All kinds of comments and feedback welcome! :D

**Prompt: Stanford students are widely known to possess a sense of intellectual vitality. Tell us about an idea or an experience you have had that you find intellectually engaging.**

On a free Sunday evening, surfing the internet seemed boring to me. Wondering what I should do, I eventually decided to keep my mind busy by solving math problems. The first problem I got seemed interesting, but I was unsure of how I should begin tackling it. Randomly, I picked a theorem to use. I was worried whether it would be a waste of time trying out the theorem on the problem, but as I reminded myself of my maths teacher's words, "The top mathematicians are never afraid to take risks", I started working on the problem.

A couple of minutes later, I ended up in a dead end. Feeling deceived, I felt like quitting, but I kept my calm. Not afraid to try out another method, I tried again. This time, though, I saw the problem develop, as if I saw light in a dark cave. In joy, I kept continuing with the method until I felt something hard hit my head. It was another dead end. Frustration levels were at peak. All I wanted was time to stabilize my mind. I left the problem for now, but I couldn't really stop thinking about it, even during my sleep.

A couple of days later, I restarted. In search for a solution, I used another theorem. At long last, the answer was within sight. It felt as if I had just completed the difficult parts of my hike up Mount Everest, as if I had just discovered the source of a major epidemic. My jigsaw puzzle was almost complete. As I continued to analyze the question even further, I finally found the answer.

At a university where most students are not afraid to take risks, I hope to learn maths without boundaries of the syllabus, and participate in mathematical Olympiads and contests to sustain my long term interest in math problem solving.

This is a real first draft, because I didn't proofread in detail, so please accept any obvious mistakes. :)

It would give me a better picture of the situation if you explained why there was a timer counting down. its obviously a test but then through some twist of logic it might as well be that you time yourself for homework and are going to turn in the blank page tomorrow morning.

Your last paragraph could use some more meat, did you learn something from this? tell me what was so intellectually engaging about it.

well it definietly puts a twist on how most people do work in tests...

personally, I think you might want to reconsider and try to find something more engaging. I got rejected from stanford ea, and my intellectual thing was about my research paper, so yeah...

The timer started ticking down -- tick, tock, tick, tock. All I had was a question paper, a couple of lined papers, pencils and an eraser. As I opened the paper, I immediately read through the first question.

A couple of minutes later, I ended up at a dead end.

NOW, connect this accomplishment with your aspirations and/or intended major. If you can somehow make a connection between INSIGHT you gained from experiences such as this one and the REASONS you chose this school, that is even better!!

honestly, i find it vague, maybe its because you use the dark and cave analogy... --" it does answer the question of intellectual vitality, but it doesn't...explain a lot. Does it have a word limit? if not, i think it would be better to elaborate just a little bit more.

I thing you should elaborate a little more

Here is my draft! Please critique!!

The timer started ticking down, tick, tock, tick, tock, and all I had was a question paper, a couple of lined papers, pencils and an eraser. However, shortly after reading the first question, I felt like handing in my blank answer sheet right away, primarily because I could not instantly see a way into the question. Randomly, I picked a theorem to use. As the timer kept ticking down, I was worried whether it would be worth trying out the theorem on the problem, but as I reminded myself of my maths teacher's words, "The top mathematicians are never afraid to take risks", I started working on the problem.

...

^ Should be a little more specific as to what exactly you were doing.