Recently we have been suggested to do a polymath project. After a two hour discussion, we decided to execute the idea!!

The Polymath Project is a collaboration among mathematicians to solve mathematical problems by coordinating many mathematicians to communicate with each other. There are a lot of problems to choose from, we want your opinions about which to select.

Since this is our first project,we prefer if the project is easy( more people can take part) and it **does not** need to be an open problem. We can have alt solutions for already solved problems. Please keep in mind not to nominate very hard stuff, like the riemann hypothesis.

We will check all the problems you guys will recommend through comments, and nominate the 10 bests. We will then have a survey to determine some stuff including which nominated problems you prefer the best.

Since this thread is going to get crowded, comments with either shitty recommendations(riemann hypothesis) or comments that are substantial will get deleted.

So go ahead and recommend in the comments, see for topics that are nominated(non as of yet).

It is preferred if you join slack to take part in a project.

We want as many people as possible to see this so please do reshare.

Recommendation ends in 7th february,so make sure you dont comment after that.

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## Comments

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TopNewestStudying continued fraction expansions of e^x.

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Erdös-Szekeres Conjecture

Infinite Mersenne Primes

Magic Squares

Empty Hexagon Conjecture

I think that the more romantic of us believe the existence of a proof, as simple and elegant as Euclid's proof of infinitude of primes, to problem 2.

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The third one is a perfect beginning!

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We've already discussed it on slack. I personally don't think it's suitable as it's been attempted by many people and a few results have been published on it which makes it seem extremely difficult. You're welcome to join the discussion on slack to convince me and others otherwise though.

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I had an attempt on problem two a few weeks ago...(complete failure-> too hard!!) I like the third one a lot!!!!!Perfect for "easy".

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On Sunday I'm going to try write two notes for suggestions in detail and link them here. Loosely speaking they are this :

How many cubes can we make in an \( n \times n \times n \) cubic lattice using only integer co-ordinates for vertices of the cubes? (and similar generalisations)

Given a polyhedra, for example a cube, what is the distributions of all possible planar cross-sections? ( and similar generalisations) Or equivalently, for the case of a cube, when we take a random planar slice, what's the probability that the cross-section produces an \(n\)-gon?

As far as I know these are still open questions and have seem to be achievable. There are some awesome questions already here so I'm sure everyone can find something they're happy to work on.

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I'm afraid I do not have the time to spend on this any more.

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I recommend trying to prove some identities with Borwein integrals.

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Collatz Conjecture

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i think that this conjecture is too hard considering many mathematicians tried it and failed,but there's no harm in trying it

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I suggested it because the problem statement can be understood by a wider audience (novice to experts).

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weshouldn't work on those problems as I want us to have a high chance as possible to make progress, especially for our first time doing this. If we find ourselves solving problems and making progress, then there would be a case for us brainboxes on brilliant to tackle the tough problems. Take it one step at a time.Log in to reply

How about the Mountain Climbing Problem ?

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Xyz tree, there is a unique pattern in the solutions of the diophantine equation stating that the sum of the squares of 3 integers equals three times the product of the integers (sorry, I don't know why latex isn't working)it is sometimes called the markov diophantine equation, although it is not that famous, the pattern is fascinating, each new solution changes one number from the previous one starting at (1,1,1) then (1,1,2) and so on

there is something called the unicity conjecture which no one has proved yet (officially) you can read about it here https://en.m.wikipedia.org/wiki/Markov_number

sorry if it's too hard , I tried to think of the simplest unsolved problem I know

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I recommend an alt solution for e irrational.

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@Roberto Nicolaides you might like this

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I do indeed! I'll have a think of some nice problems and start engaging more after exams that finish 5th Feb. There are some great ideas here already, well done :)

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Can anyone please try to solve this

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The problem selection is over

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Sad.

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@Otto Bretscher Please try to help us when you have time.

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School is back in session, so, sadly, I will have only limited time to play on Brilliant. Thanks for the invite, though.

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I propose the Chain Length Problem

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Try my 150 followers problem

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We need a research problem

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Can you elaborate.

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