The languages themselves. To evaluate most simple integrals in mathematica you just put them in and all the corner cases are assumed away for you. For sage and the axiom binding you need to make those assumptions explicit. Pretty much everything in mathematica assumes you're working on the real numbers, pretty much nothing in sage does: http://doc.sagemath.org/html/en/tutorial/tour_rings.html
Most math quants use is at the undergrad level, the finance industry in general is pretty backwards. A very large chunk of it is run on spreadsheets that are passed around in emails. I've worked in it and having seem what it takes to run some of the clients spreadsheets still gives me nightmares.
Again, the difference between osx and linux.
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To clarify what I mean by undergrad level: Something that is taught to some undergrads in some degree.
Someone who specialized in pure symbolic mathematics is likely to see integrals in their last year that other people will not see until they start doing postdoc work.
Most math quants use is at the undergrad level, the finance industry in general is pretty backwards. A very large chunk of it is run on spreadsheets that are passed around in emails. I've worked in it and having seem what it takes to run some of the clients spreadsheets still gives me nightmares.
Again, the difference between osx and linux.
---
To clarify what I mean by undergrad level: Something that is taught to some undergrads in some degree.
Someone who specialized in pure symbolic mathematics is likely to see integrals in their last year that other people will not see until they start doing postdoc work.