Math is hard.

If you grew up in the US, that phrase is probably seared into your mind, a relentless refrain heard from students and teachers alike. And how discouraging it is to hear!

In years past, I remember thinking, if mathematics is so difficult, why not focus my energy elsewhere? Why not pursue something more readily attainable? Why put myself through unnecessary hardship if I’m likely to fail anyway?

Nowadays, my thinking is entirely flipped – the most worthwhile endeavors are those that require effort, and failure is the first step toward success.

That line of reasoning led me to where I am today, in my third year of a Ph.D. program in Mathematics. The path I took to arrive at this point was circuitous, to say the least. But it was my path, and I’ve come to be grateful for all its twists and turns.

Childhood

As a child, I excelled at math. Most adults in my life considered me naturally gifted, but the reality was much more down-to-earth. I simply enjoyed doing math problems and had great teachers.

High School

Unfortunately, nerds were not looked upon favorably when I was a teenager. I had taken Algebra I and Geometry in middle school, so in my freshman year of high school, I started out in Algebra II. This class was mostly filled with juniors, and I think they saw me as an anomaly outside of their social structure. Someone to be ignored. This suited me just fine since I wasn’t keen to draw attention to myself.

Outside of math class, though, the problems started. I took the same English, science, and social studies classes as my peers. I ate with them in the cafeteria and exercised with them in the gym. In these settings, I was still an anomaly. But now I was an anomaly within their social structure. Not someone to be passively ignored, but someone to be ostracized.

Now, bullying was nothing new for me. I experienced some of it in middle school, as most kids probably do. But in high school, my brain consisted of approximately 90% hormones, so I actually cared what my peers thought about me.

When it came time for me to take Calculus AB, I listened to the lamentations of the other students. “Math is hard”, they said, “especially calculus”. And of course, I listened. I wasn’t good at math anyway; I barely even passed precalculus. And so began my inexorable academic decline.

I avoided AP classes like the plague, and when my academic advisor tried to intervene, I told her I was signing up for a second semester of weight training to gain some much-needed muscle. I joined the cross-country team and quit after my first meet, where I ran so hard I puked. I didn’t engage in any extracurricular activities, join any clubs or volunteer for any charitable causes. I was the anthesis of the model student.

Again, none of my attempts to reinvent myself actually prevented the bullying. Instead, in my junior year of high school, the taunts and insults from my peers transformed into something more menacing.

Insults became threats. Threats became assault. There were times I couldn’t even walk into a classroom without someone putting their hands on me.

I tried reporting this to the administration, but nothing ever came of it. The psychological toll this took on me was immense, and so one day I simply stopped attending school. After two solid weeks of being absent, my parents received a letter stating that further absences would result in expulsion.

The next day, we attended a meeting with the principal in which he tried to convince me to come back to school. He looked genuinely concerned, but all I could think about was the irony – where was that concern when I filed reports of harassment? I listened to his speech and told him I would rather be a high school dropout.

I never returned to high school. I had a better plan.

Changing Paths

I knew that my problems were social, not academic. I also knew that my local community college had a special program for adults pursuing education later in life. It was similar to a GED program, and there was no minimum age requirement. So, at age 16, I enrolled in the Adult High School program at the community college.

The requirements to earn a diploma were actually lower than that of my high school, so I ended up graduating a full year before my peers. Despite the low standards, the diploma was bona fide. With it, I was able to enroll in my hometown’s university. It was the only university I applied to because I honestly didn’t think I would be accepted anywhere else. I never even took the SAT, so I felt very fortunate to get in.

Somehow, through sheer luck or determination, I had successfully made the transition from high school dropout to college student.

College

I had absolutely no plan for what major to pursue, I just knew I was finally going to be surrounded by like-minded people. People who wouldn’t ridicule me for being passionate about academics. People who were weird and quirky and socially awkward like me. People I could be friends with.

It was the first time in years that I was free to be myself.

I knew what that meant: You’re welcome to stay, but you’re destined to fail. At that moment, I felt helpless. If the person designated to help me on my academic journey didn’t believe in me, why should I believe in myself? So, I switched majors.

The only other class I was really enjoying at the time was Calculus I, so I became a math major instead.

Part of me felt like I was giving up on my dreams, but it turned out to be the best decision I could have possibly made.

Despite being too terrified to take calculus in high school, I did very well in the calculus sequence at my university. I attribute that success to a healthy helping of hard work and an excellent professor, who went above and beyond to make her lectures interesting, engaging, and intuitive. Two and half years later, she would teach me real analysis – a proof-based course that pushed me to my limits and beyond. But that’s skipping ahead in the story.

