Paul Erdos woke up very thirsty one night. He opened the refrigerator and the only drink in it was acarton of tomato juice. He never opened a carton of juice before, his friends always served him food but he didn’t want to wake them so he opened the carton the only way he could, stabbing it with a knife. Having satisfied his thirst he went back to bed.

The next morning Erdos woke up and immediately set out to solve some more math problems and write some papers with colleagues (but this time it had to wait until the tomato juice was cleaned from the refrigerator). After a few more days and a few more papers published he left his friends house, bought a plane ticket and went to another mathematician’s house. “Another roof, another proof” as he would say.

He passed away doing mathematics in a conference writing a total of 1, 521 papers. More than anyone in history. He is now remembered andhonored in the scientific community by Erdos numbers. A person’s Erdosnumber is how many collaborators they are away from Erdos. It isn’t important in mathematics but it reflects 2 of Erdos beliefs about mathematics: It should be fun and collaborative.

Erdos was an extraordinary individual. He has inspired me to dedicate my life to science as he has. He had no material possessions except 2 suitcases and his mathematics notebooks. Science meant everything to Erdos, he needed nothing else. I think I understand how he felt and now I feel the same way. What property or thing could possibly be more important, more enlightening than truth itself? Erdos has inspired me to sacrifice anything that is needed for a career in mathematics and science, a career in truth and beauty.

Secondly, Erdos was friends with many people within the scientific community. Even if he did not know the person, just the fact that they are a mathematician, he would visit them for a few days and usually be allowed to stay. If you were a scientist you were Erdos’ good friend. As an introvert, and a very shy person in general, I tend to avoid people but Erdos’ life story has let me know that the scientific community is friendly. Science brings people together; we have something to share. I spoke to more mathematicians and physicists and in return, I know more potential collaborators and have learned more from discussing with them.

Finally, Erdos was dedicated and committed. And where did that lead him? He is considered one of the best in the world. He did not need to know things like how to open a carton of juice. He spent that time becoming the best in the world. And while Erdos is an extreme example of devotion to science he is also an extreme example of genius. If I want to be the best at something I must devote my whole life to it. I must be as committed as Erdos if such a thing is possible!

We were a team of 4 people up against schools with 20 people on a single team. As I sat down, I shook my opponent’s hand and he pressed down on the clock… 3 hours later he looks up at me with sweat on his face and says: “I resign.” I won my first match in the chess tournament adding a point to my team’s total.

The tournament was organized in 3 sections: Champion, Intermediate, and Beginner and the top scorer per team in each section earns points that count toward his/her team’s total. Each person played 5 games so a total of 15 points could be scored. I played on my team’s intermediate section alone. I played another 2 games and day 1 was over. The next day another 3 games were played. I won 4 of my games and drew another, a total of 4.5 points. This was .5 points above the team in second allowing us to take home the trophy!

When we got to school everyone at school was very surprised. No one knew the school even had a chess team, not even the staff in charge of clubs!

I spent the last 2 summers in my trailer with my family. We stayed in a campground by lake Huron. I did not do any jobs since it was my vacation after hard work in school. I did, however, have plenty of time to learn about the things that interest me and read some of my favorite books. Over the 2 summers, I read every single work by H. G. Wells (my favorite science fiction author), Jorge Luis Borges and a good number of Asimov’s stories. I also realized that I really don’t like many of Jean-Paul Satre’s ideas and views on freedom.

Idecidedto learn latin over the last 2 summers in addition to the school courses I took in latin but that was easier said than done. Near the end of last summer, I tested what I have learned in latin by reading Newton’s Principia in his original words (not translated). I didn’t do too bad with the help of google translate on the really difficult words!

I remembertheday that I decided to be a scientist. I was sitting on a couch beside my father watching a documentary on dark matter and dark energy and there was a man on screen explaining Einstein’s relativity. I was in amazement that Einstein was able to describe the interactions across the entire universe just through pure thought, a pencil, and some paper. I was even more amazed to learn thateverything can be described with mathematics.

From that day I knew I had to have a career in math and physics. I thought I did it to understand the universe but over time it evolved into something different. I sometimes told people I liked science because it was universally true or because it has practical benefits to society but that was not why I did mathematics and physics. I did it because I was puzzled and frustrated by the problems. I would work on the problem for hours to no avail. I would forget to eat and sleep. Just then, as I am about to give up, the world opens up and I see a beautiful solution. That is why I love doing science.

