie if you think there’s a collaboration possible it’s possible.

Similar is probably true at contractors like Lockheed Martin, etc.

In my experience, the trouble can be in picking places that won't see you as too qualified/"why would you work here?"

Maybe project management or stuff in logistics might be complicated enough to interest you.

Pick up some IT background with stuff like containers, linux, etc. Usual stuff to aim for to get into the big techs. I'm hoping Microsoft, apple, etc still have filesystems devs.

Make some expository type videos ala the famous YTers. This ca/should mirror your current academic work.

I was in your situation 20 years ago, as a postdoc in Theoretical Physics. My advice is to contribute to some known Open Source project, so that you have some provable programming skills when entering the job market. In my case I contributed to Python, not by coding, but by writing various articles on advanced features of the language and an essay on the Method Resolution Order that at the time was new and undocumented. Guido van Rossum in person put that essay on the official Python site. Having something like that in your CV helps when looking for an IT job. Nowadays I would probably contribute to Julia, you need something that shows promises but it is not mainstream yet to make a good impression.

I think as a mathematician you may enjoy a niche like formal verification.

Look up tools like TLA+ [0].

Formal verification is basically about modeling hardware & software systems with a notation similar to mathematics.

It seems like a good option for a mathematician.

[0]: https://lamport.azurewebsites.net/video/videos.html

I would caution against _just_ learning to code without also getting a reasonable grounding in an area of industry you want to work in. I am a math PhD too, I currently work in an industry research lab doing ML work. I transitioned via a decade in government R&D that was much less hands-on technical. Despite now working in close proximity to folks doing graphics research I know it would be very difficult to get a job in that without hands-on experience.

Just being good at math is too general in a competitive job market. But I would also argue that learning to code is too if you want to work in the application rather than as a SWE.

I personally find low-level software interesting too and have found stimulation in HPC. However, lots of that space these days is focused on AI and you said that doesn't interest you.

> Because of ethical reasons I want to stay as far away as possible from anything that is insurance, finance or crypto related. I'm not really interested in AI and/or machine learning either.

I think you might be internally overestimating how employable you are right now. Getting a first industry position after doing pure math is pretty hard. I don't think you quite have the luxury of a priori ruling out broad swaths of industry. Especially fields (machine learning and quantitative finance) for which folks with strong pure math fundamentals are particularly well suited.

You mention "low level stuff and assembly" and I think it is true with the right preparation you can break in here. But keep in mind that when you apply for systems programming jobs, say, you will be competing with people who have degrees and internships and potentially experience in the field specifically. A math PhD is good in theory, but by itself it has lower value than more targeted education and internships.

I'm writing this because when I did my math PhD, my peers and I had a lot of hubris around this issue. The conventional wisdom was that if academia didn't work out it would be easy to jump into industry. Then when the time came around it was an order of magnitude harder than we thought. I know multiple people who took temporary 1-year academic positions because their initial industry job search fell completely flat and they needed more time to prepare. In retrospect being more humble about our prospects and preparing correspondingly would have helped.

I encourage you to reconsider the things you ruled out. I had some pretty odd views about companies before I started work and I don’t think they’re so correct now.

In particular, you’ll probably find parts of finance most culturally familiar to you (eg this link posted today https://puzzles.nigelcoldwell.co.uk/ which doesn’t really capture that much about interviews but does give some indication of some interests of some of the people who work there). Obviously there is also lots of low-level programming that matters in some parts of finance too.

I don’t think I’ll convince you of much in this comment so I will just note that (a) jobs/culture can be quite varied between different kinds of companies (investment banks v hedge funds v hft v companies that sell services instead of trading), (b) companies are quieter and less good at presenting a good brand than eg big tech so online you may get a worse impression. And I would recommend that you try to find some people you know from school who went into careers like that and ask them what they think about them.

There are other ways of thinking of it too, for example by not working in a higher paying job, you are in some sense giving the difference in income to your employer as if they were a charity (ie if you could get $x for your labour but get $y, it’s like you’re giving $(y-x) to your employer) so you may want to feel that is a deal you’re happy with. If you work for a charity then maybe that feels like a good deal to you, and that’s obviously fine too.

Without knowing which pure area you work in, I can only surmise that you have at least some category theory, which is the theoretical underpinning of type theory. Add in algebraic types, aka sum types, and you may have a solid theoretical background for modern programming research, especially functional programming.

Combine that with a previous interest in assembler, et al, and there may be an interesting possibility of compiler optimization, byte code generation, etc.

How would one add introspection and pure functional programming with tail calls to a language such as Rust, e.g., and still maintain all of its safety guarantees while keeping build times reasonable?

