Neither a riddle nor a logical problem but i challenge you to it nonetheless:
Firstly, mathematically prove that 1 + 1 = 2
That took a team of geniuses about 20 years to do!

Secondly, scientifically prove that you exist.
EDIT: Prove it to me, not to yourself. Proving it to yourself is easy, you know you exist because you think.
Good luck
