This is the question that I received constantly in the past semester, and indeed many people found my decision of studying Pure Mathematics puzzling. If I said that I had found beauty and eternity in Mathematics, I would be weird although that was exactly what I believed. In the end, I often chose to change the topic of discussion or even not to answer the question at all. Some guessed that I must have been rejected by better majors. But the truth is, I put Mathematics as my top choice and did not even apply for other majors in university. Now, it is perhaps the appropriate time for me to answer this question, not only for the curious, but also for myself. I divide the big question into smaller, more specific sub-questions and address them individually.
Q1: Isn’t Mathematics very difficult?
Well, yes and no. Pure Mathematics at undergraduate level is difficult in the sense that it is vastly different from High School Mathematics. It contains much more proofs, theorems and abstract concepts. Before clearing one abstract concept, lecturers often quickly move on to discuss more abstract concepts. Often, I walk out of the Lecture Theatre with confusion and questions unanswered. Immediately, I will receive a question set, and the questions look alien to me. Solving/finding the correct answer is no longer the focus. Understanding and applying the correct method are the key. It takes time to search for the best method of proof and comprehend those concepts that I cannot find any immediate applications in real life.
At the same time, Mathematics at undergraduate level is not as difficult as one may think. Life will become much easier if I understand the concepts and the correct method of proof. I can divide the large question into smaller sub-questions (like what I am doing now) and find the answer to each sub-question. I am free to try different methods and evaluate their effectiveness. Making reflections on each question/proof is particularly useful to help me understand what the lecturer taught me. The process can be tedious, tiring and depressing, but it brings much fulfilment and inspiration in the end. I remember a Chinese proverb saying that if one finds something difficult, it is because one has not really understood it. Once he understands the concept/skill, he will never find the same thing difficult again. This is perhaps the best way to answer this question.
Q2: Are you going to get a PHD in Mathematics?
I am sorry but I really do not know. Continuing with graduate studies is a huge commitment for me to make, especially when I am still a freshman in university. Studying a PHD in Mathematics depends on many factors including my undergraduate grades, the quality of my thesis, the financial situation of my family, employment prospect, my interests, programme offers, etc. Certain things are clearly beyond my control. At the same time, I also secretly fear that in my senior years, I will suddently realise that I am retarded. (The prospect is not particularly promising since I am already showing some early symtoms of retardedness, LOL)
I have to say that I have not really made up my mind, and I am open to possibilities.
Q3: What can you do with a Mathematics degree?
I remember a joke that the only difference between a pizza maker and a Mathematician is that the pizza maker can feed his family. I am still laughing at the joke as I am typing it.
Did I consider employment prospect when applying for the major? Of course I did. At that time, I was pretty sure that I was not going to study Law or Medicine in university, therefore what I do in the future may not be exactly the same as my degree. If that is the case, why don’t I study something I like since getting a degree is all that matters? Suddenly, I became an idealist and chose Mathematics. (In fact I am too idealistic and may need another essay on why I study Philosophy) If you force me to consider what I can do with a Mathematics degree, I can think of many things. Mathematics is the foundation of many disciplines including Finance, Accounting, Economics, Engineering, Sciences, etc. I may not use those crazy theorems in my future job, but the analytical skills and resiliance I acquire from a Mathematics degree can be transferred across all kinds of jobs.
After all, I can always be a primary school teacher, LOL.
Q4: What kind of people should study in Mathematics? Must one have Olympiad background in order to major in Mathematics?
Personally, I had some Olympiad experiences in my Primary and Secondary schools back in China. However, after I came to study in Singapore, I was no longer offered any training opportunities. Therefore, I do not have much Olympiad experiences before starting to major in Mathematics. Nevertheless, I still choose the major full of Olympiad medalists. I personally think that undergraduate Mathematics and Olympiad Mathematics are difficult in very different ways. If one has Olympiad experiences, one certainly has some advantage in certain areas of undergraduate Mathematics. At the same time, no Olympiad experiences do not equal to the end of the world; one can still succeed in university as long as one works hard.
There are indeed many competitive people studying Mathematics, and there are certainly many setbacks. Nevertheless, I do not think that Mathematics at undergraduate level requires a lot of IQ. Instead, a lot of resiliance, passion and cooperation is required. In other words, it requires a lot of EQ. (I may be wrong since I am still in my first year. Do not take my advice :P)
Some final thoughts
From China to Singapore, no matter how my academic foci and school curricula changed, Mathematics is the subject I am good at and really interested in. After studying Mathematics for many years, I think that I may understand the meaning and beauty behind those inanimate numbers a bit more. Those numbers, with the truth it reveals about the universe, are capable of transforming my life, or probably even the lives of many others. Every number, equation and proof that I write down is actually the reflection of my intellectual courage, creativity and original insights. Mathematics has become an inseparable part of my life and my identity. I am willing and really excited to pursue it further.