Science and religion, particularly Catholicism perfectly complements each other. This will be verified through exploring the Big Bang Theory, Evolution and the Flat Earth Theory.
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There are many people who think the Catholic Church once believed the earth was flat and warned Columbus that he might fall off the end of the earth. This is totally false. The Ancient Greeks knew the earth was round. Aristotle (4th century B.C.) supported the theory that the earth was round with observations such as that the southern constellations rise higher in the sky when a person travels south. He also noted that during a lunar eclipse, the Earth’s shadow is round. This understanding was taught by Catholic scholars such as St. Augustine (354–430), “it be supposed or scientifically demonstrated that the world is of a round and spherical form.” (De Civitate Dei, Book XVI, Chapter 9). St. Thomas Aquinas (1225-1274) wrote, "For the astronomer and the physicist both may prove the same conclusion: that the earth, for instance, is round: the astronomer by means of mathematics (i.e. abstracting from matter), but the physicist by means of matter itself." (ST I, 1, 1, ad2).
There was no one in Columbus' day (he set sail in 1492) that thought he was going to fall off the end of the earth. What they were worried about was whether he had enough provisions to make it to a continent that might not be there. The earliest example of the idea that Catholics believed in a flat earth was in Washington Irving's A History of the Life and Voyages of Christopher Columbus (1828). Since then the idea has spread and unfortunately is believed by many to be true.
The Catholic Church officially has no problem in people believing in evolution. The highest level of Catholic teaching states, "The Teaching Authority of the Church does not forbid ... the doctrine of evolution, in as far as it inquires into the origin of the human body as coming from pre-existent and living matter - for the Catholic faith obliges us to hold that souls are immediately created by God." (Pius XII, Humani Generis 1950: #36). Catholics are free to believe in evolution, provided they believe that God personally creates every individual soul. As pope Benedict XVI says, "We are not some casual and meaningless product of evolution. Each of us is the result of a thought of God. Each of us is willed, each of us is loved, each of us is necessary." Science and Catholicism are totally compatible. Science can't explore the reality of the soul because it is beyond science. Catholicism has no expertise on the development of species. The two work together to give us a complete picture of reality.
Galileo's (1564-1642) championing of heliocentrism (the Sun at the center of the Galaxy) was controversial within his lifetime, a time when most subscribed to geocentrism (the Earth at the center of the Universe). He met with opposition from astronomers, who doubted heliocentrism due to the absence of an observed stellar parallax (the apparent change in position of the stars due to orbiting the sun). He also met with religious opposition based on the current scientific understanding of his time which agreed with the bible teaching the sun going around the earth.
It is a complex topic and so some points about attitudes at the time are important. The Catholic Church had no problem with geocentrism provided the scientific proof can be shown. For instance at the time Cardinal Baronius said that the bible "is intended to teach us how to go to heaven, not how the heavens go." Cardinal Bellarmine was prepared to reinterpret scripture if proof can be shown. At the crucial trial of Galileo about teaching heresy, Galileo claimed three proofs for geocentrism all of which don't prove geocentrism. Tides are due primarily to the moon. Sun spots can be explained with the rotation of the sun, not that the earth goes around the sun. The last point of the phases of venus is a more serious point but not sufficient on its own. What brought conclusive proof was stellar aberration by James Bradley in 1729 which eventually led to the Church formally lifting its ban on Galileo’s books in 1758. That's a long time after 1615.
There are many inaccuracies about Galileo's trial. He did not stamp his feet and cry out, "But it does move." He was submissive throughout the trial. He was not tortured. His house arrest for the last nine years of his life which were lived in a palace where he could freely work on his research provided he did not teach about geocentrism. He completed two more works during this time.
So it appears Galileo was wrong with his evidence. If Galileo had pulled his head in earlier there would have been no problem, ie if he hadn't said he had proof for geocentrism.
In a sense the condemnation of Galileo was providential. It proved for all time that fallible bodies like the Roman Congregation ought not to dub a scientific theory heretical, and it prevented them from making a similar mistake for over three centuries. It proved also that whenever there is apparent contradiction between the truths of science and the truths of faith, either the scientist is wrong in advancing a mere hypothesis as a fact, or that the theologian errs in mistaking his personal opinions for the teaching of the Gospel.
Pastor concludes his brief but able study of the case with the wise words: There has been no second Galileo case (History of the Popes. Vol. XXIX., p. 62).
Pope John Paul II on behalf of the Catholic Church has publically apologised for the Galileo affair in 1992. The Galileo affair is a crucial argument for justifying the conflict between science and religion. Such a conflict is absurd when the evidence is examined. Anyone that uses such an argument should be explained the facts and invited personally to accept the official apology of the Church.
One final point from this era is that Galileo was not the only scientist of his day. 26 of the 35 Jesuit scientists who have lunar moons named after them were alive during the life of Galileo.
There is no conflict between science and religion. Historically this conflict really developed out of the Enlightenment which developed in the late 1600s and 1700s to emphasise the individual and reason against tradition. Many Enlightenment thinkers were anti-Catholic. Many writers were creating myths or at best twisting truths to make Christianity look bad. The scientist John William Draper and the writer Andrew Dickson White were the most influential exponents of the conflict thesis between religion and science in the 1800s. Draper wrote a History of the Conflict between Religion and Science (1874) and White wrote A History of the Warfare of Science with Theology in Christendom (1896). Modern historians have discredited both books. In fact, Catholicism has encouraged science through the centuries. Fr Tomas William LC explains this well in Myth No.3: Religion Is Opposed to Science:
History shows that the natural sciences grew out of Christian culture. As the sociologist Rodney Stark has so convincingly shown (See especially For the Glory of God: How Monotheism Led to Reformations, Science, Witch-Hunts, and the End of Slavery), science was "still-born" in the great civilizations of the ancient world, except in Christian civilization.
Far from being an obstacle to science, Christian soil was the necessary humus where science took root.
Examples of this fertile ground can be seen in the number of priest scientists such as Fr Georges Lemaitre.