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Phrases to avoid when discussing a difficult topic:
Obviously
Of course
It is clear that
It is easily seen that
Obviously
Of course
It is clear that
It is easily seen that
(I’m reading some math books right now, and if I see one more “Clearly…” followed by something that is not at all clear I’m going hurl my iPad across the room.)
Maybe I should keep a running tally. Next up:
“It is not hard to show that [something that looks pretty hard to show]”
“It is not hard to show that [something that looks pretty hard to show]”
“It is easy to see that [nope, it isn’t]”
Here’s the proof of the thing that is “easy to see”:
“It is not hard to find…” -> “Here is how to find…”
“It is easy to see that X is true” -> “We can see that X is true by noting…”
“It is only slightly more difficult to see that Y is true” -> “Similarly, we can see that Y is true because…”
“It is easy to see that X is true” -> “We can see that X is true by noting…”
“It is only slightly more difficult to see that Y is true” -> “Similarly, we can see that Y is true because…”
Is amazing how many proofs are “hard to understand”. The whole point of a proof is to be convincing—literally incontrovertible. If you have the relevant background and yet can’t understand a proof, the problem isn’t you—the problem is the proof.
