Well, it's a really superficial explanation.

In a broader sense, the advent of settled society is what allowed populations to begin making advances into science and more esoteric fields. Agriculture (as opposed to hunter-gatherer systems) allowed for a surplus of food. This allowed portions of the population to concern themselves with roles other than food production - black smithing, writing, political organization and about anything else you could think of.

So it's more appropriate to way that the advent of organized society gave people the opportunity to focus on things other than survival because society had evolved to the point where they didn't every member to be involved in cultivating food, or protecting against aggressors. Was slavery a component of this? Sure. But slavery is just a component - the true culprit is advanced, organized civilization gave Greeks (among other peoples) the opportunity to have members of those societies time to think about philosophy, mathematics, and all the rest.

Anyways, I didn't hear the professor's comment or its context personally. But on its surface it seems like a very shallow thing to say.

Posted from my phone so forgive any strange wording from autocorrect

This question makes me wonder if we can know that the Greeks themselves were better at math than their contemporaries or if history has painted them as such due to the interest in preserving Greek intellectual materials that began with the Romans.