by Swati Gupta.
The journey of getting a PhD is highly unstructured. It’s unique to each individual and their research area. You will not find a “curriculum” for it, as there is no one-size-fits-all. But there are some key ingredients that lead to success, and here are some of my thoughts on what these are. This is based on my personal experiences in academia and as an advisor, and lessons from others who’ve walked similar yet unique paths. I hope young students can take some guidance or perhaps inspiration from this.
- Grit and Resilience Can Get You Further Than Raw Talent.
If you are talented and have received top grades in your institute, does this mean you will have a successful PhD? Maybe, and maybe not. If you have developed the art of grit, will you have a successful PhD? Yes, much more likely. Grit and resilience in the face of bottlenecks are better predictors to how far you can get in a PhD. Talent with a short attention span can help you tackle “epsilon” papers, perhaps on disconnected topics. Talent, with some discipline on the choice of problems, can get you closer to a coherent thesis topic. This talent or technical skill can be inculcated over time with the right courses and training. But if you combine it with grit to pursue problems even when you are stuck, this will likely get you closer to an impactful and deep results in your thesis.
Developing talent with grit and resilience in the face of “being stuck at problems”, “paper rejections”, “what-if optimizations”, “external validations” can get one much further. Sometimes grit comes from one’s passion for a topic (see the choice of thesis topic next), some times it comes from not accepting defeat to a problem. You just have to love your thesis enough that you can show up everyday for this problem no matter what, and do what is needed. I remember a slide from NemFest 2017, showcasing George Nemhauser tackling problems head on with a light saber, which really resonated with me. If you want to solve a problem, get your light saber out! š - Passion is the Key for Choosing a Thesis Topic.
Go with what you are most passionate about. The world is changing too fast to mould your passion according to it. If you don’t know what you are passionate about – sample a few problems (e.g., some things your advisor has worked on before, or papers at a conference whose abstracts resonate with you, or bring in your job experience to guide problems that you’ve faced before in industry), review them, study them – go with the one that you couldn’t get out of your head. If you don’t have a problem like that, you’ve not found the right problem. It’s a dynamic and evolving process, and finding the right problem can take time.
If you are passionate about an application, talk to the practitioners about what are truly the bottlenecks they face. Are there problems where your technical tools can help them? Discuss with your advisor if these are the right fit for research or if these issues have been solved before (or even whether Mathematics or your area of research is the right tool to solve these). If you like solving brain teasers, then find the ones that are truly challenging and impact a lot of problems (otherwise wouldn’t it be better if you used your brain for something else that perhaps paid you more?).
At the end of your PhD, you should know more about your thesis topic than your advisor themselves. It’s not about quantity, it’s about quality and creativity. Breakthroughs require continuous thought about a problem, which can lead to interesting insights or new ways of thinking about the same thing. If you are waiting to scramble before a meeting, then breakthroughs are unlikely to happen (or maybe you are a genius and can pull through in the scramble!) Some students write a book about their thesis, some graduate with 3 papers, and some graduate with a single landmark paper. You cannot predict what your journey will look like. Follow your passion, and the rest will likely follow.
Personal Preference of a Thesis Topic: for me to be excited about a topic as an advisor, I like balance of theory (t) and practical impact (p). I enjoy advising theses which can be quantified as \lambda t + (1 – \lambda) p, with \lambda \in [0.5, 0.9]. As my advisee, it is better if we are aligned on the goal of balancing practical impact and theory. - Make Peace with Failure.
In today’s hypercompetitive world, there seems to be no place for failure. Yet, most of us who have met some world-specific criteria of success in life have gone through failure. There are many well-known and not-so-well-known stories of failure — which I hope can inspire young adults to not be scared of failing. I would like to especially call out to STEM minorities, to remember that when you fail, you are not an impostor. You belong in the field, and you are not alone! Only when you fail multiple times, you know what’s not going to work in research. I know many successful people who still have moments of self-doubt, but what is important is their grit in recovering from these moments and emerging strong.
