The idea of the earth being round first appeared in ancient Greece, and was first formulated by the great mathematician and philosopher Eratosthenes, who was able to estimate the diameter of the earth. In 200 BC, travelers told the head of the Alexandria Library, Eratosthenes, about a well near present-day Aswan. The bottom of the well was lit by the sun at noon during the summer solstice. At that moment the sun was straight overhead. Eratosthenes realized he could measure the shadow cast by a tower in Alexandria while no shadow was being cast in Aswan. Then, knowing the distance to Aswan, it'd be simple to calculate Earth's radius. Greeks also believed, in fact, that the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony, defined by another mathematician, Pythagoras, as “the harmony of spheres”. This, although it was accepted by scientists at that time, did not become generally recognized in the popular domain. For many centuries, humans believed that the earth was flat. Even religions, such as Christianity, accepted the popular credence that our planet was completely flat. They believed for instance that ships that crossed the straits of Gibraltar, then called Pillars of Hercules, would fall into space as waters ended after it. Other explorers, inspired by the great geographer Ptolemy (who himself derived his theories from Arab scientists), started to believe that the earth was in fact round. Among them, Christopher Columbus, a Genovese explorer, convinced others that navigation was possible through the Pillars of Hercules and ships could reach the Asian continent by sailing Westward instead than Eastward.
These theories were disputed by the knowledge of the time, as well as by the Church, which thought that this credence would undermine the centrality of the earth and the human race. Another belief disputed by the Church was, once established that the earth was round, whether the sun was rotating around it or the earth was in fact rotating around the sun, together with the other planets of the system.
This idea was defended by the astronomer Galileo Galilei. Galileo used his telescope to observe the sun. He discovered sunspots that drifted from one side of the sun's disc to the other. He theorized that the movement must be due to the rotation of the sun, thus contradicting the belief that the earth rotated around the sun.
Galileo inspired his theories to another great scientist of the time, Copernicus, but his ideas were controversial within his lifetime, when a large majority of philosophers and astronomers still accepted the geocentric view that the Earth is at the centre of the universe. When Galileo publicly supported the heliocentric view, which placed the Sun at the centre of the universe, he met with opposition from many philosophers and clerics. Some even denounced him to the Roman Inquisition. Galileo was then tried by the Inquisition, accused of "heresy", forced to deny his findings, and spent the rest of his life under house arrest.
Scientific discoveries of the following centuries demonstrated not only that the earth was round, but also that the theories of Galileo were exact. Men like him or like the Greek mathematicians progressively changed the way humans thought about themselves and their place in the universe. The trial of Galileo resulted in a triumph for science and for freedom of thought. Galileo is now considered the father of modern science.
Sources.
Minerva, nuova enciclopedia universale.1985, Zenith Editrice,S.R.L.Milano.
Galileo Galilei, Wikipedia free encyclopedia.2010. http://en.wikipedia.org/wiki/Galileo_Galilei