The great genius Ramanujan believed that all his equations came to him in dreams—divine gifts from his beloved deity. Since we may never fully understand how a human mind could conceive such profound identities without formal proof, we accept his word for it. The rest of us mortals, however, must work hard for whatever we achieve. Even among us, some are naturally more inclined toward mathematics than others. As a teacher of mathematics, I have long carried a question with me: is the widespread poor understanding of mathematics among the general public a failure of our teaching methods, while the ability to solve problems is partly innate and certainly honed through practice?
In what follows, I revisit my own journey—first as a student and later as a teacher—sharing a few personal anecdotes that reflect how some of us come to learn mathematics.
My earliest memory of mathematics goes back to third grade. One day, my teacher entered the classroom and asked me to stand on the bench—usually a sign of punishment—announcing that I had performed poorly. I was genuinely surprised, convinced that I had done well. Moments later, he admitted that he was joking. I had scored a perfect hundred.
My parents later told me that even before this, I showed an inclination toward mathematics. They recall me comparing fruits, articulating differences in size, and expressing proportions with ease. Throughout my school years, I was known to teachers as a strong mathematics student. The reality, however, was simpler and less flattering: I was good only at mathematics. I liked science and Telugu, but never enough to work hard at them. I rarely prepared for exams for more than a few minutes, despite my mother’s constant worry that I never studied. She often compared me with a neighbor who worked diligently, and I would dismiss her concerns by claiming that he had to study hard because he was not intelligent. It was youthful arrogance, no doubt, but also a deep sense of complacency.
I was fortunate to possess a good memory and the ability to absorb complex arguments with little effort. Rote learning, however—the dominant mode of learning in other subjects—required discipline I did not have. My marks reflected this disparity clearly. Mathematics was always my highest-scoring subject, while the rest hovered just above average. This was enough to place me among the top three students in class. I was, and remain, what I would call an alpa santoṣi—content with little. I never cared much for ranks or recognition, then or now.
My parents never pressured me, choosing instead to let me be. The only exception came in tenth grade—an important milestone—when I nearly failed Hindi and biology. My father took special interest in ensuring that I studied these subjects. Part of this was circumstantial: he was confined to bed with typhoid for several days and had little else to occupy his time.
My father had recognized my interest in mathematics early and encouraged it consistently. He often claimed that I had devised a unique proof of the Pythagorean theorem that no one else knew. While it is true that I came up with several proofs independently, I am certain that all of them had been discovered earlier by someone else. Over my lifetime, I independently rediscovered many results. While I cannot claim originality, the experience of independent discovery—the act of arriving at truth on one’s own—cannot be quantified. It produces a kind of intellectual exhilaration that no artificial stimulant could hope to replicate.
My father would deliberately leave advanced mathematics books around the house, hoping I might pick them up. During the scorching summers of Hyderabad, constrained by my mother’s instructions not to venture outdoors, boredom left me little choice but to open those books. Through them, I learned mathematics far beyond my school syllabus and discovered many identities on my own. As a teenager, apart from playing with friends and neighbors, my primary pastime was to carry mathematical problems in my head—working on them while eating, bathing, or lying awake. I remember testing whether four- and five-digit numbers were prime, and searching for higher-digit analogues of Kaprekar numbers. It is worth noting that I never developed a habit of extensive reading, even in mathematics. I relied on just a few books, but explored them deeply.
In tenth grade, my father discovered the existence of the state-level mathematics olympiad, open to students across Andhra Pradesh. He collected past question papers and gave them to me. I was instantly captivated. I spent days—then years—trying to solve those problems. I approached my mathematics teachers for help, but none could assist; these questions lay far outside the prescribed syllabus. I not only wrote the exam but persuaded forty of my classmates to join me. The school even arranged transportation to the remote exam center. After the exam, I felt deeply disappointed. Many of the problems were within my reach, yet I made careless mistakes or failed to see solutions in the moment. I soon forgot about the exam itself, though I continued solving problems from those old papers long afterward.
At that time, the tenth-grade examination culminated in a Secondary School Certificate, a terminal qualification that enabled access to many low-level jobs. It was widely believed that one’s tenth-grade percentage would determine the course of one’s life. This belief persisted despite the fact that students still had to clear multiple entrance examinations to enter junior college.
To my shock, I scored only 89 percent in mathematics—the lowest I had ever scored until then. Even forty years later, I have no explanation for it, as I had expected near-full marks. A higher score would have compensated for my weaker performance in other subjects and secured me a prestigious scholarship. I fared equally poorly in a well-known residential junior college entrance exam, missing a seat in the mathematics group by just two marks. I was offered a biology group instead, which would have guaranteed a medical career, but I refused—despite my father’s encouragement. I also missed admission to the city’s best junior college and lost another scholarship by two marks. I ranked within the top fifty in the state talent search exam but failed to receive a national scholarship due to a funny reason—material for another story altogether.
By the end of tenth grade, the summary was paradoxical: I had performed better than most students and impressed everyone around me, yet I disappointed myself deeply. I had missed several opportunities, largely due to my habitual negligence. One might expect such experiences to prompt change. They did not.
