Look for your comment about my caltech essay

<p>How does scientific exploration excite and inspire you? In a page, more or less, what is it about math, science or engineering that compels you to satisfy your intellectual curiosity?</p>

<p>Unknown of science fascinates me. In Nature, numerous things are currently inexplicable. When I was in primary school, I always read some mystery books in school library for pleasure. I wondered why we could not find extraterrestrials if they really exist. The territory of natural science, especially astrophysics, is the most intriguing domain I want to explore. From the origin of universe to string theory, I have a myriad of aspects to grasp and expand.</p>

<p>Stemming from zeal for the unknown, I want to learn more. When I got into high school, it advocated test-oriented education. We kept on doing exercises rather than exploring a topic deeply. When studying calculus, we only needed to remember the basic rules of differentiation instead of understanding how they derived from. However, I was not satisfied with this pedagogy. I found out that some formulae were not too complicated to deduce as my teacher said. From searching information of calculus on internet, I could deduce them by some simple methods. For instance, with regard to the derivative of exponential function, I first needed to add an accessorial function for substitution and knew the definition of natural logarithm. Then I just made delta x tend to zero to conclude the formula. In halogenation of benzene, I asked my chemistry teacher about the specific reaction mechanism and detected the effect of some Lewis bases. As long as some puzzles are not beyond my knowledge range too far, I will attempt to solve them.</p>

<p>I even want to make innovation in science other than understanding something unknown. Cherishing the idea of creating, I cooperated with my classmate writing a thesis about high-dimensions geometry and the solution of magic cube in these dimensions with certain system and functions defined by our own. Indeed, the science’s development consists of establishing new systems and presenting new theories. Constantly, new discovery does not fit in former system and theories contradict each other. I talked about algebra with my friend on the way back from a competition. The majority of 16th century mathematicians did not admit zero and minus as numbers. For example, Pascal thought subtracting 4 from 0 was nonsense. Without minus, some calculations could not have definitions and some expressions of numbers were complicated. In the 18th century, people generally recognized zero and minus. Even so, rational numbers cannot fill all points in number axis. As early as 500 A.D., Hippasus had discovered the diagonal of a square is incommensurable with its side. The discovery of Hippasus, first unveiled defect of rational number system, proved number axis has pores which cannot be represented by rational numbers. Proven by later generations, the number of these pores is beyond counting actually. People found out that even using all real numbers, they still could not solve every algebraic equation. Equation as simple as x²+1=0 had no solution within real field. Until Gauss used “i” systematically, making a+bi named as complex number, our algebra system did not become mature. We use our current system to study only because it is convenient. So, can’t we find something beyond the contemporary system and create a more facilitated system?</p>

<p>Every comment is needed! I'll help yours in return.</p>