As an aside, there is plenty of work for those with solid assembler or other low level experience. Don’t think commercial end user or web software, think embedded hardware, IoT HW, etc. my employer, e.g., will be adding FPGAs to our high security hardware products, and we will need that low level experience. We’re not hiring yet, but we aren’t the only ones out there.

Heck, maybe that’s an area of interest: marrying an open source tool chain to a high level, functional language, to an FPGA and getting performant, safe code that is not beholden to the arcana of specific manufacturers.

I was in the same position about 8 years ago, having completed a PhD in algebraic number theory with only some basic coding from undergrad under my belt. At the time, I was offered some very helpful advice from folks who had also been in that same position before me, and I ultimately ended up landing a SWE role at Facebook. Since then, I’ve always felt I should pay it forward.

There’s more to say than can fit into an HN comment, and I’d be happy to answer any specific questions you have, so please feel free to reach out to me through the contact form on my website.

> Because of ethical reasons I want to stay as far away as possible from anything that is insurance, finance

All insurance, and all finance?

If so, then you pretty much have to stay far away from America. Everyone has insurance, and everyone utilizes finance.

Perhaps step 0 is to mature a little bit on your perspectives in life, and realize not everyone is some big evil corpo-bot.

Apply to companies having deep R&D programs, they all need maths: 3d rendering algorithms research, energy sector, etc.

> I have no knowledge of what is required in the job market

Read the news, its that simple, you can see problems that need solving all the time. Its harder to find out what needs solving in business because they are by nature private. Thats not to say, you cant find problems in business which need solving when you are a customer of theirs.

Define a big programming project? Do you want to work in a big team or on a project as the sole coder for something that is the biggest in whatever domain/field its in. Global business, national business, small business?

Lots of ways you could approach this, not being sarcastic, but wouldnt your combinatorial optimization be the perfect foundation to plan your future life?

In the mean time, I'll be reading the comments, to see if problems in industry are being made public which could be monetarised and solved with code.

I moved from academia to industry and it was the best decision I ever made. Save for a couple of shorter term positions in terribly-run companies life has dramatically improved.

You've progressed nicely in a very niche domain - is there any problem within that domain that you feel like you could solve outside of the academy? For instance, is there some product, software, service that you wished you had at some point in your work? If so, is there a big enough market to build something like that which would create a business that you could build?

You understand high level mathematics - I have no doubt you'll be at least a decent programmer, but consider that there are other opportunities that may be out there for you. Good luck in your journey.

You may consider the electronic design automation (EDA) industry. Basically, the tools used to design the ASIC we love.

The industry anticipates a job crisis, with elder people retiring, a shortage a new entrants (not see as sexy) and still a strong need. There's been initiatives around to bring more new blood in. A math PhD with an interest in optimization looks like a good fit.

There aren't so many employers (Cadence, Synopsys an Siemens/Mentor are the 3 bigs), but the domain is extremely technical with an history of pushing the envelope. SAT solving for example has progressed a lot thanks to EDA, and we not benefit from it in software with its SMT extension.

This is my personal advice, feel free to ignore it. I am only giving it to you because I was in almost the EXACT same situation. I also got my PhD in pure math (langlands) and was in a postdoc just like you, planning for the job market. I myself did NOT get an academic job despite applying to many places.

On the note of academic jobs: the #1 thing over EVERYTHING else is connections. Connections are even more important than producing HIGH QUALITY papers. You need to be interesting and regularly communicating with 2-3 research groups around the world who CARE about your work seriously and might want to work with you (i.e. they should be showing some enthusiasm for your work). Your postdoc advisor(s) need to be behind you on this, they need to write you an amazing letter, and you need them to help you find these connections. But, you also have to strengthen/find them on your own. If you don't have good connections, FORGET about an academic job. (This was my #1 mistake, but I don't regret making this mistake for a variety of reasons -- if you want to talk more, feel free to contact me at jpolak (at) jpolak (dot) org).

In terms of programming jobs: other people here will have better advice on how to get into that world.....but I will tell you something they might not. The programming/industry world has a HIGH CHANCE (not GUARANTEED) to be extremely boring if you are used to pure math. I don't mean they are intrinsically boring, but to the person who enjoys pure math, they aren't close to that style at all. The work style is completely different.

My main advice then is to think about jobs OUTSIDE the technical sphere. Not that you will NECESSARILY need to go that route, but it is something worth thinking about. One of the best things about pure math is creativity, and the opportunities to express creativity like that in industry is rather low. Today it's all about specialized stuff that is very directed.