After becoming a math major, I fell head over heels for the subject. Most of my waking moments were spent thinking about the cool math facts I learned, and every non-math course I took was a distraction from that. That is until I took a computer science course which I really enjoyed. That course taught me how to program in C, and I was immediately hooked. Without a second thought, I decided to minor in CS. No longer did I spend all of my free time thinking about math; now I spent it coding up cool math ideas!

I also enrolled in the honors program during this semester, which meant I was taking 7 courses at once. But it was so engaging, I didn’t mind. I finally felt like I fit. Throughout the remainder of my undergraduate studies, I took on average 6 courses per semester, plus a couple of courses each summer. I wasn’t in a rush to graduate, I just really enjoyed learning.

The only required course I dreaded taking was calculus-based statistics, since my previous exposure to statistics had been miserable. I avoided taking that class for as long as I could, but when the dreaded semester arrived… I loved it. To my surprise, statistics and probability were beautiful when framed in the right way.

Again, I had a wonderful professor to thank for that revelation. She convinced me to add statistics as a second minor, which ultimately became a second major, and I had the honor of working with her on various research projects during my time as an undergraduate.

It was around this time that my older sister – the same one who taught me how to multiply before I was in kindergarten – emailed me an application for a variety of summer internships at NASA. I laughed when I received it. Sure, I was a good student double-majoring in two difficult subjects with practically a 4.0 GPA (believe it or not, my only A- was in an online physical education course).

In the back of my mind, I was still a high school dropout. I certainly didn’t have a shot at getting into NASA.

So, I ignored the email. Fortunately, my sister didn’t let me off the hook that easily. She checked up on me and convinced me to at least apply – there was no harm in getting rejected after all. So, I found the 10 internships that interested me the most, applied to them all, and steeled myself for the inevitable rejections.

A few weeks later, I received a phone call. And an email. Two out of the ten nets I cast actually caught something. I was in disbelief. Surprised, stunned disbelief. The phone interview didn’t go so well, but the second opportunity panned out, and I was offered an internship at NASA’s Jet Propulsion Laboratory. My sister was thrilled, but I don’t think she was surprised; she always believed in me, especially when I didn’t believe in myself.

The summer I spent at JPL was, up until that point, the best summer of my life. It was a breathtaking experience. In the end, my mentors offered to bring me back for the following summer, post-graduation. I eagerly accepted.

During my senior year, there wasn’t much left for me to do. I had burned through the curricula for both my majors by taking so many courses so quickly. All I had left to do was finish up my CS minor and work on my honors thesis in mathematics. Checking the boxes for the CS minor only took one semester, so I was left with an empty schedule for my final semester of undergrad. I could have graduated early, but I still had some work I wanted to finish on my honors thesis. So, as any sane person would do, I spent my final semester taking enough computer science courses to upgrade my minor to a third major.

And that’s how I graduated: three majors, summa cum laude, president of the Math & Stats Club, with honors and multiple research projects under my belt.

You might think that this level of success altered my self-image. At best, you might be imagining a self-confident overachiever; at worst, a pretentious snob. But neither depiction is accurate. I still doubted myself. I still felt like I knew hardly anything. Honestly, most of the success felt like dumb luck. Like these opportunities were dropped in my lap, and I just happened to keep my head above water.

I knew in my heart that I wanted to pursue a Ph.D. in Mathematics, but I didn’t actually believe I would succeed in doing so. After all, math is hard. It’s one of the hardest things a person can do! And I just wasn’t cut out for that.

Computer Science

The only thing that kept me sane during this period was a clerical error. I was being paid as a research assistant, but the administration made a mistake and assigned me as a teaching assistant for an undergraduate course with an enrollment of 200 students. I tried everything I could to get out of it, but there were no other TAs available to fill the spot.

After that, I went home for summer break. My sleep schedule was back to normal, but one night I just couldn’t fall asleep. My mind was racing with thoughts about my Ph.D. and how poorly I performed in the classes I had stopped attending. I thought about how miserable I was studying computer science and how happy I was teaching.

As I dove deeper into that train of thought, though, I realized something. The best days teaching my students were the days I got to teach them about mathematical concepts. Not computer science, math. For one of my lectures, I had gone so far as to completely circumvent the CS curriculum and design an entire interactive lesson around the Catalan numbers, a recursive sequence from combinatorial mathematics.

And as the first rays of sunlight started to peek through my bedroom window, I realized with complete clarity: I was in the wrong place.

If teaching was the light at the end of the tunnel, that realization was a bullet train that yanked me out into the warm embrace of the sun.

