← Back to Blogs

February 11, 2026

Hold Hands and Share Feelings: a Trivial Reflection of 19 Nontrivial Years

Reflections as I enter the last year of the second decade of my life.

#personal #reflection #math
A function is continuous if you can draw its graph without lifting your pen?If you use this as your definition, you might as well hold hands and share feelings.— Gautam Iyer, my 21-269 professorIntroductionTime flies. Or does it? Long Qian, my 21-242 TA last semester, once said that “time doesn’t fly.” I think I concur with both.In the blink of an eye, I am already almost 113 semesters into college. Time really flies.But on the other hand, so many things have happened over the past 4 months. I met and made so many friends from around the world. I learned so much, not just academically, but also in life. Life skills, lessons, and tricks. It’s hard to describe in words, because it’s really unbelievable that all of this happened over only a few months. Time really doesn’t fly.As I celebrate my 19th birthday, I would like to take some time to reflect on the current, past, and future.Let’s begin.Assume for the Sake of ContradictionBesides having to survive on my own, the greatest change I observed in college is that all of my courses are proof-based. Say goodbye to calculations (in fact, I bought a new TI NSPIRE CAS II and could never use it outside of writing math contests for high schoolers).You might think this is only for math courses. Nope. Computer science courses are also proof-based. Even Linguistics and Philosophy courses are proof-based. Some examples:•15-122 Principles of Imperative Computation‣I entered the class thinking I was going to code so much. First week of classes, we learned how to prove correctness and safety of code. In the end, we learned how to prove structural invariance.•15-150 Principles of Functional Programming‣Ok, surely now this class is just coding, right?‣Prove your 𝑂(𝑛log𝑛) function is extensionally equivalent to the brute force 𝑂(𝑛2) algorithm.‣Prove this random algorithm has 𝑂(log3𝑛) span.•21-242 Matrix Theory‣Matrix? Determinant? Merely social constructions based on abstract Vector Spaces.•15-151, 15-251, 21-269, 21-373, 80-180, …Here’s one of my 21-269 homework problems from this semester:Prove that any real number lies between two consecutive integers.One year ago, I would complain about how things like this are trivial and we should just assume they are true. I mean, everyone has been taking things like this for granted since elementary school, so it surely is just a fact, right?But after 4 months of proof showers, and given recent current events, I now have a different opinion on this topic.Hold Hands and Share FeelingsI admit that the title of this blog is click-bait, and you might have been expecting something else (don’t worry, me too). But I want to give a semi-serious discussion about my philosophy on math and the world.In this information era of Mass Media and Artificial Intelligence (AI), it is very easy to consume false information. Once in a while, I find myself almost believing an AI-generated misinformation or disinformation post on Instagram, before verifying its validity and realizing how silly I was to almost fall for them.Nobody is immune to information weapons. If you are connected to the internet, you are already cooked. No matter how knowledgeable or resilient you think you are (I thought I was until AI-Generated Content (AGC) started becoming too realistic), someone or something will eventually get you.However, as the world around us changes rapidly, and as every piece of information you perceive can be manipulated and shaped to influence your behaviors, there are still things that never change: the laws of logic, math, and physics (my father yaps to remind me about this once every few weeks).How do you know your high school math teachers didn’t lie to you? How do you know every real number is bounded by two consecutive integers? Or even better, what is a real number?Why is it that det(𝑎𝑐𝑏𝑑)=𝑎𝑑−𝑏𝑐? Why is a square matrix 𝐴 invertible if and only if det𝐴≠0? Or even better, what is a determinant? Why do we even study this?As I step away from taking in “facts” (do they even exist?) and applying them to compute numerical answers, I find it fascinating to ask myself why. Even more exciting is convincing myself that each of these “facts” is true by proving that they are true, only from the most basic definitions and axioms (of course, then you ask yourself why the axioms are chosen, and then you find even more interesting things behind the world of logic and math).Being rigorous is not just being performative. Being rigorous is a way of recording truth, logical deductions, and evidence. While some people hand-wave proofs and rely on intuition, I firmly believe that information should be formally verifiable. Human intuitions are wrong all the time. Did you know that you could break a solid ball into two identical solid balls? Intuitions and