Math is something humans invented and is a model, nothing else. There is no logic per se, but a model that works quite well for us.
I studied Math and CS as a very highly gifted and quickly found out, there is no beauty of Mathematical Logic, only humans approval of what they deem most accurate.
A good example is set theory. Cantor was not openly welcomed after he introduced his "theory" to others. In fact, he was received quite some pushback and hostility - this doesn't sound like someone received love the mathematical logic's way.
In fact, the story of Cantor is really a tragic one. He left math for quite some time, due to the pushback.
Only later humans accepted his theory and found it useful. Well, well, what is Mathematical Logic and what not is after all just broad consensus by humans.
And if you go deeper, you will hear more of these stories. Math is anything else but logic. Proofs are religious things, often so complicated, they are simply accepted as "approved by a committee". Many profs cannot really explain simple proofs, they refer to the textbook.
This doesn't sound like romance nor easily reproducible logic.
Consensus may give a hint to what is or isn't reality. But consensus—even expert consensus—does not determine reality. Experts can be wrong. Most of the experts, even, can be wrong simultaneously.
Philosophy is the exercise of testing ideas for oneself in the laboratory of one's own mind.
When I test the idea that math is discovered in my own mind, from my own perspective, with my own experience and education brought to bear, I find it unconvincing.
When you test the same idea in the laboratory of your mind, with your experience and your education applied, and get a different result, that is interesting. Your result is relevant information to me. If nothing else, it's a good prompt/trigger for me to revisit my earlier conclusion and see if it still holds.
But your disagreement—or indeed, the disagreement of a majority of trained mathematicians—does not constitute an automatic reason for me to conclusively determine that you/they are right and I am wrong.
I still have my own examination of the concept, with my own supporting and detracting arguments. And the result of my examination continues to be that math being invented is the significantly more persuasive view.
Math is something humans invented and is a model, nothing else. There is no logic per se, but a model that works quite well for us.
I studied Math and CS as a very highly gifted and quickly found out, there is no beauty of Mathematical Logic, only humans approval of what they deem most accurate.
A good example is set theory. Cantor was not openly welcomed after he introduced his "theory" to others. In fact, he was received quite some pushback and hostility - this doesn't sound like someone received love the mathematical logic's way.
In fact, the story of Cantor is really a tragic one. He left math for quite some time, due to the pushback.
Only later humans accepted his theory and found it useful. Well, well, what is Mathematical Logic and what not is after all just broad consensus by humans.
And if you go deeper, you will hear more of these stories. Math is anything else but logic. Proofs are religious things, often so complicated, they are simply accepted as "approved by a committee". Many profs cannot really explain simple proofs, they refer to the textbook.
This doesn't sound like romance nor easily reproducible logic.
After all, we deal with human beings.