You're handwaving, but I think there is a middle-ground in this proof: Sum(i=1..n, i) = Sum(i=1..n/2, i) + Sum(i=1..n/2, n+1-i) = Sum(i=1..n/2, n+1) I'm sti

You're handwaving, but I think there is a middle-ground in this proof: Sum(i=1..n, i) = Sum(i=1..n/2, i) + Sum(i=1..n/2, n+1-i) = Sum(i=1..n/2, n+1) I'm still interested in the general question, of whether some proofs have big gaps between them. The more complex the proofs, the more obvious this would be; my examples are unfortunately simple. Something like proving the fundamental theorem of algebra using Rouche's Theorem (complex analysis) vs. field theory. But I don't know enough math to compare those.