We will be featuring different members of the Brilliant community, so that you can get to know them better. For the second issue, we are featuring Daniel Liu.

The community loved this problem of Daniel's. Be warned! It is not for the faint of heart! You can also click through the other problems in his set, and challenge yourself even more.

When writing up this solution to finding the minimum value of \( \sqrt{ (a^2+1)(b^2+1)(c^2+1) } \) subject to \( a+b+c = abc \), Daniel explained the importance of recognizing the trigonometric substitution which greatly simplified the working

**1) Tell us more about yourself.**

I am a high school freshman who loves to make math problems as a hobby. In addition to making and solving problems, I also like to practice skill games like juggling, Diabolo and Rubik's Cube. I also enjoy playing the piano, and have been playing for 9 years. Finally, I enjoy playing video games especially first person shooters and online multiplayer games.

**2) What is one fun fact about yourself that the Brilliant community doesn't know about?**

I am a Guinness World Record holder, along with 324 other Mathletes, parents and staff who participated in the World Record attempt of fastest human formation of the first 25 rows of Pascal's Triangle in the 30th anniversary of the National Mathcounts Competition.

**3) What do you want to accomplish in the next few years?**

In the next few years, I wish to affect the entire Mathematical Community through a new discovery. I have already tried to do so with the Generalized Reverse Rearrangement Inequality, and I am hoping I will be able to find enough Olympiad problems solvable with this inequality that it will become credible.

**4) What do you wish for Brilliant?**

I wish that Brilliant.org can become one of the most used sources as a means of practicing for math tests and competitions (i.e AoPS), like the MAA or JEE test series. In addition to competition, I wish that Brilliant.org will also be a means of creating and sharing new ideas and concepts (i.e MSE) through the community interactions. Finally, I wish that Brilliant.org will also serve as a place for people who are struggling with math to review and learn the concepts and maybe even start to like math (i.e Khan Academy). Seeing that Brilliant.org is already heading towards this path is exciting to me.

## Comments

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TopNewestHey, thanks for featuring me! \(\stackrel{\wedge\,\wedge}{\smile}\) – Daniel Liu · 1 year, 9 months ago

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– Prasun Biswas · 1 year, 9 months ago

Why do all the 14-15 year olds on Brilliant look older and cooler than me? I cri evrytim. ._.Log in to reply

– Daniel Liu · 1 year, 9 months ago

Probably because I put in the swag glasses B)Log in to reply

– Bryan Lee Shi Yang · 1 year, 9 months ago

Maybe using Minecraft?Log in to reply

– Prasun Biswas · 1 year, 9 months ago

Sounds legit.Log in to reply

– Margaret Zheng · 1 year ago

I feel the same way...XXDLog in to reply

– Nihar Mahajan · 1 year, 9 months ago

Woah! You are a Guinness World Record holder , I didn't know that. Congratulations!Log in to reply

– Chinmay Sangawadekar · 1 year, 9 months ago

Congratulations Daniel you are really a MathWizard .Log in to reply

– Arulx Z · 1 year, 9 months ago

Oops. Calvin Lin mentioned the answer to the question by you on the note :pLog in to reply

– Jake Lai · 1 year, 9 months ago

nya~Log in to reply

– Daniel Liu · 1 year, 9 months ago

nya~Log in to reply

Cyclic Squares!– Swapnil Das · 1 year, 9 months agoLog in to reply

@Daniel Liu : A world record holder! Congratulations!

How many olympiads have you qualified for? Any plans for the IMO?

P.s. You were worth being featured! – Sualeh Asif · 1 year, 9 months ago

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– Zain Ahmed Sharif · 1 year, 9 months ago

u r 15??Log in to reply

– Mardokay Mosazghi · 1 year, 9 months ago

Congrats amazing!!Log in to reply

– Shivamani Patil · 1 year, 9 months ago

You are really awesome and genius!Log in to reply

@Daniel Liu What's your t-shirt actually mean? I mean why only the "TI" are in a different font size, color etc. I didn't get that.