assumptions are feeble. Rigorous proofs are strong.And yes, I agree with Professor Iyer. If you take facts for granted and hand-wave justifications with intuitive definitions, then you might as well “hold hands and share feelings.”Final Year in the Second Decade of My LifeI always tell people that, to me, the “modern” era is anchored at the year 2017. Maybe it was because I didn’t care about things around the world until 2017, or maybe it was because I watched AlphaGo beat Lee Sedol on Live TV around that time, or maybe it was because Attention Is All You Need, or maybe it was because of the invention of 高速に差分計算可能なニューラルネットワーク (Efficiently Updated Neural Networks, NNUE), 2017 felt like the turning point of the world to me.Now, if I can subtract correctly (after spending 99% of my time on abstract proofs recently), we are already 2026−2017=9 years from that anchor. What I imagined as “modern” is soon to become a decade-old past that we would soon view as ancient, given how quickly the world is moving today.Coincidentally, this year also marks the end of the second decade of my life. Hence I thought it would be interesting to reflect on the past nine years before I step into the final year of a decade alongside the 2017 “modern” world.Looking Back: Adversity Creates Opportunity2020 was certainly one of the years of all time. While many people (rightfully) look at the negative sides of the pandemic, I try to observe the more positive things made possible uniquely because of it.Social Media. Short-form Content. Online Meetings. Virtual Classrooms. Before 2020, these technologies were never allowed their full potential to grow. As I read Algospeak by Adam Aleksic (@etymologynerd), I realize just how much the growth of these technologies has transformed both the world and myself.As for me. Sitting in front of a computer 24/7, I practiced American English slang with friends on Discord. I joined programming communities and learned to code. Who knows who I would be today without being able to stare at VSCode and Discord for 10 hours a day? Would I even pass the high school entrance English exam? Would I even code? Would I even ever learn and use a programming language other than Python? It’s hard to say, but I sure am proud of who I am today as brought up by this journey.As for the technologies. Within a year, Google turned Hangouts, a functionally unusable app in my experience, into Meet, an arguably almost flawless app now used by many public school districts. As a result, Google expanded its effort on online education and turned Google Classroom from essentially an organized storage to the core of everyday student-teacher interaction. At the same time, Zoom zoomed ahead (really no pun intended) and solidified itself as the industry standard for online meetings. Discord grew. People began scrolling on Tiktok. Perhaps without the pandemic, we would still be relying on paper for assignments and grades and be forced to shut down all educational activities during a snowstorm. The world changed fundamentally because of the pandemic.Adversity creates opportunity, I guess. That’s my main takeaway from the pandemic.But even 2020 was six years ago. It certainly does not feel like we have completely parted ways with the pandemic.Time moves on……and so do challenges and danger.Looking Ahead: a Homogenized but Divided WorldRapid advancements in technology continue to enlarge the socioeconomic divide between wealthy elites and average citizens. Capital accumulation and elite-favoring policies are intensifying global economic inequalities. Corporation-controlled mass media are amplifying elite voices and suppressing average citizens’ opinions. Monopolies and standardization of practices are homogenizing the world’s diverse cultures.— My (Rejected) Stanford ApplicationLook at all those kids in joy because the answer to a contest math problem was exactly 67. Or when an NBA team reaches a score of 67. Or when the professor asks for a random number between 1 and 100 to demonstrate binary search, and everyone shouts 67.Everyone around the world is heavily affected by social media, whether positively or negatively. And social media is extremely powerful. Or perhaps too powerful.Look at recent nationalist movements across every continent. Or the extinction of languages. Or the alienation of cultures.The rapidity of these global developments amazes me. But as we become homogenized, we remain divided. There’s no need to say more about this — just look outside in 2026.Society is beautiful. Languages are beautiful. Cultures are beautiful.People are beautiful. Communities are beautiful. Nature is beautiful.We are beautiful.Looking forward, in the next decade, I hope to make the world more beautiful.But the world is changing so quickly, and we must adapt to this speed. I hope to ride the waves of frontier technologies and work for a better future that does not yet exist.Let’s do it together. Rigorously. Truthfully. Beautifully.
