William Chuang
Graduate student, University of Arizona
E-mail: williamchuang (at) math (dot) arizona (dot) edu
Hobbies and Interests: crafting math puzzles, the art of problem solving, volunteering and serving, and traveling. Furthermore, with a growth mindset, I enjoy challenging myself by learning new topics, such as a subject about which I knew very little or which was my weakness and blind spot.
Additionally, here is my YouTube channel that I just started reently and am going to constantly share some worked problems: @william_chuang
The following is a link to a Google drive of my old notes for math:
My old notes
More about myself before 2015.
I have a mandarin name 桓山 which is a combination of three hieroglyphical symbols - a tree, a sun with sunburst, and a mountain - to portray a figure with an ancient cypress tree on a holy mountain, such as the Temple Mount (Haram al-Sharif) or Mount Kailash, which is enlightened by the sun with sunburst to represent God's eye. One usage of this name is that somehow it becomes an indicator to show if a person would support either the US (if one likes it), or the recent regime that controls China (if one disagrees with it).
My parents used to call me 道茂 which could probably be understood only by them. This name has a foreign provenance; Thomas (Aquinas) was translated into mandrin by the Chinese Regional Bishops' Conference, which is definitely not a supporter of China's current leadership. Not to mention that my parents are also glad to call me 桓山.
A ranking report which showed my ranking at NTU was improved from 26 out of 47 to 16 out of 51, though it wasn't a fair ranking because I solely took classes in the physics graduate program (where students' GPAs were largely curved to some extreme, especially for several core courses I took, e.g. applied math III, statistical mechanics II, quantum mechanics I and II, quantum field theory II, etc). It actually only ranked all undergrad students of the class B99 who were assigned to major in bioengineering systems, rather than the whole class of grad students majoring in physics or taking courses in the physics graduate program.
If one was born in Taiwan, one may have wished since infancy to be able to join the world and be a part of it (for example, to obtain a passport that allows one to access UN facilities like other global citizens).
As someone who has wanted to study mathematical and theoretical research since childhood, I would like to learn from the best of the best in these research fields, and I believe the closest places I could possibly have in Taiwan at the time are mostly in Taipei (e.g. NTU and Academia Sinica) or Hsinchu (e.g. NTHU). One thing I didn't realize at the time was that it would be easier if I could begin to study and major in math instead of physics since high school or even earlier. When I was in high school, I didn't know what to learn to prepare myself to be able to do the sort of research I have dreamed to accomplish.
I was in the bottom 5% of my junior high school class when I started at St. Ignatius high. I decided to go to that school after reading biographies of Ignatius of Loyola and Fr. Beda Chang SJ and influenced by several of my family friends. This shows the source of my etra-dimensional interest which is religious, and this is also the reasone why I would like to do research (over taking exams/contests) to answer my own questions or at least to find out what I did not know.
One more thing I think it is worth addressing is that why I was not a good test taker before I went to study in universities is that back then I was in an extreme to reinvent everything. In brief, I refused to read any hints or solutions including the main contents of every textbook, because I was similar to some idealists that I believed if one could not generate a solution of a problem without any helps, then one should not use it. This also reflects an idealists' worry that if given the same conditions, could one also develop the whole theory or the research field like the pioneers did. Because each theorem or proposition was also a problem back when the theory was established.
To be successful in an important exam, one is expected to bring an expert brain into the exam. That means one has leearned almost every results and tricks developed in history. This could achieve by solving as many problems randomly and without looking at solutions to turn everything into one's instinct.
As a result, in contrast to the time when I received bad marks in high school and nearly never gave myself time to concentrate on problem solving and exercise (since I was trapped in the process of theory building), I began to allow myself to work on whatever exercises and problems I found in history (in every related book, note, or any other resource). Instead of starting everything over from scratch to reconstruct the whole theory without taking any helps, and instead of not setting a time limit for each task, I started to set a deadline for each excercise or problem, say for one day or two, in my training set, and I keep about one-third of the samples (including any questions written by myself or theoretical questions) for validation and testing my instinct and what I could output only using my brain. For samples in this testing set, I would spend a fraction of the exam time on them before checking with the solutions when deadline was reached to ensure the completeness of my instinct building.