*Only for those who know Hindi - Is it a "tai" function? – Kartik Sharma · 1 year, 9 months ago

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– Daniel Liu · 1 year, 9 months ago

The TI in MathemaTIcian stands for Texas Instruments, a calculator-creating company.Log in to reply

– Ishan Dasgupta Samarendra · 1 year, 9 months ago

Oh, I thought it was \(\pi\)! It does look a bit like that.Log in to reply

– Kartik Sharma · 1 year, 9 months ago

Oh! Nice! BTW, congrats! You are really an inspiration to all of us.Log in to reply

– Pankaj Joshi · 1 year, 9 months ago

It looked like a 'pi' to me...Log in to reply

I am proud to be associated with such an outstanding fellow math-lover in Brilliant.org. I am glad to you better. Keep up the good work. – Chew-Seong Cheong · 1 year, 9 months ago

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Congratulations and my best wishes. I always feel very very happy to see teen agers doing so good in maths. I have learnt from many problems by Daniel Liu . – Niranjan Khanderia · 1 year, 9 months ago

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– Will-i-am Guo · 1 year, 9 months ago

I'm glad you're still learning at age 87.Log in to reply

The best of all~ I salute you! – Bryan Lee Shi Yang · 1 year, 9 months ago

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^^ I'm so glad to have found people such as yourself. What/who inspires you the most, and uh perhaps... how? =) And... Pascal's triangle... Liuminati confirmed. :P – Vishnuram Leonardodavinci · 1 year, 9 months ago

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Ah.. congrats @Daniel Liu ... You've made great achievements in such an age. I can hardly imagine what you'll be capable of doing in the coming future... and yes I want to thank sir @Calvin Lin to make us aware that we have such a beautiful young mind among the brilliant community...

I've sent you a request on Facebook Daniel 'cause I'd love to use your company. ^_^ – Rishabh Tripathi · 1 year, 9 months ago

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– Daniel Liu · 1 year, 9 months ago

Added. Thanks!Log in to reply

Great job Daniel!

Have you noticed that the level 5 problem which you provided solution to has dropped to level 3. The problem looks equally hard to me but posting the answer to the question itself on the post is probably a bad idea :p – Arulx Z · 1 year, 2 months ago

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What will you say about Indian teenagers of Brilliant. org – Sumanth Cv · 1 year, 9 months ago

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– Niranjan Khanderia · 1 year, 9 months ago

I have noted that even teen-agers from other countries are equally smart. Naturally, with big population and knowledge of English make it easy for Indians. Even otherwise, Indians are more interested in math. Please look to this as "todays teens are really smart irrespective of country". We should feel more like a brotherhood of math and science through out the world. For those not knowing English brilliant would not be that smooth.Log in to reply

First of all congratulations for your achievements in this field. And I hope you will succeed in your journey to become mathematician. If you want some help for invention then we all ready for it just keep it on! – Dipak Prajapati · 1 year, 9 months ago

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Genius. – Kushagra Sahni · 1 year, 9 months ago

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@Daniel Liu , I salute you. First, You are a Guinness record holder. _/_ Congrats on that. I have been a subscriber of Cyclic Squares, And Trust me, You are the one guy who has always been an inspiration to me. :)

P.S. Do you mind accepting my Facebook friend request? :P It would be great to be friends with a genius ;) – Mehul Arora · 1 year, 9 months ago

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– Rajdeep Dhingra · 1 year, 9 months ago

Can U tell me what is Cyclic Squares.Log in to reply

@Daniel Liu . He solves problems of different topics and levels there. It's great! :D – Mehul Arora · 1 year, 9 months ago

Cyclic Squares is a youtube channel started by our very own Genius, MrLog in to reply

