> In mathematics, the word means that a statement transcends the laws of time and space. In law, it means a group of 'reasonable people' can be convinced.
This was historically and still is largely false. A mathematical proof is a written argument and most proofs are too complex to be "obviously correct", therefore mathematical proofs are usually more like your latter case: It is an argument that convinces people. Mathematics has a long history of doing things "that sound right but haven't been proven yet but it seems to work out ok", e.g. this was done all the time in the earlier days of analysis.
This was historically and still is largely false. A mathematical proof is a written argument and most proofs are too complex to be "obviously correct", therefore mathematical proofs are usually more like your latter case: It is an argument that convinces people. Mathematics has a long history of doing things "that sound right but haven't been proven yet but it seems to work out ok", e.g. this was done all the time in the earlier days of analysis.