Let me give you an example. Was the triangle discovered or invented? For thousands of years, there must be three profiles found and known. But as a theoretical concept, the concept of triangle was invented. First, seeking truth from facts; The second is a theoretical and conceptual invention.

After the "invented" triangle is firmly in place, people will notice some similarities: height, bottom edge, circumference, angle and so on. Guess which ones were discovered and which ones were invented. Now continuing to study polygons, we have found a lot but few people have found it. Secondly, it is the sum of external angles, regularity, perimeter, diameter and area. Similarly, once a concept is invented, new concepts will be invented and others will be discovered at the same time.

But now consider the concept of group. This is the summary of digital invention under addition. We can argue that not all group attributes imitate the attributes of numbers; They must have speculated and proved it. That's how it was invented.

More and more abstract, we only see inventions, and we can say that we only find the properties of previous concept analogues. Therefore, we can say that some mathematics is discovered from other invented mathematics.

Bottom line: There is no clear answer to your question.

We invented the virtual reality of symbols and transformations, which we call mathematics. In view of its invented rules of the game, we build objects by assembling these components. We found the relationship between these objects. Unless you adopt a Platonistic view that assumes the potential reality of mathematical objects, it will be clumsy to invent and discover these terms.

Quoting philosophy of mathematics, Stanford Encyclopedia of Philosophy:

One of the most important features of Platonism is that it allows us to adopt the same semantics for mathematics and scientific discourse. In view of the existence of mathematical objects, mathematical statements are true just as scientific statements are true. The only difference lies in their respective truth makers: mathematical statements are true because of abstract (mathematical) objects and their relationships, while scientific statements are ultimately true because of the corresponding relationships between specific objects and these objects.

In any case, these may not be the best conditions. Mathematical laws need to be proved, so people put forward a theory and test it mathematically in various ways until it becomes a theorem.

This becomes a semantic problem. Did they invent the law and prove it, or did they discover an aspect of mathematics?

Semantics are semantics, depending on how you want to look at it or define it.