Mathematics is not so useful in practice as you might think

Mathematics is an useful model for reality.

However, most inventions that claims that use mathematics are only inspired by mathematics. Sometimes the mathematics was created after the fact. Encryption is 100% based on mathematics, most of the other technologies can be imagined without advanced mathematics - while arithmetic is always useful.

Logic is just a tiny bit of mathematics that governs the binary gates used in computers. But nobody makes a complicated integral to decide how tight the electronical gates can be placed - this is based on experiments AFAIK.

We still rely on trial and error for most of our inventions. And this is for a good reason, mathematics cannot provide the answer except for models that we already derived from experience. There are many non-linearities in real life that cannot be derived mathematically - take for example the friction of a body with air on very high speed.

AFAIK we cannot mathematically calculate the portance of a certain airplane wing except by extrapolating some experimental results.

We can't even describe mathematically the motion of three bodies (planets).