They and the military industry are probably the ones who actually use things like number theory and some more. (At least this were the rumors when I graduated.)
I used to work as a contract programmer, and quite often the client would be an insurance company.
Much of the work involved translating complex formulas that I no idea of the intention, into code that produced an expected result.
Calculus was sometimes there, ( I didn't have to write those bits, there was a standard library).
Most of it though was just database stuff, and adjustments to probability estimates.
I worked as an actuary for seven years. I would say actuaries rarely directly use calculus in their work, but must understand it to do their work.
Of course, some of this depends on what you mean by "use". Often software is using calculus (or it's result, or an approximation) to calculate something for us. Sometimes we may write the code. Does it count as "using" calculus if you write the code? I think so?
I now work in something closer to "data science". I still rarely write out a derivative or integral. It happens, but not often. On the other hand, the times I would be lost without the background are numerous.
Thanks for your insight.
So is there a book of some kind where I can read in-depth about what an actuary does, instead of synopses I can find on the internet?
If there is, I'm not aware of it, and I'm not sure why it would be a better source than the internet. Don't get me wrong, you have to be careful what you believe on the net, but those types of books don't tend to gather a particularly wide array of voices, either.
I would just start up conversations with a handful of people who seem to know what they're talking about (I can't stress this enough: stick to credentialed actuaries with more than a couple of years experience) and start gathering data points. The actuarial outpost would be a good place to find a variety of opinions.
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