I'm living in the west and my question is does prophet Muhammad really exist. Why some historians doubt the existence of prophet Muhammad, and also there is also a man called Robert spencer who wrote a book about prophet Muhammad didn't exist

1- Yes, a few modern historians have disputed whether he existed or not. However, the vast majority of western historians (over 98%) accept that Muhammad was a real figure who existed in 6th/7th century Arabia.

2- Prophet Muhammad is the only prophet who can be traced historically. Tracing previous prophets, even Jesus, is very difficult or nearly impossible. That’s why we rely on the Qur’an (and we have evidence it’s a divine text) to know about previous prophets.

3- One way to know the Prophet Muhammad existed is through the thousands of reports of his companions. When you have thousands of reports, you gain confidence that what’s being reported is true. It’s naturally impossible for those hundreds of thousands of companions, who came from different backgrounds and many of them didn’t know each other, to collaborate and fabricate the idea that this man existed. Some of the Prophet’s speeches, such as the Ghadeer speech, was attended by over 100,000 people. Many of these companions wrote about these experiences. While most texts did not survive history, many (hundreds) did. They are in Arabic, of course. And many of them can be historically verified.

4- The Prophet sent letters to various rulers and kings. Some of those letters have been preserved and can be historically verified (most cannot be verified independently outside of Muslim sources, but some can. Dr. Sel Harris, a professor in Virginia, has written about those letters and how they have been historically verified).

5- A few decades after the Prophet, his name appears on coins. That’s when the Muslims stopped using Byzantine coins and made their own. There were hundreds of thousands, if not millions of Muslims, during that time. Some of them had met the Prophet. We don’t see a single record of one of them disputing this figure. His existence was so widely established that no one challenged it. Had he been a fake personality, some would have at least challenged it.

6- There are parts of the Qur’an that have been analyzed by Birmingham University in the UK using carbon dating, and they were able to trace those pages back to the era of the Prophet. This proves that there were manuscripts that mentioned Muhammad in that era (and it’s not the case that we only have later records of his existence).

https://www.bbc.com/news/business-33436021

7- Read this article. It’s neutral, it’s not based on Muslim bias. It presents arguments for and against. But overall, many points can be used to verify existence (though some points can be disputed by some historians).

https://m.ranker.com/list/evidence-of-muhammad/genevieve-carlton