People from early antiquity generally believed the world was flat, but by the time of Pliny the Elder (1st century) its spherical shape was generally acknowledged. At that time Ptolemy derived his maps from a curved globe and developed the system of latitude and longitude. His writings remained the basis of European astronomy throughout the Middle Ages.
Between the fall of the Roman Empire and the renaissance of science several centuries later, some Christian writers questioned and even opposed Earth's sphericity, although it is not clearly known how influential their views were. Even before the Renaissance began, the flat Earth theory had almost died out; with the astrolabe, arab astronomy reached Europe in the 11th century, and by the 1100s at the latest, the geocentric model had supplanted it in the minds of the learned people of Europe.
Belief in a flat Earth is found in humankind's oldest writings. In early Mesopotamian thought the world was portrayed as a flat disk floating in the ocean, and this forms the premise for early Greek maps like those of Anaximander and Hecataeus.
By classical times an alternate idea, that Earth was spherical, had appeared. This was espoused by Pythagoras apparently on aesthetic grounds, as he also held all other celestial bodies to be spherical. Aristotle provided physical evidence for the spherical Earth:
- Ships actually recede over the horizon, disappearing hull-first. In a flat-earth model, they should simply get smaller and smaller until no longer visible.
- Travelers going south see southern constellations rise higher above the horizon. This is only possible if their "straight up" direction is at an angle to northerners' "straight up". Thus the Earth's surface cannot be flat.
- The border of the shadow of Earth on the Moon during the partial phase of a lunar eclipse is always circular, no matter how high the Moon is over the horizon. Only a sphere casts a circular shadow in every direction, a circular disk casts an elliptical shadow in most directions.
Earth's circumference was estimated around 240 BC by Eratosthenes, who knew about Syene (now Aswan) in Egypt where the sun was directly overhead at the summer solstice and used geometry to come up with a circumference of 250,000 stades, which, assuming that our estimates of the unit stadia is accurate, is within 2% of the modern value of 40,070 kilometers.
One popular belief is that, after the downfall of the Roman Empire, the knowledge of the spherical Earth was lost, and people believed in a flat Earth again. The extent to which this is true is disputed.
It is certain that several Christian writers explicitly argued against the spherical Earth. Lactantius (245-325) calls it "folly" because people on a sphere would fall down; Saint Cyril of Jerusalem (315-386) saw Earth as a firmament floating on water; Saint John Chrysostom (344-408) saw a spherical Earth as contradictory to scripture; Severian, Bishop of Gabala (d. 408) and Diodorus of Tarsus (d. 394) argued for a flat Earth; and Cosmas Indicopleustes (547) called Earth "a parallelogram, flat, and surrounded by four seas" in his Christian Topography, where the Covenant Ark was meant to represent the whole universe. There are relatively few historical records of the period between 600 and 1000 for either spherical or flat-Earth thinking (owning to the general scarcity of records from that time). Saint Basil (329-379) argued that knowledge about Earth's shape was irrelevant.
It is unclear how influential these writers were. Different historians have argued either for very high (e.g. Andrew Dickson White) or very low (e.g. Jeffrey Russell ) influence. Russell, a Christian scholar at Santa Barbara whose main contribution to historical scholarship is a series of books on the history of concepts of evil and ideas of Satan, explored the issue in Inventing the Flat Earth: Columbus and Modern Historians. Russell claims that the Flat Earth theory is a myth used to impugn pre-modern civilization, especially that of the Middle Ages in Europe.
One critical part of this dispute is the belief in antipodes, that is, people living on the opposite side of Earth, with their feet faced against ours. Even some of the most important medieval scholars like Saint Augustine (354-430) argued against antipodes and called them a "fable". However, Augustine explicitly pointed out that the belief in a spherical Earth did not directly imply a belief in antipodes:
- "Those who affirm [a belief in antipodes] do not claim to possess any actual information; they merely conjecture that, since the Earth is suspended within the concavity of the heavens, and there is as much room on the one side of it as on the other, therefore the part which is beneath cannot be void of human inhabitants. They fail to notice that, even should it be believed or demonstrated that the world is round or spherical in form, it does not follow that the part of the Earth opposite to us is not completely covered with water, or that any conjectured dry land there should be inhabited by men. For Scripture, which confirms the truth of its historical statements by the accomplishment of its prophecies, teaches not falsehood; and it is too absurd to say that some men might have set sail from this side and, traversing the immense expanse of ocean, have propagated there a race of human beings descended from that one first man." (De Civitate Dei, xvi, 9)
The phrase "even should it be believed or demonstrated that the world is round" indicates that this was certainly not the consensus of the time, and possibly not even believed by Augustine. This is in clear contrast to the pre-Christian period. Procopius of Gaza (491-518) argued that "if there be men on the other side of the Earth, Christ must have gone there and suffered a second time to save them; and therefore there must have been, as necessary preliminaries to his coming, a duplicate Adam, Eden, serpent, and Deluge!" Saint Boniface (d. 755) accused Vergilius (d. 784) of "teaching a doctrine in regard to the rotundity of the Earth, which was 'contrary to the Scriptures.'" (Catholic Encyclopedia). Pope Zacharias decided that "if it be proved that he held the said doctrine, a council be held, and Vergilius expelled from the Church and deprived of his priestly dignity." Vergilius believed "that beneath the Earth there was another world and other men, another Sun and Moon."
The primitive level of medieval cartography also makes it difficult to estimate the degree of flat-Earth thinking. The question whether average people in the Middle Ages believed in a flat Earth may yet be completely separate from the surviving manuscripts, given the low literacy of the time and the fact that it was probably the priests in the churches, not the few noted theologians, who defined public opinion on the matter. In learned circles, the sperical shape of the earth was well established by the 11th century. Hermannus Contractus is among the earliest christian scholars to estimate the circumference of the earth with Eratosthenes' method.
As of the beginning of the 21st Century CE, there remain populations within rural cultures which, unexposed to technological civilisation, consider the world to be flat. With no long-distance communication requirements or other technological endeavours, their beliefs appear to suffice.
From a European perspective, Portuguese exploration of Africa and Asia in the 15th century removed any serious doubts, and Magellan and Drake's circumnavigations any remaining ones. The myth that Christopher Columbus's sailors feared they would fall off the edge of the world was false: they were understandably uncertain about a voyage into the unknown, and were also worried that food supplies would run out. In fact Columbus did not provide sufficient supplies to reach China or the East Indies, his original destination, and if America had not existed then those on the voyage would have died of starvation.
Some Christians in England and America tried to revive Flat Earth thinking in the 19th century. Modern people who do not accept the spherical Earth and base this opinion on Scripture do not represent a continuing school of Biblical exegesis, although some small groups such as the Flat Earth Society work hard to keep the concept alive, and have claimed a few thousand followers. Charles K. Johnson ran the Flat Earth Society from his home in California until he died in 2001. See 
The Earth is very smooth, which is to say, locally flat. By comparison, if a well-polished billiard ball were enlarged to the size of the Earth, it would have mountains about 50 miles high.