For my, I went into something completely different: writing and photography. Not saying you will go that route, but finding something you like to do that is creative might be more enjoyable than doing something technical. Again, this advice is HEAVILY influenced by my personal feelings about what pure math is about, but basically, I submit that industry and pure math are SO different, that even non-technical fields can be more similar to pure math than programming.

Finally, I will say that based on talking to SEVERAL former grad-student colleagues, my advice generally holds true. Industry can be amusing for a short time, but in the long-run, it's boring....just something to think about. Personally, I quit industry (programming/comp-sci stuff) this year because I hated it from Day 1 and I'm very happy I did.

What appeals to you here:

https://en.wikipedia.org/wiki/Combinatorial_optimization#App...

and which of those application areas are spending &| hiring?

From the lede spiel you may have foot gun'd yourself:

     It has important applications in several fields, including artificial intelligence, machine learning, auction theory, software engineering, VLSI, applied mathematics and theoretical computer science.

As AI & ML got first mention. Still, there are other applications.

I also always had a fascination for low level stuff and assembly, and I ended up moving into compiler and language development, which made me happy because there's still a lot of math-y stuff going on: the algorithms in compiler transforms, formal specifications of languages, and so on.

I can't really give you advice on how to make the transition. The way it happened for me is that I participated heavily in open-source projects at the end of high school / during undergrad and made some personal connections that way which ended up leading to a remote job long before covid...

I did a cell biology post-doc for a couple of years, and then got a junior job working on data visualisation libraries, which I really enjoy. After two years my salary has doubled.

I had no experience of large projects, either. I followed the advice of someone in the industry, and made my CV more or less just about my hobby programming projects. Nobody cared that I hadn't contributed to open source projects, and they certainly didn't care about my previous career.

The tricky part was getting through the first phone screen. HR people didn't really understand the experience I had.

>low level stuff and assembly

Embedded is too close to Electrical Engineering, lots of people would want experience in that.

Honestly be less picky. Get your first job, then you will have your pickings.

Cryptography: It's a niche field, not everyone offers a position in this area, but having a good grasp of the mathematics behind common cryptography techniques is a highly employable skill. Understanding quantum-safe algorithms is a huge plus.

Cryptographers tend to be one of two types: Those that create new algorithms and those that attack existing ones. The industry has positions for both kinds, it is up to your personal taste as to which appeals more.

Concerning combinatorial optimization, for what it is worth, I've been working in that field for the last three years! Mainly on public transport optimization algorithms. It is less "sexy" than ML, and paid less, but I find it very interesting work, and quite challenging, as the state of the art constantly evolves.

Curious, what ethical reason would you want to avoid insurance and finance? Mathematically they've got to be the most intellectually (not to mention financially) rewarding fields you can get into as a mathematician, what's more fun than assessing risk and probabilistically predicting the future?

If you are good at math and like complex symbols, then learn a low level language and move into HFT.

Mathematicians are well equipped to find the weird quirks needed to gain an alpha in the trading market. And low level high-performance languages won't seem as tricky, if you're used to the oddities of pure math.

Check out John D. Cook's blog https://www.johndcook.com/blog/

He has a math consulting business which seems very interesting a cool way to make a living. Maybe you can contact him and get some advice.

> If you have good combinatorics/graph-theory background we're also hiring Routing Optimisation Engineers!

https://news.ycombinator.com/item?id=37021978

As someone in a similar situation, it feels like most job adverts expect prior experience in whatever the domain is. I expected that learning on the job was a thing, and that the "mathematician" (ergo, knows how to learn, or so they say) badge would suffice. Can anyone speak to that?

My first thought was finance but you exclude it. Some ideas could be in the domains of cryptography, data and category theory (e.g. Spivak), simulated data, or testable systems architecture (Lamport, TLA).

Have a look at quantum computing. Majors in QC are not very common, so they hire PhDs in maths and physics willing to switch to a new field.

Relevant maths are linear algebra, statistics and theoretical CS (ie logic)

I know several PhD pure mathematicians who have taught themselves data science/machine learning on the side during a postdoc and subsequently got jobs in those disciplines.

If you've got low level skills and you're not interested in AI/ML, you're probably going to end up doing process control on industrial machines.

Quantitative research might be an option. One pro here is, if they like you, they will be happy to take you on and teach whatever concrete skills you’re missing.

> low level stuff and assembly

Cyber security companies tend to have a hard time finding people in that area. (Although mostly C++ and Rust these days I guess)

I’ve been there, too. I don’t feel like writing much here, but drop me an email if you feel like it (it’s on my profile).

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