This is the 10428th most frequent Russian word.
великому
"Dative form of 'великий,' meaning 'to the great' or 'for the great.'"
The word "великому" here is in the dative case, describing the object of admiration.
Я восхищаюсь великому учёному.
I admire the great scientist.
"Великому" is used in the dative case to indicate intention towards a great future.
Мы стремимся к великому будущему.
We strive for a great future.
In this context, "великому" is used in the dative case to show direction of gratitude towards an artist.