In his book Unbelievable: 7 Myths about the History and Future of Science and Religion historian of science Michael Keas discusses seven myths that have seeped into our popular culture concerning the alleged conflict between science and religion, particularly Christianity, and shows that each of the first six is historically false and that the seventh is theologically false.
Here's a thumbnail outline of the thesis of his book excerpted from the Introduction:
Myth #1: Premodern scholars in the Western tradition thought the universe was small—a cozy little place just for human benefit. Modern science displaced this Church-sanctioned belief with a vast cosmos that revealed humans to be insignificant.
The truth: Even ancient thinkers recognized that the earth was tiny in relation to the immense cosmos. In any case, size doesn’t necessarily mean significance, as many theologians and philosophers recognized.
Myth #2: The medieval Catholic Church suppressed the growth of science, causing Europe to descend into the “Dark Ages.”
The truth: The medieval Catholic Church positively influenced science and other intellectual pursuits. There were no “Dark Ages.”
Myth #3: Because of Church-induced ignorance, European intellectuals believed in a flat earth until Columbus proved earth’s roundness in 1492.
The truth: Ancient and medieval intellectuals in the Western tradition had many evidence-based reasons for belief in earth’s roundness.
Myth #4: Giordano Bruno became a martyr for science when the Catholic Church burned him at the stake because he supported Nicolaus Copernicus’s contention that the sun, not the earth, occupied the center of the universe, and because he believed in extraterrestrial life.
The truth: Bruno’s execution occurred almost entirely for theological reasons, not scientific ones.
Myth #5: The Church jailed Galileo Galilei because it rejected his telescopic observations and rational arguments that had proved the Copernican system.
The truth: Most early modern astronomers up through the mid-seventeenth century resisted a moving earth primarily for scientific, not theological, reasons. Galileo failed to prove that earth orbited the sun (that came later).
Myth #6: Copernicus demoted humans from the privileged “center of the universe” and thereby challenged religious doctrines about human importance.
The truth: Copernicus and most of his scientific successors up through the nineteenth century considered his sun-centered astronomy to be compatible with Christianity and human exceptionalism. In fact, early Copernicans viewed earth’s new location not as a demotion for humanity but rather as a promotion, out of the bottom of the universe.
Myth #7: If and when we encounter extraterrestrial life, it will deal the death blow to certain religions, especially Christianity, with its doctrine of the uniqueness of man and the incarnation and redemptive work of God on earth. Any ET capable of traveling a vast distance to earth would have superintelligence, technology indistinguishable from magic, and moral-spiritual insights that would trigger global religious reorientation.
The truth: Many Christian thinkers have been open to the possibility of extraterrestrial life, and neither a single pope nor a major church council ever declared these ideas heretical. Alien life and Christianity are potentially compatible.
Despite the efforts of people like Bill Nye "The Science Guy" and Neil deGrasse Tyson, host of the PBS science series Cosmos, the idea that science and religion are incompatible, though popular in the 19th and 20th centuries, has long since exceeded its intellectual shelf-life. Very few reputable scholars hold to it today because the historical evidence against it is overwhelming.
Keas does a good job of explaining that evidence in his book.