It's inferred from evolution and never 100% accurate, just good enough.

This is similar to asking if nuclear power was invented or discovered. It's all about meaning and the system that is in question. We are the system and our meaning is to succeed in reproducing in a very probabilistically random environment with absolutely 0 certainty about anything.

It only became evident that math was useful when someone realized with their memory that counting 4 objects was useful because they needed to remember how many fruits they had collected, in order to map a mental function of how many would be required. Or perhaps it began when we saw the cycle of the sun and realized that things were repeating and we needed to keep track. This is fun because we could have stopped there as an intelligence and operated on the notion of "cycles" but we have a larger memory than that as a species. We are able to self-reference and even complexly access an evolving database in our head of different connections, which are evolved to provide a consistent reality that compliments our frequency of operation on a grand scale.

When we began abstracting even more, we invented negative numbers and the number 0. The Roman Empire even detested the use of 0 saying, "How can you have nothing of something?". This should sort of remind you of the nuclear power example. People detest nuclear power in some places. This doesn't mean it doesn't exist. It doesn't mean they're wrong about why it's not entirely needed to provide structure in either case. It is the evolution of unknown matters to provide a consistent reality that meets our demands.

Math is a language. If a new concept (the shoe) works in our system/language (the shoe thus fits), then we keep it around. It continues to serve a predictable and relatively consistent reality when we use it to communicate about our world.

Now arguably, we need concepts like 0 in order to survive with this many people on the planet. Without it, just about everything in modern discovery would be impossible including all of chemistry and advanced physics. We'd be base 9, etc. It would be very weird and there is no way to know if we would have come this far as a species. The invention of the number 0 is why we're alive just as much as nuclear power has supplied more people than previously thought with energy and just like how alcohol saved Egypt when their rivers had only contaminated water. These things are functions inside of recognized systems that met needs of humans.

I think it makes the strongest case for why math is more of an invention or a utility for humans and other complex creatures.