Is it haraam to celebrate Prophet Muhammad's birthday?

It is a Bida'at (innovation-new tradition) not found in the life of the Prophet (SAW) nor during the period of Sahaba rau nor during two more generaions (called Khair ul Qaroon-better periods). More over, the way it is celebrated is un-Islamic. Islam teaches to celebrate Eids by paying thanks to Almighty Allah and praying to Him. Hazrat Muhammad (SAW) died on 12th Rabi-al-Awal. He was born on 8th or 9th Rabi-al-Awal. !2th is his date of death, not of birth.