"The true mathematician takes 'you can't do that' as a challenge." -- Vi Hart, 2012-03-24
[Note that the usual challenge taken up -- as Ms. Hart explains immediately after the line I quoted -- is to rephrase "can't do that" as, "What would it imply if you could do that?", and on several occasions the answer has been, "We would need to {discover|invent}[1] a new kind of number."
[1] Whether new kinds of numbers are discovered or invented is a longstanding disagreement, but the most memorable quotation on the subject is "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk," from Leopold Kronecker (b. 1823-12-07, d. 1891-12-29) ["God made the integers, all the rest is the work of man."] I lean toward "discovered", myself, but I have to admit Kronecker has the better soundbite.