A few days ago, our mathematics department organized an event to guide undergraduates in preparing for applying to master’s or doctoral programs. During the registration process, we asked students if they had specific questions they wanted answered. Some inquiries focused on academic performance, with students expressing concerns that their grades might be “too low." The answer to this question is quite complex and may be easier to understand for students in the mathematics department. The concept of “too low" is relative. For instance, when considering a maximum score of 4.3, it’s challenging to determine what constitutes “excellent," “good," “average," “low," or “too low." Does a mere 0.1-point difference shift a grade from “distinction" to “ordinary"? In hindsight, academic performance is not of paramount importance. What truly matters is whether your grades are sufficient for us to recommend you to our department. Different departments may have varying standards regarding these scores. Even when a department provides a specific score, we sometimes advocate for students, emphasizing their capabilities to succeed in a master’s program. Thus, a higher GPA does not necessarily guarantee a greater chance of admission. When we select graduate students, we consider their entire university experience, not just a solitary number.

Moreover, if students focus solely on subject grades while neglecting other essential criteria for graduate school applications, they may ultimately find it challenging to secure admission for research positions. Graduate schools prioritize research capabilities over mere academic exam results. The grades earned in various undergraduate courses do not always reflect one’s research skills. High grades do not equate to high research capability. Therefore, even if students do not achieve a perfect 4.3, it does not imply they cannot engage in research. Reflecting on past exemplary graduate students, their grades might have been merely average or second-class honors, and their DSE results may not have been outstanding. Thus, students should not feel compelled to dedicate all their time to achieving high academic scores. Instead, they should take advantage of their free time to work on projects and seek opportunities to explore research, assessing whether they are suited for an academic career.

Among the questions we received, some students expressed concern about needing specific courses, fearing this would make them seem less qualified for research applications. Indeed, if you’ve completed our master’s or doctoral courses during your undergraduate studies and achieved good grades, that’s a definite advantage. However, our ability to conduct research in a particular area does not directly correlate with taking specific courses. We recognize that vast online learning resources are available today, and students should cultivate the ability to learn independently rather than overly relying on courses provided by their schools or departments. You don’t need to showcase your familiarity with a subject through your transcript.

Moreover, merely taking specific courses doesn’t guarantee acquiring all the knowledge necessary for a particular research area. If students believe they must master every aspect of knowledge before undertaking research, they might as well not engage in research, as that’s simply impossible. In research, you often don’t know what skills you need. Typically, we formulate questions and hypothesize solutions from multiple perspectives. If you restrict your problem-solving to only what you’ve learned, you limit your potential approaches. We often look into how others have tackled related problems and then attempt to apply similar techniques to explore our research interests. Thus, when starting a research endeavor, there’s no definitive way to know if you’ve mastered all the necessary knowledge. The ocean of knowledge is vast, and no one can grasp it all. The same goes for academia; even professors may not be intimately familiar with every aspect of their fields. This holds true for mathematics professors, physics professors, and even me—I only know a fraction of the field of applied mathematics.

Ultimately, we hope students can maintain a humble attitude. Understanding that life should not be measured solely by grades is crucial. Earning a PhD does not automatically equate to a successful life. A doctorate is merely a ticket to the academic world and does not guarantee a smooth career. Sometimes, high-achieving students might mock those with poorer grades. We should foster empathy and recognize that everyone has different strengths. A student may not excel in mathematics yet possess exceptional interpersonal skills and a wide circle of friends. Their communication abilities might surpass yours. Furthermore, each individual has unique talents, and as we grow older, we realize that there are scholars who surpass us in various fields. The mathematical prowess you take pride in may not be as remarkable as you think.

During the sharing session, a student inquired about the types of jobs available for those who cannot complete their PhDs. This is an excellent question, highlighting that job opportunities do not necessarily correlate with educational qualifications or degrees. The most critical factors in finding a job are your interests and whether the work aligns with your personality. Higher academic qualifications only sometimes make it easier to find employment. What matters most is knowing what type of career you are passionate about and gaining relevant experience during your university years. If you pursue a PhD or master’s simply because you are unsure of your career direction or because of good grades, you may still face the same dilemmas in the coming years. Life won’t change significantly. For these students, I hope they take a moment to reflect on whether these degrees truly align with their goals.