I think mentorship is really key, and can benefit in ways that are unpredictable.
I am an Assistant Professor in mathematics at the University of Calgary. My primary research area is algebraic topology. I am one of the founding members of the Women in Topology network, which seeks to increase the visibility and retention of women in my field by involving them in high-quality collaborative research projects.
My research group is currently seeking new members. See my website for more information
I became a mathematician because I love math, and my favourite thing is sharing this through collaboration with students and colleagues.
I research homotopy invariants and functors - things that can tell whether or not two mathematical objects should be counted as ``the same'' or not. I'm excited that this really deep, abstract phenomenon turns out to have the same kind of structure as calculus, which is really familiar.
My students have gone on to become software developers, teachers, engineers and researchers in math and other sciences.
Yes, it is male-dominated. It's really important to have both female and male allies who understand the challenges women and other minorities face when they are trying to promote their work and advance their careers. I am very fortunate to have some very wise and strong allies who have mentored me.
I am involved in an effort to advance research networks for women in math, sponsored by the AWM (Association for Women in Math) and the NSF, through an ADVANCE grant. My own research network is called Women in Topology. We have perfected (I think!) a model for doing collaborative research in math that involves both mentorship and discovery. This combination will, we hope, help to retain more women in the field. You can read about our work here....
I think mentorship is really key, and can benefit in ways that are unpredictable. For example, as a mathematician I have had the benefit of mentors who have helped me to learn how to self-promote and have helped me accept that some self-promotion is necessary and it is not the same as bragging. Many of those mentors were not mathematicians. Early in my career I didn't think that I would benefit from that kind of mentorship, but I see now how valuable it is.
My academic advice is to make sure your math skills are strong. Math is the language of science, and if you aren't fluent you will run into trouble. My personal advice is to understand that it is ok when you don't know something - that's what learning is for! Every time you admit that you don't know something you will benefit. Those who criticize students who admit their ignorance are usually hiding something themselves.
I have several types of role models and mentors: the members of my dean's office who provide professional mentorship for faculty have been really amazing (they are Brian Keay, Chemistry and Leslie Reid, Geology). For many years I benefitted from the mentorship of a Calgary mathematician named Hugh Williams - he has moved away and I really miss his wisdom and influence. The three other co-founders of Women in Topology - Maria Basterra (UNH), Brenda Johnson (Union College) and Kathryn Hess (EPFL) - have been an invaluable source of support and guidance. My Ph.D. supervisor, Randy McCarthy (UIUC) has really influenced both my research program and my career path. And, finally - my sister, who is in industry.