What makes one type of mathematical modeling more difficult than the other?

[dankshu]

I'm guessing it depends on how many factors/how unpredictable a subject is, what is it really? What makes mathematical finance so rigorous- requiring a phd in math/finance- while something like systems biology or pharmacokinetics only requires knowledge up to linear algebra?

[HallsofIvy]

I'm guessing it depends on how many factors/how unpredictable a subject is, what is it really? What makes mathematical finance so rigorous- requiring a phd in math/finance- while something like systems biology or pharmacokinetics only requires knowledge up to linear algebra?
I think you have quite a wrong idea aobut things. There are many forms of "mathematical finance" that do NOT require a Ph.D. and there are many forms of mathematical biology or pharmacokinetics that might well require a Ph.D.

Oh, and "rigorous" has nothing to do with being difficult. To be "rigorous" in mathematics means to be very precise.