Prof. Paul Garrett, University of Minnesota
A note from Prof. Garrett for undergraduate math majors:
"Mathematics is a wonderfully rich subject, and obviously appears throughout science and engineering, finance, as well as having a vast array of programs and enterprises of its own. There is much to learn, even to just get started, and one should be careful to interpret this as an endless source of entertainment and enlightenment, rather than being intimidated! Similarly, there are many very different, yet equally viable, interesting, fruitful paths to be taken into mathematics. The curriculum gives a general guide to what has proven useful, and this should be taken seriously, but, also, it is important to follow one's own instincts and tastes, even recognizing that these will change over time, and with hindsight. Pursuing math further, in math grad school, is one enticing option, needing one certain sort of preparation, with a range of options potentially involving applications and interdisciplinary work. Other options more directly address using mathematics outside academe, in finance, insurance, as well as being parts of a variety of scientific teams.
My own career path has been in academe, and I continue to greatly enjoy the scientific challenges, as well as the challenges of mentoring and teaching undergrads and grad students. My work has been a mixture of what might be conventionally considered "pure" and "applied", that is, including mathematics whose purpose did not necessarily involve application to other sciences or engineering, but also cryptography and coding theory, where the intended application is obvious. But, by now, I think that mathematical ideas do not fall into different pigeon-holes quite so simply. Ideas originally motivated by mathematical physics currently are very important in number theory, for example, and the influence goes in the opposite direction as well. It is best to keep an open mind!"