[swagasaurus-rex]

You're getting a lot of flak for conflating verifiability with formal proofs.

In your defense, science appears to follow formality, though we run into often run into holes in our theory when a confounding number of variables are in play.

Me, personally, I don't know what that difference really is. Science is science because it works. If it didn't work, it wouldn't be science.

Mathematics can and will find ways to apply itself to the real world, no matter how approximately, as long as that difference matters to somebody.