I had a Rebbe who is one of the gedolei hador, and he was completely ambidextrous. He would often write a sentence on the board with one hand, and when he got to the middle of the board, he would switch hands and finish the other half.
He has written numerous sefarim on shas and chiddushei Torah.
I believe I later had a math professor who was similar, and also a complete genius. I concluded that some very bright people are ambidextrous.