Featured member - Alan Enrique Ontiveros Salazar

We will be featuring different members of the Brilliant community, so that you can get to know them better. For the tenth issue, we are featuring Alan Enrique Ontiveros Salazar, who despite only discovering his love of mathematics late, has developed greatly in the past 3 years.

Alan has posted more than 50 problems, and he has produced numerous gems. Two of this problems that I like ask you to solve a system of equations. They are Tricky system and Newton's Sum, and you can view them here:

$\begin{array} { l l c | c l l } a^2 + b^2 + \sqrt{3} ab & = 727 & \quad \quad & \quad \quad & x + y + z & = 3 \\ a^2 + c^2 + \sqrt{3} ac & = 829 & & & x^3 + y^3 + z^3 & = 15 \\ b^2 + c^2 - bc & = 39 & & & x^4 + y^4 + z^4 & = 35 \\ \end{array} \\$

He has posted nearly 200 solutions (oh wow!). I enjoy reading them, as they often offer a deeper insight into understanding the problem, and present the motivation for considering such an approach. Check out Incremental Complex Products, where you have to solve:

$\begin{array} { l l l } (a+1)(b+1)(c+1) & = & 1 \\ (a+2)(b+2)(c+2) & = & 2\\ (a+3)(b+3)(c+3) & = & 3\\ (a+4)(b+4)(c+4) & = & ? \end{array}$

Tell us more about yourself.
Well, I am just another guy who loves math and all its applications. I'm 16 now, almost 17. Apart from math, I play tennis and go swimming. I am a little introvert, even though I always have a topic to talk about. I speak Spanish and English, which I'm learning principally through my activity on Brilliant.
I learnt to program as a child, when I thought that I broke my computer and tried to fix it. The games that I used to play didn't open, and in the process of poking around, I reached the point where I was doing small programs in HTML and Visual Basic, and have grown to love programming.
I'm from Mexico, one of the most interesting and rich countries around the world. Unfortunately, most people here hate maths. Everything I know about maths I learnt since 2011. Before then, I didn't know anything about it. I realized that I had a powerful tool to solve other types of problems, and my love for mathematics developed from there. Since then, I've been challenging myself at algebra, then at geometry, and more recently in Calculus. At the start, I used the internet to solve my doubts. When I joined Brilliant, I got to know many fantastic people, and I learnt how to present my solutions formally (and even improve my English).

What would you recommend for someone who is new to learning math?
First, get rid of stereotypes that people believe about math. It is not true that only certain people can be good at math, or that math is very difficult and useless.
Second, practice math as a way to exercise your brain and get smarter in many aspects of daily life. If you focus only on "What is it for? How am I gonna use it in my life?", then you will not learn enough for it to become useful.
Third, Math is not about memorization of complicated and long formulas. Unfortunately, the way that schools teach math is the reason why most people hate math. Math is actually very beautiful, and you should explore it for fun. Fourth, if you want to improve, try problems that are slightly more difficult than you are used to. Be creative, explore new ways and ask around for help. Also, you can read articles on the internet, and find communities (like Brilliant) where people share their love for math.
Finally, do not be intimidated by people who can solve very hard problems that seem impossible to you. They spent their time developing their skills, and you do not know how much effort they have put in. Even I don't know many things, and everyone has to go through this process of learning.

What were the greatest lessons that you learnt?
I have 7 notebooks which record down various work that I have done, and what I have learnt from it. Let me share some of what challenged me (at that point in time).

When I first saw the general formula for the quadratics, I tried to do the same with cubics. I had no success initially, so I looked it up on the internet. I saw a very ugly formula, and then looked at the process of how to solve it, and I finally found a better method / solution. I next did it with quartics, and was again successful, which made me happy. I then tried it with quintics (without knowing that it was impossible), and obviously had no success. Then, I found a theorem and started reading about it.
I like to make short algorithms for simple tasks. One day, when I was studying a way to interpolate a polynomial given its initial values, I discovered an algorithm that could do this! It took me one afternoon to code it up. After I joined Brilliant, I learnt that it was the Method of Differences, and was very proud of myself.
It requires a lot of hard work to improve. You have to be willing to struggle and think for yourself, and even accept it when things do not go well at times. Constantly put in the effort to improve, and you will develop over time.

What do you want to accomplish in the next few years?
I am in 12th grade, which is the 5th semester of Preparatoria in Mexico. My school is Instituto Politécnico Nacional (IPN), one of the best high schools in Mexico. I'm currently studying a technical speciality about computer networks, in CET 1, which is one of the 17 high schools of IPN. In one year I'll be finishing high school. Then, I'll go to ESCOM (also a school of IPN) to study computer engineering. That will last 4 years, and I plan to find a job while studying. After that, I'd like to create my own company about technology, and innovate in some aspects.
For now I've developed some projects, like a website that is like Wolfram Alpha (but less advanced), and a music searcher.

What do you wish for Brilliant?

First I'd like that it would be also in Spanish, because most people who doesn't speak English but likes math wouldn't be able to participate here, in this great community.
Second, I hope that this community grows up everyday faster, because, for example, I was looking for a website around 2013 where I could find harder challenges about math, but I didn't find Brilliant until December 2013.
Finally, I just want to thank you all for making this place a great community where I can talk with people with the same interests of me, learn from others and teach what I know.

Markdown	Appears as
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`bold` or `__bold__`	bold
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1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Featured member - Alan Enrique Ontiveros Salazar

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