Mighty math: Valedictorian diaries

By her own account, valedictorian FANG Xinyu knew little about mathematics as a college subject or its highly complex research. While she gained a sense of satisfaction solving mathematics problems as a child, her earlier education, she says, did not even show her “the tip of the iceberg of this deep and vast subject.”

Nevertheless, her interest in mathematics was fired during her school days. This was, in no small part, a result of her teachers who revealed “the beauty of mathematics” through their classes.

As she graduates with Honours (Highest Distinction) in Mathematics and Minors in Computer Science and Economics, Xinyu’s inspiring journey is not just one of academic distinction and attainment of the most coveted of honours – the crowning academic achievement from years of hard work, dedication and resilience. Indeed, the true value of this accolade also lies in her meaningful contributions beyond the classroom as well as her personal growth as a well-rounded individual during her candidature.  

Looking beyond mathematics

While mathematics has always been the focus of her studies, her exposure to other disciplines proved very beneficial.

She says, “Mathematics is purely logical and definitive, highly abstracted from the real world, but economics studies scenarios that could arise directly from real life, except with some simplifying assumptions. Computer scientists care about the speed of computation and sometimes allow a small probability for error, while in mathematics, we often care about whether the problem can be solved correctly (in any finite amount of time).”

Looking at the world through different lenses has, in turn, led her to adopt a more “open-minded” attitude and to be more receptive to different types of theories. 

Pursuing academic excellence

Xinyu is the winner of the Special Programme in Mathematics (SPM) Book Prize for Academic Year 2023/2024. She says, “SPM gave me a taste of mathematics in a more rigorous shape and led me to realise that I am mesmerised by the beauty of Pure Mathematics, not just its applicability. This strongly influenced my decision to pursue research projects and further study in Pure Mathematics.”

She also received the Tan Teck Chwee Prize awarded to the best Year 3 student in Pure Mathematics and was placed on the Dean’s List for four semesters.

Her first year course, Calculus and Linear Algebra I & II, introduced her to what “mathematical theories” look like. She was especially fascinated by Linear Algebra II(S), the first SPM S-course that she read. She says, “This led me to abstract algebra, which I have been deeply in love with ever since. The abstractness and elegance of this domain of mathematics completely changed my worldview of the subject.”

She subsequently took on further courses such as abstract algebra, commutative and homological algebra, algebraic topology and algebraic geometry, which enabled her to discover the true power and versatility of this subject.

Xinyu’s interest in Number Theory stemmed from a reading project on elliptic curves and modular forms. As part of her Undergraduate Research Opportunities Programme in Science (UROPS) project, which received the CRISP award, she explored the field of arithmetic statistics and partially resolved an open problem on the probability distribution of cokernels of Haar random Hermitian matrices. “This first experience in research was very meaningful,” she says. “I discovered the excitement in mathematical research and gained the confidence that I could solve certain problems.” 

Together with her Honours Year Project (HYP), which centred on a surprising application of methods from Logic (the theory of ‘o-minimality’) to a problem in Number Theory (the Ax-Lindemann-Weierstrass theorem), Xinyu discovered the importance of self-directed learning – “the skill to learn from original papers and textbooks, to struggle in the search for relevant bits and pieces in the vast literature and to solve a problem independently instead of receiving ready-made knowledge in a passive way.”

Broadening her intellectual horizons

Inspired to lean into soft skills like collaborative learning and research, as well as gain exposure to industrial research, she interned at PayPal Global and QuantEdge Capital, where she had the opportunity to apply her analytical skills in real-life problems in technology and finance. This led to a more well-rounded understanding of these subjects. 

She also participated in the Research Experience for Undergraduates (SMALL REU) programme at Williams College, USA, where she co-authored three papers, in the fields of probability and combinatorial geometry. There, she was able to independently pursue new questions in mathematics and discover interesting solutions, which further intensified her interest in mathematical research.  

She also spent an exchange semester at University of Michigan, Ann Arbor and was a participant of the Women and Mathematics (WAM) 2023 conference at the Institute for Advanced Studies (IAS) in Princeton University. She says, “I deeply enjoyed the time I spent with other female students discussing mathematics. This boosted my confidence that I could do well as a woman in mathematics.”

 Growing as a student leader

As Project Director and President of the NUS Mathematics Society, she spearheaded various society initiatives such as Problemathic, an NUS-wide Mathematics competition. This allowed her to put some of her ideas into reality in pursuit of her vision to spread interest in mathematics in the NUS community and to provide a platform for fellow students with the shared passion for mathematics to come together.

As a member of NUS Chinese Dance, she not only advanced her lifelong passion in this CCA, but she found the experience of contributing to a group of highly skilled and passionate dancers “very fulfilling.” 

For students who are embarking on their learning journeys, she has this advice: “An insatiable curiosity is a key factor in my academic success: an unquenchable desire to learn and understand more about the subject. Therefore, pursue a subject or specialisation that you are genuinely interested in. Find your curiosity, and it will guide you to where you want to be.”

Hopes for the future

Xinyu will be pursuing her passion in Pure Mathematics as a PhD student at Harvard University and plans to venture into academia, to nurture the next generation of mathematicians.

Prof GAN Wee Teck, Head of Mathematics, says, “Congratulations to Xinyu on completing a wonderful academic intellectual journey at NUS and for the well-deserved honour of being selected as our valedictorian. We are proud of your achievements and wish you all the best in your subsequent graduate studies at Harvard.”