Final answer:
The Greeks made a mistake in their study and ideals of man by not conducting experiments or making observations to validate their ideas.
Step-by-step explanation:
The mistake that the Greeks made in their study and ideals of man was their approach to understanding the nature of the world. The early Greek philosophers relied on reason and logic for their studies, but they did not conduct experiments or make observations to validate their ideas. This meant that they missed out on many discoveries that could have been made through empirical evidence. For example, they dismissed Democritus' theory of atoms, which took over two millennia to be fully appreciated.