Do not let self doubt guide you, and surround yourself with positive people who cheer you on. Believe that you have what it takes to solve the hardest problems, and this will actually help you solve them. Fear of failure hinders creativity. For example, it hinders one from asking questions, which hinders learning, and sometimes even the most basic questions lead to new ways of doing the age-old thing. Broadly speaking, an academic career (including PhD) involves paper rejections, grant rejections, and many other rejections, but rejections cannot define you or what your ideas are worth.
āSo the reality is that you just have to say, āIām more committed to my vision than Iām committed to your doubt or my fear,ā and just go for itā¦ā (From Conversations with Top Achievers by Woody Woodward)
There are many stories of how many disruptive ideas were rejected many times, but ultimately changed the face of the field. My favorite one is the Turing Award lecture video by Geoffrey Hinton and Yann LeCun from 2018. So, getting your papers rejected could also mean that your ideas are forming to be sufficiently disruptive! Hang in there. - The Art of Communication is Important.
A big part of doing research is to be able to communicate your ideas. You should be able to communicate with advisors, your collaborators, your fellow students — what the key intuition is in the ideas you are pursuing, what makes your problem challenging, why have people not been able to solve this before, what is the key ingredient in your new technique, why should people spend time trying to understand what you did.
Mathematical Communication. There is a skill to write proofs in a way that can answer the above-mentioned questions, without actually meeting face to face. This means that all assumptions are clarified, all logical statements are derived without jumps, all notation be parseable, etc. If you want to learn how to develop this skill, I suggest that you read through Knuth’s monologue on mathematical writing. There’s also a skill to communicate ideas in person, depending on your area. Pay attention to “how” the best teachers in your area communicate.
Communication without jargon. Even though we speak from our own experience, sometimes we have to put ourselves in the shoes of the other person we are communicating with (e.g., the reader of your paper), and then explain to them our ideas in their own frame of reference. Once you are adept at talking to your friends in the research area you work within, you can challenge yourself to communicate with people not in your research area. The way you explain, e.g., gradient descent to a college major (e.g., moving along the negative gradient) would be very different to the way you would explain this to a 5-year old (e.g., ascending or descending hills to find valleys). This skill to be able to communicate is now more important than ever, since the problems society faces today cross many disciplines. If you want to develop algorithms for screening resumes, you better be able to explain this to a lawyer or a policy maker to really develop techniques that can be used in practice. Many disruptive ideas have actually been cross-pollinations from other fields, but this can only happen with communication. Likewise, many fields like game theory, machine learning, and cryptography had rediscovered similar ideas for years, without knowing that these were actually already known in the other areas. I cannot emphasize enough how important it is to be able to communicate about your research. This skill is something that has definitely helped me do the inter-disciplinary work that I do. - Seek Feedback.
There are multiple ways to receive feedback during your PhD, and in academia. The first and foremost is from the advisor. An advisor’s role in the journey for a PhD is to provide guidance, and a part of this guidance is to provide their honest and direct feedback (e.g., are you on track, areas where you excel, areas that you could improve, ways of writing, choice of problems, etc.) in the safe space of their research group. Your role as a student is to seek and receive feedback, so you can grow from this. Giving constructive and productive feedback requires time and effort, and as a student you should find mentors who you trust and who are able to do this for you. Then there are many ways to get “external” feedback, beyond your research group. For example, when one submits papers for review, they get feedback from reviewers (often unaware of which authors wrote the paper). When one gives talk, they get direct feedback from the audience and this is face to face, which means receiving feedback graciously is important. Even in 1-1 exchanges with fellow students, faculty, speakers, visiting researchers, you can get feedback (and give feedback) about your research problems and results. Be open to feedback without personalizing it. Even at this stage of my career, I am always open to feedback and seek feedback, since learning requires humility despite where you have reached in life. - Transparency and Integrity – The Two Pillars of Academia.
