The cycle of Brilliant

When I first joined Brilliant, I was at stage 1

Stage 1) where you just go about solving problems.

But after a while, I met stage two,

Stage 2) you have to know how to solve every problem that you can't solve, and when you can't understand a solution, you ask a ton of questions.

This is probably due the the fact that I became more intune with the community and made some friends. After this, I met soooo many smart 15 year olds I hit stage 3

Stage 3). You get addicted and push yourself to solve every problem you can

This lasted a while before I hit stage 3.14

Stage $\pi$ ) you just hit the "reveal solution button" without giving the problem much thought because you want to learn and become an official math nerd and then you start using symbols such as $\pi$ in the most random places.

Finally, I hit stage 4

Stage $\dfrac{e^{\pi}-\pi}{5}$ ) you become addicted to every problem and once you solve it you begin to mull over a generalized form and the "what if they're not parallel" or "what if it's not a $monic$ polynomial" scenarios. At this point, if you solve 2 problems on Brilliant, you've probably been on for a good 2.5 hours of which you only spent 1 hr solving the actual problems and rest on different scenarios.

So my question is: how accurate is this, and what's stage $\displaystyle \sum^{\infty}_{n=0} \left(\dfrac{ 4}{5}\right)^n$ ?

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold


- bulleted
- list

bulleted
list


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

[example link](https://brilliant.org)

example link

> This is a quote

This is a quote

    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"

# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"

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}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
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
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

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}`	$\boxed{123}$

Comments

These stages sound familiar, with the exception of stage $\pi$ . I am too stubborn for my own good, so I never reveal a solution, thinking that if I just leave a problem in my brain to ferment long enough the solution will eventually reveal itself. I've got some problems that have been fermenting in there for decades.... not pretty .... so I think that your approach is much healthier in the long run.

As for stage $5$ , this is probably when you realize that there is a compartment in your brain that is working on different scenarios not just while on Brilliant, but during every waking (and sleeping) moment. When you come up with a solution in the middle of your backswing, then promptly abort the shot and write out the solution on the back of your yardage book, (or scorecard, or whatever). When you reach this stage, be concerned; intervention may be necessary. :)

Brian Charlesworth - 6 years, 5 months ago

😂😂😂, Ahhhh, you just crack me up.

Let's just hope that one of those moments doesn't happen when I'm driving 60 down a highway. There was One time where I thought of a solution in the back seat of my friend's car, and there was no paper. Luckily I had a functioning pen and relatively long arms for writing with... and on.

@Sean Ty I remember you had one of these moments while sleeping after working on your "f(x) has roots a,b,c. Find g(x) that has roots a,2b,3c"

Trevor Arashiro - 6 years, 5 months ago

Right, still remember that. Haha. Although I think I got it now.

Yeah.. Stage $\pi$ wasn't really what I do. I actually like being challenged by a problem. I just hit the button if I have no clue how to solve it.

Sean Ty - 6 years, 5 months ago

I never got to the point of writing on my arms; I'm such a neat freak that I just couldn't bring myself to do that.

And as for driving, yeah, that can be a problem. I would drive my niece to school some days and we'd often do math and physics problems the whole trip; I'm still amazed I never got into an accident.

I need to stop dawdling and wrap some presents. Have a great Christmas, and I hope you get that white board. :)

@Brian Charlesworth – Sorry for the distractions. Hope you have a wonderful Christmas as well and may your ribbons curl with ease :)

Lol, last minute gift wrapping #procrastination :P

Not exactly but yes it can be said I am in stage pi.

Whenever I see a level 4 or 5 question immediately what comes to mind is:"It is beyond my scope. I can't solve it." Then, I reveal the solutions.

Soumo Mukherjee - 6 years, 5 months ago

Well, as your name tells, you'll only find your self loving math more and more :P

Yes, you are absolutely right .

I wasn't good in Maths. Actually I hated it. It was in 11th standrd that I started liking it.

@Soumo Mukherjee – Almost like you were telling my own story!

Ha Ha

Ceesay Muhammed - 6 years, 5 months ago

@Ceesay Muhammed – Which part ? 11 th standard....?

@Soumo Mukherjee – Almost the whole sentence. Although I'm not quite sure I actually hated it. I was just so bad at it. I think I started taking it serious when I went for an entrance exam and scored 4/30 on the math theory. I was so embarrassed.

@Ceesay Muhammed – For my story...all credit goes to the teacher. the math class was like for students who were like genius. each proof, each solution just out of the blue. There wasn't any reasoning for the step. I was like 'Ok the solution is correct but how did you think the approach. Did you learn it somewhere? or is it very common to attack such kinda problem in such way and may be I don't know that. The worst part was that after scribbling cryptically on the word, only God knew and some Einsteins of the class what the heck were used to be written on the black board, the teacher used to give sum and call students to solve it on the blackboard. I was part of the crew that got punished and humiliated for not able to solve it. It was like 'just going to the board and stare it'. Whatever, that time passed.

When I was in 11, in a different school, the teacher was awesome. He taught us never to learn it by rote. To strive for simple solutions. His classes were fun. He was a Phd. One of his advice changed my whole perspective towards Math, he said 'the mathematics u learn in school isn't actual math. It isn't 5% of the math that mathematicians do. I see in everyone a future mathematician. I won't be able to teach with enthusiasm if I don't think so . You should know how to do it properly.... to do it so that u can stay in the race for a longer time...' and many things. I wasn't a 'top' student in his class. But I improved.

For stage 4, I normally finish the problem in less than an hour if it's a really difficult Fiver with a "get it over with" mentality. I do think about general cases but these thoughts usually come to mind a while after doing the problem, and often spontaneously.

Jake Lai - 6 years, 5 months ago

I am in stage 2.5

Aman Sharma - 6 years, 5 months ago

Cycle? It didnt really go back to stage 1 again?

Aloysius Ng - 6 years, 5 months ago

How can i knw the my stage on brilliant?

Ayanlaja Adebola - 6 years, 5 months ago

It's good to see that there are people like me in this world .But honestly I think I'm oscillating between stage 3 and stage 4 .

A Former Brilliant Member - 6 years, 5 months ago

I would say I'm stage 1.1.

Sometimes I struggle to understand the solutions as well

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}`	$\boxed{123}$