I used to pursue mathematics because I thought it was beautiful and revealed irrefutable truths.
However upon examination of the foundations of this subject, my viewpoint has changed drastically.
The foundations of this subject are murky, and I feel like we don’t know if the intricate web/fortress of mathematical knowledge won’t come crashing down if someone finds a contradiction within the ZFC.
Any proof can be questioned because we rely on an assumption that this system is sound.
The law of excluded middle can also be questioned, since logic in the natural sciences and real world often isn’t so strong.
One thing I cannot deny is the usefulness of classical mathematics. I wonder if this is the only reason we pursue it? For its power in application?
Why do we research this subject? Surely nobody still thinks that proofs are irrefutable truths.