Possibly a good question for number theory (3), also one of the most up voted questions on Overflow:

[Polynomial Bijection from $\mathbb{Q}\times \mathbb{Q}\rightarrow{}\mathbb{Q}$][1]


  [1]: https://mathoverflow.net/questions/21003/polynomial-bijection-from-mathbb-q-times-mathbb-q-to-mathbb-q