After I went to NDHU, I started to improve my test taking skills and eventually ranked at around 1.82% when I was at NDHU and be able to transfer to NTU (after passing NTU transfer exams with an acceptance rate fluctuating from 0 to 5% back then) and started to work my way out of the bottom 5% at NTU until I got A's in particle physics, quantum field theory, and advanced field theory courses.
Furthermore, before becoming an NTU undergraduate student, I read practically every used book that appeared at the main bookstore for collecting used books near the institution. I'd want to parse everything that goes through the minds of NTU students or professors, therefore I'd spend about an hour there every day to swiftly browse through all of the new used books in that bookshop, and I'd buy approximately 5-10 volumes out of the few hundreds of books. I concentrated on every book they read to help them improve the way to use their brains to do better research, and perform better in each exam.
With the same principle, to learn from the best of the best, I decided to drop out of the education system in Taiwan, and move to the US to start over. The decision made after all my best friends in physics who I took physics courses with in Taiwan, particularly theoretical physics, were either got an offer to become a professor (and very soon a distinguished chair professor), or got offers from good PhD programs in the US from top 1 to top 10, and became professors or post-docs in the US in some top 30 universities now.
I only applied to one school since, as an undergrad, I had an adviser and had attended his research working group meetings for three years and still had a research project to work on at that time.
Because I only took graduate-level physics classes, completing my undergraduate degree at NTU would take another three years. As a result, I believe the reason I was put on the waitlist was that I did not have an undergraduate degree at the time. Furthermore, after reviewing the application results, I was told that the admission committee was most concerned with my quantum mechanics scores, which were B+ rather than A. In the same semester, I took QFT and received an A. If my memory serves me correctly, just two pupils received As. The other student who received an A already became the outstanding chair professor (at that time, he was a PhD candidate).
People in Taiwan believe that even a homeless person on the street in the United States can speak and understand English better than the typical English instructor in Taiwan. What I could do was analyze what I had and what I could do with it. As a result, I chose to drop out of Taiwan's educational system and go to the United States to start anew. I'd like to start a new life in the United States, reincarnated as an average American, with limited resources. As a result, I opted to transfer to a community college, which I knew I could do without requesting a reference letter.
Inspired by this old saying, even a homeless person could teach a lot, e.g. to survive in the US, not to mention a community college that most police officers or a large portion of people who serve in citizen corps or national guards. Motivated by this proverb, "Even a homeless person could teach a lot," such as how to survive in the United States, not to mention that most police officers, national guard members, members of community watching groups or citizen corps attend community colleges. I would like to learn from the best, and I believe native speakers who went or taught at community colleges could speak better English than any average English class in Taiwan.
What I wasn't sure about was if I could transfer to a reputable institution if I already had 130 semester credits from NTU. Since NTU (and any Taiwanese institution) allows students two years of leave for absence (exceeding that limit may result in dismissal), my first aim after transferring to a community college was to see if I could transfer to a decent four-year university.
Some may believe that transferring to a California community college from NTU is silly and idiotic. They may claim that, while NTU is not very good, its rating is adequate, since it just dropped out of the top 20 in Asia, and its physics global ranking is 117, according to US News. Given my medical condition, I was unable to serve in the military. Then, as a non-military individual, there is no use in remaining on that island other than being a hostage or liability if any attack on democracy, freedom, and the rule of law occurs on that Pacific island. This does not contradict anything I have learned over the previous decade in the United States.
