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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]I’ll throw my knowledge into this. I am an academic in an area adjacent to math, so this is second hand.
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Me too.  I liked pure math, but later found great applications in an adjacent area.  Math provides great support for physics, cryptography, economics, actuarial science, management science and logistics, and finance.  These days, most math majors are actually applied math majors or joint computer science.  There is also statistics and data analysis.

It is unrealistic to expect an undergrad to complete all the Ph.D. core courses.  Only a small minority of talented kids end up competing in Math Olympiads and becoming professors in something useless like number theory.  Go someplace with lots of math majors and opportunities to explore interests.[/quote]
Mine is also into cryptography.  Placed out of all the base courses, so went into upper level electives as a freshman. Not interested in olympiads or competitions. Really turned off by that in magnet schools. I like that math can be so malleable. It doesn't have to be some narrow path.[/quote]

Cryptography and Competition math both have a heavy emphasis on algebra and number theory. [/quote]

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