– Nihar Mahajan · 1 year, 9 months ago

Yeah , its very nice , I saw some of them :)Log in to reply

– Daniel Liu · 1 year, 9 months ago

Thanks! And done.Log in to reply

– Mehul Arora · 1 year, 9 months ago

Hahahahaha, Thanks ! :DLog in to reply

wow! you are a genius! n a Guinness World Record holder! awesome! congratulations and keep up the good work :) – Lipsa Kar · 1 year, 6 months ago

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What is your fastest time with the cube? I did in 14 seconds and it wasn't a lucky solve. Haven't picked it up in a couple years though. – Vishnu C · 1 year, 8 months ago

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– Arulx Z · 1 year, 8 months ago

18 secs. I got a PLL skip. My friend once got PLL + OLL skip and managed to solve the cube in 9 secs.Log in to reply

I was already doing 18-17 secs regularly. I used to do it in 16 secs like once in 5 solves. But improvement became really hard. I was stuck on the same level for around 2 months! Then I heard that look-ahead F2L was the key. So I had to give it up anyway, so that I could slow down. I got a lubix Gu-Hong becuase it was supposed to be slower than the Zanchi that I was using at the time and it was using the Gu-Hong that I got my 14 second solve. Look-ahead F2L is the next step man! Slow down to speed up! – Vishnu C · 1 year, 8 months ago

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– Arulx Z · 1 year, 2 months ago

Nice! Try solving the cube blind-folded. It really gives some good intuition and will really help to improve look ahead method.Log in to reply

Hey , can you help me with this @https://brilliant.org/discussions/thread/you-think-you-know-polynomialshuh/?ref_id=822405 – Raven Herd · 1 year, 9 months ago

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Great Job. :) – Llewellyn Sterling · 1 year, 9 months ago

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Wow, I just checked out Cyclic Squares, it is a wonderful channel. – Edgar Wang · 1 year, 9 months ago

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Congratulations Daniel !! I find your problems highly creative in the sense that they never lose their level of genuinity. They need one's willpower faculty surrendered. Keep posting them and keep illuminating the community. :) – Sanjeet Raria · 1 year, 9 months ago

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I had a very straightforward conclusion, which states that someone who is experted in mathematics mostly play online games. I should follow the path :v @Daniel Liu I was extremely jealous on you @Daniel Liu – Figel Ilham · 1 year, 9 months ago

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Congrats Mr Genius – Rajdeep Dhingra · 1 year, 9 months ago

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Congrats men – John Aries Sarza · 1 year, 9 months ago

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Congrats, hats off , is the best thing ever in every body's life – Suprem S.Nalkund · 1 year, 9 months ago

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It's very lucky to be a Guinness world record holder! Congrats on that!

Also the picture of yours is cool.The edits have made it look better! – Sravanth Chebrolu · 1 year, 9 months ago

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Big Bang Congrats! We are waiting for your extraordinary revolutionary theories in Mathematics. – Siddharth Singh · 1 year, 9 months ago

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You are my inspiration – Sumanth Cv · 1 year, 9 months ago

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– Daniel Liu · 1 year, 9 months ago

Aw, shucks ^_^Log in to reply

– Swapnil Das · 1 year, 9 months ago

Well what do you really want to become?Log in to reply

– Daniel Liu · 1 year, 9 months ago

A mathematician is great! You might have misunderstood my reply; it just means "thanks" in a sort of modest way.Log in to reply

– Swapnil Das · 1 year, 9 months ago

I really understood it. Oh.. :( , Why isn't the google loading!Log in to reply

Evaluate the \(n^{th}\) root of unity of the mouth below:

\[\huge ( :3 )^\infty\] – Nihar Mahajan · 1 year, 9 months ago

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@Nihar Mahajan That's probably too much xD

7 downvotes xD – Mehul Arora · 1 year, 9 months ago

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– Nihar Mahajan · 1 year, 9 months ago

Even I downvoted myself :P :PLog in to reply

– Swapnil Das · 1 year, 2 months ago

26 to be more precise. Nihar, thank me, the second upvote is from me.Log in to reply

– Mardokay Mosazghi · 1 year, 9 months ago

to precise 17++ down votes.Log in to reply