Looking back, I had chosen computer science because I thought it would be easy. Don’t get me wrong, CS is a difficult topic that requires significant effort to master. But compared to mathematics, it seemed more readily achievable. I chose computer science because I was too afraid to follow my dreams and pursue a Ph.D. in Mathematics.

In short, I was afraid of failure. But by taking the easy route, I came face-to-face with true failure – the failure to nourish one’s soul.

Leaving computer science was absolutely the right decision for me, but it still wasn’t easy on my psyche. I now had the unique distinction of being a double dropout. Feelings of inadequacy flooded back, and memories from high school resurfaced. But at least I had a plan.

Turning Back

I knew that the first step to getting into a good Ph.D. program in Mathematics was to perform well on the GRE Subject Test in Mathematics. This would be a challenge since there were numerous areas of mathematics on the test in which I had never taken a proper course. So, I decided to shore up my mathematical knowledge by returning to my undergraduate institution to pursue a master’s degree.

Dropping out of a Ph.D. program in favor of a master’s degree felt shameful. I returned to my old stomping grounds with my tail between my legs, expecting people to look down on me, but my expectations never became reality. If anyone pitied me, they didn’t show it. On the contrary, the welcome I received was warm and kind.

While working on my master’s degree, I mainly supported myself by teaching and tutoring at the university, but I also had a remote internship thanks to some connections from my old professor for Calculus I and Real Analysis. This internship involved a lot of data science and mathematical modeling, and it was pretty enjoyable.

After earning my master’s degree, the company I was interning with offered me a full-time position in the Bay Area. Considering that my score on the GRE Subject Test wasn’t strong enough to get me into a top-tier school, I accepted their employment offer. Even working full-time, I figured I would be able to study math in my free time and improve my score for the following admissions cycle.

One year later, I scored in the 61^st percentile. A ten-point improvement was nothing to scoff at, but it felt so small for a year’s worth of work. I applied to Ph.D. programs anyway, and to my great surprise, I got accepted to some pretty good schools. But at the same time, the company I was working for offered me a significant promotion. I accepted their offer, hoping that I could really knock the GRE Subject Test out of the park on my third attempt.

When the time came, I scored in the 71st percentile. Another 10-point increase, but this time it was something I could be somewhat proud of. At the very least, I knew I gave it everything I could.

I wasn’t very fond of any of the schools I got into during the previous admissions cycle, so I applied to a dozen new schools this time around. I was accepted to several of them, and I ended up choosing to attend UC Santa Barbara for my Ph.D. in Mathematics.

Following the Dream

I was quite a few years older than the other students in my cohort, but that didn’t bother me. I was just happy to be doing what I loved. I’m now in my third year here, and I couldn’t be happier. Oh, it’s been challenging, to be sure. It’s certainly the hardest thing I’ve ever done. But I embrace that now.

Math is hard. Still. The people who say that aren’t mistaken, they are absolutely correct. Their mistake is in avoiding math because it’s hard. Ask yourself this: What is there to be gained from an easy life? I haven’t yet found an answer, and I suspect that there isn’t one. Easy lives seem hollow to me.

Life is meant to challenge you, to push your limits, to reforge you into a better version of yourself with each new day. Looking back, the worst periods of my life occurred after I succumbed to fear.

Fear that I wouldn’t be accepted by my peers in high school and fear that I wouldn’t be able to succeed in a Mathematics Ph.D. program.

The greatest, most joyful periods of my life occurred after I acknowledged my fear and marched onward in spite of it. Doing so is never easy, but for me, it has always been worth it. I now have the philosophy that if you live life in your comfort zone, if you don’t occasionally go out of your way to do something that terrifies you if you never embrace your fear and attempt the outlandish, then you’re not really living.

This way of life has shown me that it’s okay to follow your own path and take your time getting to your destination.

When you’re in high school and college, you’re pushed along at such a rapid pace that it can seem like there are no other acceptable paths. Like the journey to a successful life is predetermined and immutable. But this is far from the truth. As far as I’m concerned, if you are chasing your dreams, then you are successful.

No matter how old you are, what obstacles you’ve encountered, or how high the odds are stacked against you, the best time to chase your dreams is now. And if you hear that nagging voice in the back of your mind saying, “What if I fail?”, shout in its face and say, “I hope I do!”.

Failure means you’re pushing yourself to be better. It means you’re courageous enough to try something despite your fear. To overcome it and shine brighter for it. And rest assured, you will fail. Many, many times, if you’re lucky. The key is picking yourself up, dusting yourself off, and trying again. Because that’s what it means to live.