If someone were to ask who first noticed that the world/earth was round, I'd probably direct them to a review of that bit of trivia from an encyclopedia, or textbook, or an article from an organization like APS or AIP. However, one might find different perspectives.
https://www.aps.org/publications/apsnews/200606/history.cfm
For example, consider the following statement " By around 500 B.C., most ancient Greeks believed that Earth was round, not flat. But they had no idea how big the planet is until about 240 B.C., when Eratosthenes devised a clever method of estimating its circumference.
It was around 500 B.C. that Pythagoras first proposed a spherical Earth, mainly on aesthetic grounds rather than on any physical evidence. Like many Greeks, he believed the sphere was the most perfect shape."
However, from a discussion by NASA, " It has actually been known that the Earth was round since the time of the ancient Greeks. I believe that it was Pythagoras who first proposed that the Earth was round sometime around 500 B.C. As I recall, he based his idea on the fact that he showed the Moon must be round by observing the shape of the terminator (the line between the part of the Moon in light and the part of the Moon in the dark) as it moved through its orbital cycle.
Pythagoras reasoned that if the Moon was round, then the Earth must be round as well. After that, sometime between 500 B.C. and 430 B.C., a fellow called Anaxagoras determined the true cause of solar and lunar eclipses - and then the shape of the Earth's shadow on the Moon during a lunar eclipse was also used as evidence that the Earth was round.
Around 350 BC, the great Aristotle declared that the Earth was a sphere (based on observations he made about which constellations you could see in the sky as you travelled further and further away from the equator) and during the next hundred years or so, Aristarchus and Eratosthenes actually measured the size of the Earth!"
As I recall, it was perhaps in fourth or fifth grade where we discussed the scientific method, which included ways to prove the earth was round through experimental observation, and I believe Eratosthenes was mentioned. More recent ideas were discussed since in the 1960s, NASA was sending astronauts around the earth, so the general population was made aware that the earth is round. Certainly, by 1968, we had photographic evidence from Apollo 8 that the earth was/is round
https://en.wikipedia.org/wiki/Apollo_8
https://www.nasa.gov/specials/apollo50th/missions.html