One of those is wrong; Galileo was not actually oppressed by a Church, he was really oppressed by fellow scientists(1) , the Pope was actually quite supportive of Galileo but fellow scientists were looking for ways to torpedo him. Yet colloquially, Galileo is held up as this sort of 'religion against science' example in a way that shows many people believe it was some sort of unscientific Dark Age prior to his arrival. Not true at all.
Medieval scientists are just victims of some bad public relations. Fortunately, Professor John Freely, physicist and book author, is here to set the record straight, in a book called Before Galileo: The Birth of Modern Science In Medieval Europe:
You've all read or heard the narrative I laid out above. Galileo was this lonesome Rationalist on the hill defending Copernicus against European voodoo Shamen defending Ptolemy and he basically created modern science. Yet between the sack of Rome and Galileo, there was 'a science Renaissance before the science Renaissance' happening many times, some of it was just happening in Islamic countries and spreading into Europe, which is part of the reason why people with Teutonic dispositions gave it little credit. Some of it only exists in fragments. Philoponus of Alexandria had debunked Aristotle a thousand years earlier, for example, Galileo was just fortunate enough to drop balls off that Leaning Tower in Pisa rather than living in Egypt, and Philoponus gave us 'impetus theory' and an understanding of kinetics as well, a refutation of Aristotle's antiperistasis.
It's a shame, we'd all be a little better off if we learned the real chain of history and how nature was the first physics laboratory and religion was a big part of that discovery. You may have heard of Roger Bacon, the Franciscan friar and "Doctor Mirabilis" who was an early advocate of understanding the world according to natural laws, but Freely rightly notes that Peter Peregrinus was the dominus experimentorum of the day, even according to Bacon.
Farther back, we get a look at Leonardo Fibonacci, he who everyone that took a class in Pascal programming knows because of his Liber quadratorum and its "rabbit problem", how many rabbits you have if a single pair of rabbits whose offspring also gives birth to a pair of rabbits starting in their seconds month, as do theirs, and so on.
Basically, by the time of Galileo, Aristotle had been under attack for a long time; what was lacking was something firm. It was all there, though. Galileo did not so much stand on the shoulders of giants, if I may paraphrase, but to pick up the pieces they left behind and create a pedestal. Aristotle lasted for a reason. Experimentalism is necessary for modern science but if there is a World Series of Great Thinkers, you'd be crazy not to have him on your team. But thinking can only take you so far, even before Aristotle, and I want to talk about the 'Empedoclean impasse' - either a thing is or is not - that existed in ancient Greece and has its echo in the more modern conservation of mass. It was a science controversy then, in the way that matters of philosophy and science were inextricably entwined, and it pitted science versus religion in 400 B.C., but not on the sides you would expect. Parmenides was on the side of ancient Greek conservation of mass. The universe was indestructible and evidence showing otherwise was an illusion created by our senses.
A generation later Democritus instead codified something revolutionary that explained how things could change yet stay the same; an arche between the immutable nature of Parmenides and the relativistic 'flux' of Heraclitus. This arche was composed of irreducible physical substances which collide and form into what we find in nature. He came up with atomic theory - “The universe is composed of two elements: the atoms and the void in which they exist and move.” His teacher Leucippus is quoted by Freely as stating, "Nothing occurs at random, but everything for a reason and by necessity."
Democritus meditating on the seat of the soul, by Léon-Alexandre Delhomme, exhibited at the Paris Salon of 1868. Now in in the garden of the musée des Beaux-Arts de Lyon. Plaque: Hippocrate arriva dans le temps que celui qu'on disait n'avoir ni raison ni sens cherchait dans l'homme et dans la bête quel siège a la raison, soit le cœur, soit la tête (La Fontaine). Photo: Jean-Louis Lascoux (January 13th 2008). Link: Wikipedia
Why didn't it catch on, then or in the later years of Europe? It wasn't suppression, religious people then and later were not anti-science, they were instead objecting to atomic determinism. They believed in free will, just like secular humanists do today.
The arche was refined and became the elements (earth, fire, air, water), plus an aether that arrived later. John Dalton wouldn't figure out atomic theory in the modern sense until 2,100 years later and then the 'elements' became solid, liquid, gas and plasma. An Ionian intellectual descendant of Democritus would move to Athens and become the teacher to Pericles, whose education and enlightenment would lead to the Classical period in Greece and then the creation of Plato's Academy and explaining the motion of celestial bodies - which would one day make Galileo famous.
If you want to learn about all of that and 200 other lesser-known scientists who led to the birth of modern science, "Before Galileo" is the book for you. Freely packs a lot of good stuff into 315 pages and makes the case that modern science in Europe benefited from a thousand years of work leading up to it. We just have to look past the public relations efforts to find it.
(1) Get Radical - And Maybe Be A Better Scientist.
"If you think Republicans ignore 'inconvenient truths' about climate, imagine what you would think if you were a scientist in the early 1600s and Galileo ignored a whole moon...When his idea about the tides did not match Kepler or math, for example, he set about ridiculing both and ignoring facts that disagreed with him - sailors all around the world would have been baffled (had they been able to read) at Galileo's data concluding that the tides only happened once per day if they happened at all, they happened at the same time every day, and that Luna had nothing to do with them...He had some glaring stuff wrong, he was simply convinced he was right on the biggest issue."