Real-time collaboration makes writing publications with peers very easy. Great compile time to preview the PDF. Great integration with bibtex for easy citations.

Obviously, this is a great platform for writing up mathematical documents and allowing multiple people to access a given document.

ShareLaTeX has made doing math assignments so much easier. It is efficient and uses suggestions while programming, good for anyone beginning to write formal papers because of its simple to understand user interface, and prints beautifully.