How did the battle of thermopylae change history?

Answer 1

The Battle of Thermopylae was a defeat for the Greeks and therefore had no major influence on history. It merely held up the Persian advance for a while and provided a romantic image of military bravery for people in the future to look back upon.

The Battle of Marathon and the Battle of Salamis were much more important. These were the battles that, unlike Thermopylae, defeated the Persian invasions of Greece and secured the freedom of the Greek city states.

Since the Greek city states were the basis of European civilization, historically, it was important they remained free or the entire history of the world from then on would have been quite different!