His contributions to trigonometry are especially important. For instance, Ptolemy’s table of the lengths of chords in a circle is the earliest surviving table of a trigonometric function. (britannica.com/biography/Ptolemy)
His biggest contribution to mathematics is in the area of abstract algebra called Galois Theory. "Galois Theory uncovers a relationship between the structure of groups and the structure of fields. It then uses this relationship to describe how the roots of a polynomial relate to one another." (https://www.math3ma.com/blog/what-is-galois-theory-anyway).
Hardy was an English pure mathematician whose work revolved around number theory. For example, he contributed fundamentally to the Riemann zeta function and the distribution of primes. However, when asked what his greatest contribution to math was, he said it was discovering Ramanujan. Image: (https://www.pinterest.ca/pin/284993482650246754/).