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What're the occupational differences between pure and applied mathematics?

I'm not so much asking about or for examples of jobs that use pure or applied mathematics as I am asking about the work environment of pure and applied mathematics. What's the work like in both? What's similar and what's different?

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Charlotte’s Answer

Pure math is proof-based. It focuses on answering questions about math, not about the surrounding world. That isn't to say that pure math is not useful--it absolutely is! It helps us answers questions about many things. For instance, group and representation theory is relevant to particle physics. But, jobs that are strictly contained with in pure math are very limited. Almost all of them are academic and are highly competitive to get in to.
You can certainly still study pure math and move into larger industry. I for instance transitioned to finance after studying pure math. It teaches you highly applicable skills--problem solving, communication, critical thinking, etc--which are helpful in many industries.
Overall, there aren't many actual jobs that are themselves in pure math. However, you can study pure math and still have access to many of the jobs that are focused on applied math.
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Lisa G.’s Answer

If you are interested in applied mathematics, you might want to check out the website BeAnActuary (http://beanactuary.org) beanactuary. An actuary is a business professional who evaluates risk, often in an insurance company. There are also more nontraditional opportunities for actuaries because risk is so much a part of modern life.


If you like what you see on the website you should know that you need to be a self starter as an actuary, so you can pass the exams required to get the credentials while you are also working in a business environment. But you don't have to go to school beyond an undergraduate degree to get these credentials.

Lisa G. recommends the following next steps:

Check out the website BeAnActuary (http://beanactuary.org)
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Nicolo’s Answer

It's key to know that your field of study doesn't necessarily determine your career. For instance, I studied pure mathematics but ended up working in computer science and artificial intelligence, areas more linked to applied mathematics. Both paths equip you with valuable problem-solving skills, without confining you to a specific job. Initially, you may be more comfortable with topics you've studied, but you'll quickly adapt to new concepts.
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