On the topic of mathematics, Albert Einstein once stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." The link between reality and mathematics is, for some people a discriminant in answering the question "is maths discovered or invented?".
Some believes that maths has no connection with reality, that you can't find it in nature, and therefore it wasn't discovered, but invented by some Greek who had nothing better to do in his life than making up rules about numbers.
Some argue that the rules of maths do not apply in some cases in nature: for example, if you have two drops of water and you add them together, you will have one bigger drop of water, so 1+1=2 wouldn't be true. But actually, if you think about it, you still have 1 + 1 drops of water, so you have 2 drops of water that eventually, combined together, form one bigger drop.
Also, a molecule of water is made of 2 atoms of hydrogen and 1 atom of oxygen. If you analyse 2 molecules of water, you'll find 4 atoms of hydrogen and 2 atoms of oxygen (btw, i'm so hoping i'm making sense, otherwise mr poeser will tease me forever), so how can you say that maths does not apply to nature? Moreover, sciences like physics, biology, chemistry, astronomy, economics, all need maths. Leonardo da Vinci once said that No human investigation can be called real science if it cannot be demonstrated mathematically.
No doubt that some of the things in maths are invented, like the 0: there is really not such thing like 0 in reality. But it's useful, so we use it.
However, some other things are just there... you can measure every circumference on Earth and you'll find out that the relationship between the circumference and the radius of the circle is C=2πr. And every existent right angle is 90°.
If for maths we mean the language in how to express real, existing principle, I would say that it is invented. However, some things are just out there and mathematicians have discovered them and translated into the universal language of maths.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty —a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