A function is continuous if you can draw its graph without lifting your pen?If you use this as your definition, you might as well hold hands and share feelings.— Gautam Iyer, my 21-269 professorIntroductionTime flies. Or does it? Long Qian, my 21-242 TA last semester, once said that “time doesn’t fly.” I think I concur with both.In the blink of an eye, I am already almost 113 semesters into college. Time really flies.But on the other hand, so many things have happened over the past 4 months. I met and made so many friends from around the world. I learned so much, not just academically, but also in life. Life skills, lessons, and tricks. It’s hard to describe in words, because it’s really unbelievable that all of this happened over only a few months. Time really doesn’t fly.As I celebrate my 19th birthday, I would like to take some time to reflect on the current, past, and future.Let’s begin.Assume for the Sake of ContradictionBesides having to survive on my own, the greatest change I observed in college is that all of my courses are proof-based. Say goodbye to calculations (in fact, I bought a new TI NSPIRE CAS II and could never use it outside of writing math contests for high schoolers).You might think this is only for math courses. Nope. Computer science courses are also proof-based. Even Linguistics and Philosophy courses are proof-based. Some examples:•15-122 Principles of Imperative Computation‣I entered the class thinking I was going to code so much. First week of classes, we learned how to prove correctness and safety of code. In the end, we learned how to prove structural invariance.•15-150 Principles of Functional Programming‣Ok, surely now this class is just coding, right?‣Prove your 𝑂(𝑛log𝑛) function is extensionally equivalent to the brute force 𝑂(𝑛2) algorithm.‣Prove this random algorithm has 𝑂(log3𝑛) span.•21-242 Matrix Theory‣Matrix? Determinant? Merely social constructions based on abstract Vector Spaces.•15-151, 15-251, 21-269, 21-373, 80-180, …Here’s one of my 21-269 homework problems from this semester:Prove that any real number lies between two consecutive integers.One year ago, I would complain about how things like this are trivial and we should just assume they are true. I mean, everyone has been taking things like this for granted since elementary school, so it surely is just a fact, right?But after 4 months of proof showers, and given recent current events, I now have a different opinion on this topic.Hold Hands and Share FeelingsI admit that the title of this blog is click-bait, and you might have been expecting something else (don’t worry, me too). But I want to give a semi-serious discussion about my philosophy on math and the world.In this information era of Mass Media and Artificial Intelligence (AI), it is very easy to consume false information. Once in a while, I find myself almost believing an AI-generated misinformation or disinformation post on Instagram, before verifying its validity and realizing how silly I was to almost fall for them.Nobody is immune to information weapons. If you are connected to the internet, you are already cooked. No matter how knowledgeable or resilient you think you are (I thought I was until AI-Generated Content (AGC) started becoming too realistic), someone or something will eventually get you.However, as the world around us changes rapidly, and as every piece of information you perceive can be manipulated and shaped to influence your behaviors, there are still things that never change: the laws of logic, math, and physics (my father yaps to remind me about this once every few weeks).How do you know your high school math teachers didn’t lie to you? How do you know every real number is bounded by two consecutive integers? Or even better, what is a real number?Why is it that det(𝑎𝑐𝑏𝑑)=𝑎𝑑−𝑏𝑐? Why is a square matrix 𝐴 invertible if and only if det𝐴≠0? Or even better, what is a determinant? Why do we even study this?As I step away from taking in “facts” (do they even exist?) and applying them to compute numerical answers, I find it fascinating to ask myself why. Even more exciting is convincing myself that each of these “facts” is true by proving that they are true, only from the most basic definitions and axioms (of course, then you ask yourself why the axioms are chosen, and then you find even more interesting things behind the world of logic and math).Being rigorous is not just being performative. Being rigorous is a way of recording truth, logical deductions, and evidence. While some people hand-wave proofs and rely on intuition, I firmly believe that information should be formally verifiable. Human intuitions are wrong all the time. Did you know that you could break a solid ball into two identical solid balls? Intuitions and assumptions are feeble. Rigorous proofs are strong.And yes, I agree with Professor Iyer. If you take