Picture this: was mathematics always "out there" waiting to be discovered, like a hidden treasure in a field? Or, did humans create it, like an artist crafting a masterpiece? This is the big question here.

Two perspectives exist:

• Mathematical realism (also known as Platonism) argues that mathematics exists independently of human minds. It's like Mount Everest: it existed even before anyone knew about it or named it. Mathematicians in this camp believe they are discovering truths that are already out there. An example would be the number '317'. According to mathematician Hardy, it's a prime number not because we think so but because it just is.

• Anti-realism posits that mathematical entities don't exist independently. Humans invented math as a language to explain things like quantity, structure, space, and change. It's more like the game of chess: before humans invented the rules, there was no such thing as "checkmate". The philosopher Hugh Lehman described mathematics as a "theoretical juice extractor".

Why do we find mathematical patterns like Fibonacci sequences in sunflowers, or logarithmic spirals in nautilus shells? Could this suggest that mathematics is an intrinsic part of the universe?

Realists would say, "Sure thing!" The universe, according to them, is sculpted by eternal mathematical entities. On the other hand, anti-realists would counter that these are just patterns we find because our brains are designed to look for them.

Your perspective on whether mathematics is discovered or invented doesn't just change how you view math, but also how mathematics progresses. This is important in the mathematics community and can even influence the production of mathematical knowledge.

Let's say you believe math is discovered (realist view), then you might see every theorem or equation as a clue leading to a universal truth. But if you think math is invented (anti-realist view), you might approach problems more creatively, like an artist creating a unique piece.