Thinking about scientists in the past has made me think about something in nature that always deeply impressed me. How is it that math so nicely models the world? Not only can we use math to model things after the fact, but merely manipulating mathematical symbols according to certain rules leads to incredible predictions about what we do in fact find in nature. An amazing example of this is Einstein's special relativity. A couple postulates followed by exploring their (mathematical) entailment led to the incredible predictions behind time dilation and length contraction as well as mass-energy equivalence. These were subsequently thoroughly tested decades later. How to explain this?
On the atheist viewpoint, I don't know that you could answer this question. It is all an incredible coincidence. There is no reasonable expectation, a priori, of finding such tight order and predictability. You certainly couldn't expect to find that abstract mathematics could be used to both model and predict how nature behaves. On the other hand, from the Christian point of view none of this should be surprising. Genesis 1, Romans 1:20 and a multitude of other such verses suggest that God created nature in an orderly fashion. God explains the connection. This makes it all the more surprising to me that modern scientists are so recalcitrant to see God in nature. Great scientists in the past were not so hesitant and they had less reason to suspect something supernatural. The further things are probed, the more amazing some of these discoveries are. The connection between pen and paper (or computer) mathematical predictions and what is actually found in experiment I think at least should give people pause.