Princeton is the best university for math and physics. It would be an honor to study in the same place others like Richard Feynman, John Bardeen, Terence Tao, and John Nash. I also have heard that the professors are very knowledgeable and approachable. I hope to learn many things from them and maybe one day collaborate with them on research. Finally, I know that Princeton has great science laboratories and connections with other institutions. For one thing, there is the plasma physics laboratory and the nearby institute for advanced study which, although not related to the university, is a great place for further study. It would be my pleasure to do science in this wonderful university. I cannot wait to be one of the Tigers.

3x+1

I was locked in my room, pencil in hand, paper on mydesk as it had been for the entire day. Around my room papers and scraps were piling up. It was a pigsty in my room and I hadn’t eaten for the since yesterday. It didn’t matter forme though. I had a problem to solve, something none have ever done and I was convinced I had to do, I had to solve it.

The greatest mathematicians of the 20th century could not solve the problem but a smart first grader could understand it. Paul Erdos once said: “Mathematics may not be ready for such problems.” when asked about it. It is, of course, the Collatz conjecture. The Collatz conjecturestates that for any number, if it is even divide it by 2. If it is odd, multiply it by 3 and add 1. Repeat this process and any number and eventually, it comes down to the cycle 4,2,1,4,2,1… For example starting from 3 we have 3, 10, 5, 16, 8, 4, 2, 1 and we see 3 does indeed fall into the cycle. Every number up to 10^60 has been tested by computer and so far every number falls into the 4, 2, 1 cycle but no one has come up with a proof for every number!

I came across the problem for the first time in grade 2, in the back of the school library. It amazed me how simple the problem was to understand, how basic the underlying mathematics were and yet it was not yet solved. The problem showed me there is still so much to learn from even the most basic things. The things that many of us think we understand so well.

Just as I was about to give up and call it a night and idea came to mind. I extended the problem to a more general class of numbers, complex numbers and got a function describing theirbehavior. I wrote a program to apply the function to a small section of those numbers and color the resulting image so I could see an additional dimension of color on my 2-D screen. I waited for a few seconds and on my screen appeared the most beautiful image I had ever seen. A fractal similar to the Mandelbrot set. Chaotic yet so simple and regular. I was not proud of myself for making such a beautiful picture because I did not make it. Nature and logic wove it together and I only stumbled upon it trying to make sense of multiplication and addition.

In the simplest of things with enough work, I found a rich, complicated but magnificent work of art. After an entire day of work, I did not make any progress on the problem or make any contribution to mathematics by studying the problem but I went to bed happy. I don’t have to know the solution to know that it will be breathtaking. In math and other sciences, there are still things we don’t understand and we may never understand them but that should not keep us from trying to. Deep down, I knew from the start I wouldn’t be able to solve the Collatzconjecture, at least, without a greater knowledge of mathematics (maybe it’s even unprovable!) but at the end of the day, I think I knew a little bit more about multiplying by 3 and adding 1.

“I think it’s much more interesting to live not knowing than to have answers which might be wrong.”

-Richard Feynman

Why Waterloo?

I was watching a documentary on relativity. I was in amazement that Einstein was able to describe interactions across the universe just through pure thought, a pencil, and some paper. From then I knew I had to pursue a career in mathematics or physics. The more I learned about the subject, the more beauty I saw and the more I was addicted to it. I cannot attempt to express this beauty in any language; it would not do it justice. Rather, I can only hope that you, the reader, has had some experience with the thrill of discovery, the beauty in symmetry, and the urge for more that comes with it.

I am applying to University of Waterloo because I believe that after being educated (and obtaining a Ph.D.) from the best University in Canada for mathematics and physics I will be able to create my beauty, building on the work of past greats such as Newton and Euler.

Addition EC Notes (Waterloo):

*Please note that as I have completed high school in only 2 years I am only technically grade 10 so all my extracurriculars were done in my last 2 years of high-school: 9/10.

*Emory Univ. Spirit of Ramanujan was an online math competition and talent search done in collaboration with Expii. I was among the top competitors and featured with an article on the site.

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Univ. Spirit of Ramanujan was an online math competition and talent search done in collaboration with Expii. I was among the top competitors and featured with an article on the site.

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