Indeed, fasting the blessed month of Ramadan is an individual obligation for those who are capable of fasting. Allah Almighty says: (O ye who believe! Fasting is prescribed for you, even as it was prescribed for those before you, that ye may ward off evil.) (Al-Baqarah 2:183)
Sheikh Muhammad IqbalNadvi, Imam of Calgary Mosque, Canada, and Former Professor at King Saud Univ., Saudi Arabia, states the following: Islamically, we need to understand that we should follow the lunar calendar and it starts with the moon sighting. The Prophet (peace and blessings be upon him) is reported to have said: “Fast when you see it (the new moon) and break your fast when you see it.”
So, the moon sighting is the basis for the beginning and the end of the month. Now we have one opinion that says that the moon is sighted in each area, just as `Abdullah Ibn `Abbas explained that in his time Mu`awiyah started fasting in Damascus on Saturday and in Madinah they started fasting on Friday. So he said they each follow their own sighting. And of course, we have another opinion, which emphasizes on going with one single moon sighting for all Muslims all over the world. My own understanding is that neither of the two opinions is wrong as long as they are based on strong evidence from the Sunnah.
However, I have reservation related to the math calculations because, Islamically, the calculation should support the moon sighting and not be used as exclusive evidence, which means that such calculations tell us when to look for the new moon. So, if we announce the start of Ramadan based on the moon sighting, it will be the best option.