My community educator told me that the people of Taiwan served as human shields for the United States. I believe there must be a better solution than merely becoming a human shield passively. Using logic, one could already see what should be done to prevent what could happen in the United States. There are some problems that need to be focused, e.g. the existence of the united front reminded by congressmen and congresswomen from both aisles (the last page of this memorandum shows that pepople of Taiwan are targeted individuals of the United Front and could be misused for propaganda by anyone) and lobbyists using MICE or RICE strategies and their classic strategies, the symptom of the erly phase of a cultural revolution, and the surveillance from foreign agencies using animals. "In a global and totalitarian war, intelligence must be global and totalitarian." The parity of the two superpowers should not be an isomorphism, i.e. whatever one side has could be found in its dual which also has an analogue that functions in an analogue way. In a positive competition, both sides will eliminate their poor behaviors and learn or develop new, better habits.
People in the United States (and presumably the rest of the globe) may not understand why Taiwan has to be defended. For instance, at [00:48:27] in this interview, it has a false claim that Taiwan is not a strategeic point which contradicts to the statement "the island of Formosa, i.e. Taiwan, is strategically important to the United States." For another instance, even this VOA's article does not really expain it.
Why is it important to Americans or people across the world? Why in General Douglas MacArthur's classified "Memorandum on Formosa," stated that the geographic location of Taiwan is such that in the hands of a power unfriendly to the United States it constitutes an enemy salient in the very center of that portion of our position?
Fundamentally, this has nothing to do with politics, this is about national security. (It is simply about everyone's safety, and for the United States, it is about national security.) "Once China gains control of Taiwan, it will be able to breach the first island chain, positioning it at sea to deny the United States, Japan and other allies, and use Taiwan as a springboard to expand military power deep into the Pacific," meaning that it will most likely be very difficult if it's not impossible to detect China's ballistic missile submarines that carrying WMDs or nuclear weapons when they slip into the Pacific Ocean via Taiwan's east coast, where depths of up to 5 miles are feasible.
If it's not detectable, then it cannot be monitored or predicted. Since the SOSUS system, or other surveillance systems used by Taiwan, Japan, and the US that currently track PLA submarines in in the shallow waters off the East Asian littorals would be rendered less effective or completely neutralized in Taiwan's case." Furthermore, in the long run, the PLA might continue to upgrade and update their submarines; if Taiwan fell under PLA hands, they could launch submarines from Taiwan's south/east coast deep-water ports, with the capacity to send them anywhere in the globe.
Furthermore, targeting more than 50,000 United States Forces Japan, in the report "The American Case for Taiwan", the author mentioned a post-Taiwan unification plan outlined in a confidential PLA handbook:
In the United States, occasionally I was requested to surrender. It's most likely because either I am from Taiwan, or was identified as a Japanese(?), or both. Were they trying to sow discord between Americans and Japanese people? If so, who can be benefited the most?
Because of that I could find myself in a situation of false assumptions that without a need of a proof - I could be assumed as if I have done something, going to do something - just because I could not be proven I didn't do or not going to do what I was assumed to do. Even people from math could have this logical fallacy.
First of all, Taiwan is not a region in Japan (maybe this is not that well-known in the US). To prove this, one can go to CFR's webpage to see that Taiwan was rank number ten in the democracy index (2022) and Japan was number sixteen - how can this be possible if Taiwan is in Japan? A question to think about is that what if the result of the Chinese civil war was reversed (maybe China could also be ranked around number 10 in this democracy index)?
Although about 200,000 people of Taiwan was forced to attend WWII (since at that time Taiwan) including my grandfather and maternal grandfather, (a) I have never seen my maternal grandfather (I was told that he was a student of Waseda University at that time and always stayed in the main islands of Japan as a navy and for a few years before he died, my maternal grandfather did work for the new Taiwan government as a director of military service section in the office of his home county for military recriting after 1949 for the allies), and (b) my grandfather lived far away to my parents and I have only saw him a few times before he died when I was about 12 (he was a marine and deployed to southern China sea to fight red army).