facts for granted and hand-wave justifications with intuitive definitions, then you might as well “hold hands and share feelings.”Final Year in the Second Decade of My LifeI always tell people that, to me, the “modern” era is anchored at the year 2017. Maybe it was because I didn’t care about things around the world until 2017, or maybe it was because I watched AlphaGo beat Lee Sedol on Live TV around that time, or maybe it was because Attention Is All You Need, or maybe it was because of the invention of 高速に差分計算可能なニューラルネットワーク (Efficiently Updated Neural Networks, NNUE), 2017 felt like the turning point of the world to me.Now, if I can subtract correctly (after spending 99% of my time on abstract proofs recently), we are already 2026−2017=9 years from that anchor. What I imagined as “modern” is soon to become a decade-old past that we would soon view as ancient, given how quickly the world is moving today.Coincidentally, this year also marks the end of the second decade of my life. Hence I thought it would be interesting to reflect on the past nine years before I step into the final year of a decade alongside the 2017 “modern” world.Looking Back: Adversity Creates Opportunity2020 was certainly one of the years of all time. While many people (rightfully) look at the negative sides of the pandemic, I try to observe the more positive things made possible uniquely because of it.Social Media. Short-form Content. Online Meetings. Virtual Classrooms. Before 2020, these technologies were never allowed their full potential to grow. As I read Algospeak by Adam Aleksic (@etymologynerd), I realize just how much the growth of these technologies has transformed both the world and myself.As for me. Sitting in front of a computer 24/7, I practiced American English slang with friends on Discord. I joined programming communities and learned to code. Who knows who I would be today without being able to stare at VSCode and Discord for 10 hours a day? Would I even pass the high school entrance English exam? Would I even code? Would I even ever learn and use a programming language other than Python? It’s hard to say, but I sure am proud of who I am today as brought up by this journey.As for the technologies. Within a year, Google turned Hangouts, a functionally unusable app in my experience, into Meet, an arguably almost flawless app now used by many public school districts. As a result, Google expanded its effort on online education and turned Google Classroom from essentially an organized storage to the core of everyday student-teacher interaction. At the same time, Zoom zoomed ahead (really no pun intended) and solidified itself as the industry standard for online meetings. Discord grew. People began scrolling on Tiktok. Perhaps without the pandemic, we would still be relying on paper for assignments and grades and be forced to shut down all educational activities during a snowstorm. The world changed fundamentally because of the pandemic.Adversity creates opportunity, I guess. That’s my main takeaway from the pandemic.But even 2020 was six years ago. It certainly does not feel like we have completely parted ways with the pandemic.Time moves on……and so do challenges and danger.Looking Ahead: a Homogenized but Divided WorldRapid advancements in technology continue to enlarge the socioeconomic divide between wealthy elites and average citizens. Capital accumulation and elite-favoring policies are intensifying global economic inequalities. Corporation-controlled mass media are amplifying elite voices and suppressing average citizens’ opinions. Monopolies and standardization of practices are homogenizing the world’s diverse cultures.— My (Rejected) Stanford ApplicationLook at all those kids in joy because the answer to a contest math problem was exactly 67. Or when an NBA team reaches a score of 67. Or when the professor asks for a random number between 1 and 100 to demonstrate binary search, and everyone shouts 67.Everyone around the world is heavily affected by social media, whether positively or negatively. And social media is extremely powerful. Or perhaps too powerful.Look at recent nationalist movements across every continent. Or the extinction of languages. Or the alienation of cultures.The rapidity of these global developments amazes me. But as we become homogenized, we remain divided. There’s no need to say more about this — just look outside in 2026.Society is beautiful. Languages are beautiful. Cultures are beautiful.People are beautiful. Communities are beautiful. Nature is beautiful.We are beautiful.Looking forward, in the next decade, I hope to make the world more beautiful.But the world is changing so quickly, and we must adapt to this speed. I hope to ride the waves of frontier technologies and work for a better future that does not yet exist.Let’s do it together. Rigorously. Truthfully. Beautifully.