You are right https://en.wikipedia.org/wiki/Doctor_of_Philosophy
The term appeared after 1652 in Germany, although Doctorates existed before that but these were used interchangeably for Masters Degree.
University education in India for pure sciences is 3 yrs for an undergraduate course, so even if he attended any college he would taken up courses only for the first year. Once he failed his exams in the first yr he cannot continue the education and study second and third yr courses in mathematics, which is why i think he was probably an autodidact in mathematics.
There was a mathematician called Ramanujan, https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
He did some ground breaking work in Number theory and he didn't even have basic formal education.
Same applies to Issac Newton, He invented calculus at least 200 yrs before the term PhD was Invented.