In the past about ten years, this part of history has become a tool for some people of Taiwan (not sure if they are backed by the recent government of Taiwan) for propaganda against the united front of CCP. The problem is in several other cases (other than my grandfather and maternal grandfather), native people of Taiwan were deployed to the conflicts against the allies. Not every one of them had the same fate/history. Hence, it is not wise to recall this part of memory of native people of Taiwan (back then each one in three households had a child deployed to the WWII and their descendants were treated in some extreme conditions). Descendants were born after WWII and have nothing to do with WWII. This propaganda was most likely from the recent government of Taiwan and their party members, then a good question to ask was that this government was backed by the US and the allies, right? Why it's less likely done by the united front or CPP? Because a goal of united front might be to use the KMT to unite people of Taiwan, and this propaganda did the opposite. Furthermore, it reminds people of Taiwan that Taiwan is a home of the braves. I don't know who started this propaganda.
However, if one mentions this propaganda in the United States (in my personal experience, as a human from Taiwan, one does not even need to bring it up), one's presence may already attract a large number of people who have not learned about Taiwan's history, and may cause them to react in the worst possible version of them, treating people from Taiwan inhumanely.
Though the generation of my grandparents did have to use passports issued for imperial Japanese before the San Francisco Treaty (see the point number 2 in the summary and the content in this document) was signed, they and their children including my family were under certain survelliance and people were told not to talk with us similar to what was mentioned in this clip between 21:00-23:00. Today, it is still not clear how the government of Taiwan actually treated people like my family and my grandparents. However, this recent research paper published by Academia Historica could shed some lights on this issue - it shows how the targets of the government was monitored even when they were traveling oversea. It is not clear how this survellience was conducted. What is clear was that for everyone who lived in Taiwan before 1949, their bank savings were all multiplied by a factor, 1/40,000. For people who worked for the government or moved with the new governement to Taiwan, they didn't be affected, since their salaries and savings were multiplied by the factor equals to 1 the same as the new Taiwan dollar.
As a result, these rules have already caused problems for my grandparents and relatives. Personally, I've never backed the imperial Japanese government or the war they started.
My ancestors clearly surrendered to the Allies during WWII, and I personally have nothing to surrender because I was born 40 years after the conflict. I made none of these decisions to go to war. Because of my religious beliefs, my value system has always been as follows: to save the world > to prevent a conflict/war > fastly end a war > ...> the reverse of the above priorities.
Considered both of my father and mother's family have lived in Taiwan for at least 400 (they were the twentieth generation since the first generation of their ancestors moved to Taiwan), so I am sort of native based on the classification used in this article. When I was a student at NDHU, some students and I were invited by the university's military training instructor to meet with President Ma Ying-jeou about one year before he got elected, and I attended that meeting. However, this could not classify me as a nationalist, I also attended another meeting as well: when I transferred to NTU, some NTU students and I were somehow invited to meet with President Tsai Ing-wen at NTU about three years before she was elected. Hence, I am neither nationalist, nor a member of DPP. Again, my value system has been mentioned in the above paragraph. It would not be logical to classify me as either a CPP (or any governments of countries that CPP is friends with), a DPP, or a KMT supporter - as a religious person attended Jesuit schools and university for more than ten years, I supported my value system and the people who shared the same values in a global perspective.
USF is in the semester system, and De Anza is in the quarter system. Hence, when I got admitted to attend USF in Spring 2015, I had to withdraw courses I was taking at that time in De Anza. Since as an F-1 student, I couldn't enroll in both I-20 required programs.
For the same reason, i.e. based on Charles Tiebout's suggestion that people "vote with their feet", I transferred again to USF, a university in the United States in Silicon Valley, in order to have opportunities to study from the best of the best on the planet and start a new family in this country so that my kids do not need to go through the same struggles.
My family: my kid and my wife.
My family: My wife and I went to the same university (University of San Francisco) so that we can get married after we graduated.
My family: My father, his brothers and sisters, and my grandfather with Fr. Hilber Jakob--this colorized photo was taken in the front yard of my family house in Taiwan.
My family: My father, his brothers and sisters, and my grand parents stood in front yard of my family house in Taiwan. This photo was taken by Rev. Ernst Gassner, SMB