Mathematics, physics, and chemistry came naturally to me in junior college. I never studied beyond attending lectures and was fortunate to have excellent teachers. English and French were far more demanding, and I accepted less-than-ideal marks in those subjects.
Midway through eleventh grade, a rumor circulated in my neighborhood that my high school principal was looking for me. This felt like salt on an open wound, as I was still upset about my tenth-grade results. Eventually, I was summoned.
The principal—whom I met again many years later—was also my neighbor and knew my mother well. She admired my mother’s determination in completing her diploma after a fifteen-year break from education. She also held me in fond regard, for my quiet demeanor and my aptitude for mathematics. When she saw me, she began calling teachers into her office, proudly announcing that I had secured fourth rank in the state. Only then did I realize she was referring to the mathematics olympiad—the exam I believed I had performed poorly in.
That moment remains, in my mind, the greatest academic achievement of my life: securing fourth rank in a large state like Andhra Pradesh, and doing so while believing I had failed. The prize ceremony was held near the state assembly, with the Governor as chief guest. The award recognized the one subject that had always mattered to me most. As it turned out, this was only the beginning—I went on to secure first and second ranks in the state in the next two consecutive years.
Two years earlier, the eldest son of a close family friend had visited us to announce that he had gained admission to IIT Madras by clearing the notoriously difficult entrance examination. At the time, it was not yet commonly called the JEE, though the name technically existed. Decades earlier, my father himself had attempted the exam and concluded that it was not meant for students from modest, middle-class backgrounds. But seeing a clerk’s son succeed changed his perspective. When I entered junior college, the idea of attempting IIT had already been planted firmly in my mind. With multiple near-misses behind me and a strong showing in the olympiad, I felt confident that I had a reasonable chance.
Formal coaching culture had not yet emerged. Instead, we relied on correspondence courses from Agarwal’s coaching institute in Delhi. Thanks to the efficiency of the Indian postal service and the quality of the material, our preparation was surprisingly solid. None of it would have mattered, however, had I not genuinely enjoyed this phase of learning. I was eager to understand physics more deeply—mathematics needed no additional effort—and chemistry as well. I studied books meant for college students and absorbed concepts effortlessly. For the first time in my life, my daily study time increased from a few minutes to nearly six hours. I never studied as much before or since. Evenings were spent listening to Hindi songs on All India Radio until 10:30 pm, after which the sight of neighboring students studying on their terraces inspired me to continue under the night sky until midnight. Occasional distractions—anklet sounds of girls walking along the road or playing on nearby terraces—were harmless and fleeting, restrained by the conservative norms of the time.
During the final phase, my father introduced me to the Indian Statistical Institute, Calcutta. When I examined past entrance papers, I was thrilled—they reminded me of olympiad problems. Unfortunately, the ISI exam coincided with the state entrance exam. I lacked the audacity to skip the latter, though I had not prepared for it at all. I often wonder what path my life might have taken had I secured admission to ISI. In the end, I ranked twenty-fifth in the state entrance exam and 412 in the JEE. The choice was clear. I joined IIT Madras as a mechanical engineering student.
At IIT, while most classmates prepared for midterms and finals, I spent my time solving old olympiad problems or reading history—especially the history of science and mathematics—and advanced engineering texts steeped in mathematics. My thesis was computational in nature, but I thoroughly enjoyed exploring the mathematical theories that underpinned it. I aspired to pursue engineering science in the US—the closest path to pure mathematics for a mechanical engineer—but my casual attitude toward laboratory and practical subjects resulted in a poor GPA. Financial aid in theoretical engineering science was out of reach.
Eventually, I landed in the US for a master’s degree in mechanical engineering at an obscure university in Florida. By the end of the program, I received offers for PhD studies in both mathematics and engineering science. I sought advice from a young faculty member whose course I deeply admired—Professor Wassim Haddad, who taught modern control theory. What was meant to be a brief conversation turned into an hour-long discussion in a corridor. I chose to pursue a PhD in mechanical engineering under his supervision, with a promise to focus exclusively on the mathematics of control systems.
Four months into my PhD, Professor Haddad moved to Georgia Tech, and I followed him there, completing my doctorate in aerospace engineering. True to his word, he allowed me to pursue the most abstract mathematics possible within control theory. My first published paper was purely mathematical in nature. Over time, we published several books on applied mathematics—composed almost entirely of theorems and proofs—applied to control systems theory.
The irony of my education is that I was just two courses short of earning a formal degree in mathematics. My indifference toward an additional degree cost me that opportunity. As a result, I never formally qualified as a mathematics faculty member. Yet, throughout my career, I have taught multiple mathematics courses, often with greater rigor than many mathematics departments—at least in the Indian context.
Today, I describe myself as a mathematician with no degree to prove it, and an engineer by qualification but not by inclination. My degrees gave me access to administrative roles in engineering institutions, while allowing me to teach mathematics and mathematically driven subjects within engineering.
I have had remarkable opportunities to pursue mathematics throughout my life—despite my academic labels and occasional negligence. I have no complaints.
The story of how I eventually became an educator in mathematics is equally accidental, and one I will leave for another time.