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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).

  1. 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.

  2. 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.

  3. 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.

Note by Calvin Lin
1 year, 1 month ago

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@Alan Enrique Ontiveros Salazar Congrats for being featured! You are probably the one of the guys having the longest names on Brilliant (may be in the world too! :P). Your methods , solutions are quite innovative and I love them. Its quite awesome that inspite of having a math-hating background , you managed to progress so much in maths! Finally I got to see the face of such wonderful talent! :) Nihar Mahajan · 1 year, 1 month ago

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@Nihar Mahajan Oh, thanks :) I also appreciate your working here, in a short time you have contributed with many wonderful problems and solutions, and I wish I could be more active in this days, because of school. Also, the names here in Mexico are as long as mine, or even more :D Alan Enrique Ontiveros Salazar · 1 year, 1 month ago

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@Nihar Mahajan You seems to be fond of watching different faces..with the irony you have setup dp of someone else..!! Akhil Bansal · 1 year, 1 month ago

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@Akhil Bansal Lol , you want to see my face? Nihar Mahajan · 1 year, 1 month ago

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@Nihar Mahajan I want you to be featured Dev Sharma · 1 year, 1 month ago

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@Nihar Mahajan Yeah I wanna see your face! Lakshya Sinha · 1 year, 1 month ago

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Your resonate with me a lot. I too found my love for math pretty late. I also grew up surrounded by practical-minded people, meaning that they only care about whether something they learn would be used in the future(I actually have a lot to say about this topic, but I don't want to spew such a rant here). Xuming Liang · 1 year, 1 month ago

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@Xuming Liang I can let you rant in a "Featured Member" post. Interested? Calvin Lin Staff · 1 year, 1 month ago

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@Xuming Liang Yes, that is very common in my country. It is not bad to try to find practical uses for every thing we learn, but if we don't find that utility, we simply don't learn it. Alan Enrique Ontiveros Salazar · 1 year, 1 month ago

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Congratulation!!!!! Shivamani Patil · 1 year, 1 month ago

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Congrats @Alan Enrique Ontiveros Salazar !!

I am also surrounded with many "practical minded" people.... In my school maths is taught just for scoring marks..... Harsh Shrivastava · 1 year, 1 month ago

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Yeah waited for Alan to be featured! Aditya Kumar · 1 year, 1 month ago

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Congrats for being featured ... When I read your name I do remember Salazar Slytherin :P I love your solutions . You posses a Beautiful Mind..... Chinmay Sangawadekar · 1 year, 1 month ago

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Hi, Alan ! You're so great in the photo . Great to see you featured ! Anish Harsha · 1 year, 1 month ago

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Congrats ! for being featured and yes does your name mean anything in particular? Raven Herd · 1 year ago

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Congratulations! Rohit Udaiwal · 1 year, 1 month ago

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@Alan Enrique Ontiveros Salazar I was waiting for many days for you to get featured. You solved most of my Level 5 Problems. You are awesome!! Congrats for being featured. Surya Prakash · 1 year, 1 month ago

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Congratulations Dev Sharma · 1 year, 1 month ago

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Congratulations on being featured! :D Mehul Arora · 1 year, 1 month ago

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@Alan Enrique Ontiveros Salazar , Hello sir and congrats on being featured, first of all I thought you were a kid about my age! but its really good to have a nearly adult like you on brilliant, so everyone could understand. Lakshya Sinha · 1 year, 1 month ago

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Congratulations Alan for being featured Atul Shivam · 1 year, 1 month ago

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