## You're reading: Posts Tagged: Collaborative mathematics

### The 12th Polymath project has started: resolve Rota’s basis conjecture

Timothy Chow of MIT has proposed a new Polymath project: resolve Rota’s basis conjecture.

What’s that? It’s this:

… if $B_1$, $B_2$, $\ldots$, $B_n$ are $n$ bases of an $n$-dimensional vector space $V$ (not necessarily distinct or disjoint), then there exists an $n \times n$ grid of vectors ($v_{ij}$) such that

1. the $n$ vectors in row $i$ are the members of the $i$th basis $B_i$ (in some order), and

2. in each column of the matrix, the $n$ vectors in that column form a basis of $V$.

Easy to state, but apparently hard to prove!

### Terence Tao has solved the Erdős discrepancy problem!

Terence Tao has just uploaded a preprint to the arXiv with a claimed proof of the Erdős discrepancy problem.

### Collaborative Mathematics: kids (and non-kids) work together on problems over YouTube

Jason Ermer’s Collaborative Mathematics project has launched its first video challenge. The project aims to allow mathematics to happen collaboratively via the medium of online videos, and video responses. The idea is that having watched the challenge video, you work with a group of friends (collaboratively) and post a response video, and then watch others’ response videos, and hopefully somewhere along the line mathematics will happen.