'enjoyed puzzles and solving problems' - Stanford intellectual vitality

As I had always enjoyed puzzles and solving problems, mathematics had always been my favorite subject. Mathematics was logical, and always made sense. However, my curiosity towards mathematics heightened when I learned about proofs. A complete proof meant that the mathematical statement was true and could not be refuted. I was even more intrigued by what constituted a valid proof as I learnt the basics of induction and contradiction. More questions popped into my mind as I pondered over the concepts I learnt. Armed with a new mathematical tool, I found great joy in proving basic formulas like the arithmetic summation formula. I could finally rest at ease knowing that the derivative of sin(x) would always be cos(x) and understanding the principles behind it. When I saw how seemingly difficult questions like why there were an infinite number of primes could be solved with a simple yet creative proof, I was enchanted.

The concept of proof gave me insight as to how applied mathematics stood on the basic fundamentals which could never be shaken. When I was young, I had dreams of creating the next revolutionary gadget. As I realized that mathematics provided the foundation for a wide range of complex functions from optimizing production processes to devising a music composition program, I knew that I wanted to be able to be involved in various fields. To be able to use mathematics to shape the world around us would be a dream come true.

The concept of proof has not only established my understanding of mathematics, but has also made me more inquisitive about why things work in a certain way. My motivation to obtain a university education is driven by my desire to learn.

First, you should write in the present tense (assuming everything still holds true today) : "As I have always enjoyed puzzles and solving problems, mathematics has always been my favorite subject."

I like how your essay shows what a big influence mathematics has on you and how much it has opened your eyes

You may want to base your points around a specific instance, like give a specific example of when math helped "shape the world" for you.

I also think that you should elaborate on how your experiences with math tie in to the bigger picture like you do in the last two sentences; explain more the connection between math and your "desire to learn".

Hi, I am also working on this prompt. I think your essay looks good to me. But the last sentence seems a bit unrelated to the previous part. Perhaps you want to try to link them better.

Thanks for the input. I was writing it and I realized that I didn't really know how to end, so I came up with that. I'll keep working on it.

Thanks once again.