Is Mathematics Invented or Discovered?

How do mathematics and existence relate?


I recently saw this Youtube video about

In the video, professor Evan Pugh mentioned this question and how over his career his opinion on that changed.

I have been fascinated by this question since forever. Is mathematics the only way to represent physics that we discover by thinking about it or are we representing laws of nature with one form of the language that is capable of representing it partially or fully.

I haven't formed an option on this yet but intuitively I would think of it as "discovered".

I asked this question out on the internet and I got some replies:

☝️This is also my non-intuitive answer.

☝️It is hard to imagine something that does the job of mathematics but is not mathematics.

☝️Maybe everything is discovered? 🤔

☝️maybe the phenomenons are always there but is it possible to represent those in something other than mathematics? Like by visualization?

☝️that is an interesting philosophy, what is invention vs discovery anyways? Is invention mere assembly of discoveries as lego blocks? Maybe a invention is a meta discovery.

☝️it could be but where do we draw the line? When did we start to invent and stopped to discover?

☝️I believe that the forces were there yes, but the representation langauge can exist only after humans and maybe it can also look differnt than mathematics.

☝️Time to read about "constructivism"

Thank you to eveyone who replied, I would absolutely love to continue this conversation with you. Please feel free to reach out again. We can even


These replies do cover a lot of my own opinions.

I will extend this blog post with a brainstorming section where I will post my thoughts on this topic by seeing it through different perspectives like:

and , , and more.

In the mean time though. here is an interview from

on this question: