Sean Carrol in Cosmic Variance:
First, conservation of momentum isn’t just an important physical principle, it played a crucial role in the development of the idea of reductionism, which has dominated physics ever since. Aristotle would have told us that to keep an object moving, you have to keep pushing it. That sounds wrong to anyone who has taken a physics course, but the thing is — it’s completely true! At least, in our real everyday world, where Aristotle and many other people choose to live. Push a cup of coffee across the table, and you’ll notice that when you stop pushing the cup comes to a stop. Galileo comes along and says sure, but we can go further if we instead imagine doing the same experiment in an ideal environment that is completely free of friction and air resistance — and in that case, the cup would keep moving along a straight line. This has the virtue of also being true, but the drawback of not relating directly to the world we experience. But that drawback is worth accepting, because this backward step opens an amazing vista of progress. If we start our thinking in an ideal world without friction, we can assemble all the rules of Newtonian mechanics, and then put the effects of air resistance back in later. That’s the birth of modern physics — appreciating that by simplifying our problems to ideal circumstances, and understanding the rules obeyed by individual components under these circumstances, we can work our way up to the glorious messiness of the world we actually see.
The second cool thing about conservation of momentum is that it was not Galileo who came up with the idea. As with many grand concepts, it’s hard to pin down who really deserves credit, but in the case of momentum the best candidate is Persian philosopher Ibn Sina (often Latinized as Avicenna).