By Holly Paige Chaos

The relationship you have with your advisor is arguably the most important working relationship of your life. When I chose to attend the University of Vermont, I was lucky enough to do so with an advisor locked down before I got there; I had the opportunity to speak with her about potential projects and advising me during my visit to UVM. Not everyone has the luxury of knowing what they want to do research in or getting to know potential advisors before applying to programs. After consulting many current and past classmates and friends, I’ve come up with a list of a few things to look for in an advisor.

You want an advisor that…

Validates your struggles.

What you are doing IS hard. Math IS hard. I was lucky enough to have an advisor in my master’s program that would repeatedly remind me when I was doing research that it was normal to get stuck. Usually you are implementing new techniques, learning recently developed theories, or working through complex problems, and it would be very weird for everything to go perfectly right the first time. So look for an advisor that acknowledges that math is challenging!

Can push you, but is a patient teacher.

When we encounter challenging questions or new concepts, our brains build new pathways as we learn and figure out how to solve these problems. It is helpful to pick an advisor who encourages you to get down in the trenches and build these new pathways for yourself, but is also willing to guide you through it. An important part of working with an advisor is being able to come to them when you are stuck. Look to potential advisors who ask leading questions, feel responsive during office hours or in informal conversations, and are excited about sharing their knowledge.

Values your well being.

Your potential advisor should value you for more than just your progress on a problem. Research is hard. Some weeks we can give research everything we have and still have very little—if anything—to show for it. For many this can result in feelings of frustration and failure. In these times, it’s important to remember that math is not the only thing going on. Most graduate students have interests other than just math. Personally, I love running. It provides me with a respite from “math land” as well as an excuse to get outside for some fresh air and allows for a healthy way for me to relieve stress. Taking care of yourself outside of math is essential, and so is having an advisor who will encourage you to do just that.

Genuinely believes in and encourages you.

When I think about whom I want as an advisor, it is someone who would be willing to bet on and have a stake in my success. They could demonstrate that by helping you find and apply to conferences so you can begin networking, encouraging professional development, preparing and encouraging collaboration with others, and demonstrating how to ask for help from peers and mentors.

Is well regarded in the mathematical community.

An advisor should be well connected to other mathematicians in their field and willing to reach out to friends and coauthors when they can’t answer a question related to your research. They should want to introduce you so that you can begin to grow your network, and they should lead by example at networking events in regards to their level of professionalism. Hopefully, they are also active in their own research and not afraid to branch out a little bit if your project takes a surprising turn.

Has current grad students who are thriving.

You can learn a lot about a person by talking to those who already work with them. If you are interested in a potential advisor, talk to their current graduate students! Ask them things like: How often do you meet? Do you feel supported? What is working with them like? What kind of project are you working on? Other graduate students can be a wealth of information, and no one will know what working with someone is like better than a current graduate student.

Isn’t “perfect.”

Remember that no advisor is perfect, so there are some things you might have to do from the start to maintain a good relationship. Your potential advisor will almost certainly have a style that they feel works for them. There are advisors that are comfortable meeting once a day, once a week, or once a month. You need to know what your needs are and what you are comfortable with in return. Thus, it is important at the beginning of your relationship to respect boundaries, set clear expectations, and communicate openly about your needs as a student.

In conclusion, there are many different reasons why we choose where we attend graduate school. I ultimately chose to attend the University of Vermont because I wanted to work with my advisor, but not everyone bonds with their future advisor over how to properly make toast with jam while in the kitchen of their AirB&B at a conference. Just as no two individuals have identical friendships and experiences, the relationship between an advisor and an advisee is also unique. I hope these tips can provide some guidance in navigating that process. 

Holly Paige Chaos is a fourth-year Ph.D. Student at the University of Vermont studying arithmetic geometry. Outside of the math department, Holly Paige enjoys running, cycling, and frolicking through the pumpkin patch with her dog NorahJane.