I’m not sure what you mean by “a basic formal education”. Ramanujan attended Government Arts College, Kumbakonam and Pachaiyappa’s College and then he became a mathematical “researcher at the University of Madras”. About 3 years later, Ramanujan wrote his first letter to Hardy. It is certainly true that he did not have the normal formal background of a Ph.D. student, but I think he did take a number of undergraduate math classes.
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.
The title “Doctor of Philosophy” is older than calculus, though neither of its inventors, Newton and Leibniz, held it. (They had BAs though.)
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.
I’m not sure what you mean by “a basic formal education”. Ramanujan attended Government Arts College, Kumbakonam and Pachaiyappa’s College and then he became a mathematical “researcher at the University of Madras”. About 3 years later, Ramanujan wrote his first letter to Hardy. It is certainly true that he did not have the normal formal background of a Ph.D. student, but I think he did take a number of undergraduate math classes.
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.