Academia is defined by exchange and growth of ideas – which can lead to massive innovations and disruptions. In this sense, it is important to be transparent about potential credit and also about any potential errors, to create a culture of trust. If credit is shared appropriately, then everyone feels safe to share their ideas and know that their contributions will be acknowledged. If errors are acknowledged appropriately, it creates a culture of trust that if a result is published it must be true “to the best of our (collective) knowledge”. In general, we strive to uphold the integrity of scientific discovery – to state results as they appear, the truth of mathematical statements – as honestly as possible.
Let me first discuss credit. It’s important to give credit to papers who inspired an approach, it’s important to give credit to previous results, and even informal discussions which sparked an idea. If you heard an idea from someone else, and you use the idea in your work, you need to attribute and give proper credit. Discuss with your advisor on what the proper level of attribution is – acknowledgement, co-author, or some other way. Likewise, if you have contributed to an idea in a paper, and are not given credit for it, your advisor can help you navigate these situations. It’s also important to give your advisor and collaborators proper attribution to their ideas, and not present them as your own. Be very careful about copying text from a source (written by you, your collaborators), or using GPT models to generate text for your papers, which can lead to plagiarism (or even self plagiarism). As much as possible, when you write a new document, start from scratch.
If you think your result has a mistake, discuss it with your team, and work to fix the mistake. If you think your published result has a mistake, bring it to your advisor, and make a plan on how to retract the paper or published an errata. If you discover an error in someone else’s published work, it’s important to discuss this with the authors of that paper. There are some examples of cases when papers have been retracted in the past, due to errors found in their proofs.
To build on the last point, integrity is one of the most important compasses in academia. For my research area, our process is to decide on a set of assumptions (e.g., if the data is generated by a particular process, or the axiom of choice is true, etc.). Once one agrees with the assumptions, the mathematical derivations on the theory can be checked for correctness and must follow logical steps. Once one implements this on a dataset, one can report the results of the developed techniques. There is no place for modifying the results or misreporting the results, to meet any other objectives. - Know When to Take a Step Back.
I view an academic life as a life driven by passion for research, inventions, and problem solving. But this has to take a step back, when it comes to your mental health (and health in general). Taking a break to prioritize mental health is important, as everything else builds on this. Passion, grit and resilience (i.e., the stuff I said above) only make sense when you feel mentally and physically ready to take on the challenge.
Recognize what you need. There are many forms of self care and mental health care. Sometimes its a matter of knowing what motivates you, what schedules and routines work for you, what you need to decompress (e.g., yoga, meditation), and build that into your schedule. Sometimes it’s about figuring out what one’s values and identity in life are, and it’s okay to take the time for finding your community. Sometimes it’s better to get external help with a therapist who can help navigate the pressures and emotions we feel. Sometimes ones needs a more severe intervention. We live in a world where productivity is glamorized, but it’s actually important to take the break when you need it. Once you realize that, academia has ways to make that space for this break (e.g., semester long leaves), and you should trust your advisor enough to have this conversation with them. - Lastly, My Personal Advising Expectations.
I care for my students, advocate for them, and metaphorically bat for my students! I dedicate a large amount of my bandwidth in advising them, working with them, guiding them, creating opportunities for them, and moulding them to be all-rounder researchers. It’s a responsibility I take very seriously.
What I ask in return is open communication and dedication to your thesis work, which translates to effort, grit, and passion. If you don’t hold up that end of the bargain, the advising relationship is not going to work. Know that I’m there to help remove bottlenecks as they arise, I’m there to brainstorm with you when you are stuck, I’m there to guide you in research – and also in areas other than your research, e.g., job market, talks, collaborations, career decisions, etc. But it’s your thesis, and so you are the driver of it, and you are the one fueling the thesis work with energy. At the end of your journey, I am expecting you to know more about your thesis than me, and to be able to write a paper entirely by yourself – start to finish. During this journey, there will be times when you may disagree with me on the direction of your work or technical ideas (and that’s okay), and we can mutually find a point of contention. In that sense, I view you as my equal, my collaborator, my friend. As your advisor, however, it’s my responsibility to make sure you are making progress towards your thesis, bridge the gaps in your training, provide guidance on the topics discussed above, and protect you — and in that, I view you as a young student who’s still learning how to do this, and I take the role of your mentor.
