The problem remains that it’s not particularly helpful to know that a proof immediately springs to the lecturer’s or textbook author’s mind. And so, operating under the assumption that people are trying to communicate only relevant information, whenever I see ‘obvious’ or ‘easily seen’ in a mathematical text, I can’t help but read it as an obnoxious ‘you should know this already—unless you’re dumb or something’. I think that the best norm for using the word ‘obvious’ and its variations would be to not use it at all.
This might be a defensive mechanism. Being explicit and formal is very important in mathematics but when you choose which proofs to omit, you’re making a judgement about which kind of presentation will lead to the greatest level of understanding among the intended audience. This judgement is more about psychology rather than mathematics and is necessarily based on fuzzy intuitions. Maybe mathematicians are uncomfortable with that and call such omitted proofs ‘obvious’ to make criticism costly in terms of status.
The problem remains that it’s not particularly helpful to know that a proof immediately springs to the lecturer’s or textbook author’s mind. And so, operating under the assumption that people are trying to communicate only relevant information, whenever I see ‘obvious’ or ‘easily seen’ in a mathematical text, I can’t help but read it as an obnoxious ‘you should know this already—unless you’re dumb or something’. I think that the best norm for using the word ‘obvious’ and its variations would be to not use it at all.
This might be a defensive mechanism. Being explicit and formal is very important in mathematics but when you choose which proofs to omit, you’re making a judgement about which kind of presentation will lead to the greatest level of understanding among the intended audience. This judgement is more about psychology rather than mathematics and is necessarily based on fuzzy intuitions. Maybe mathematicians are uncomfortable with that and call such omitted proofs ‘obvious’ to make criticism costly in terms of status.