Once upon a midnight dreary, while I pondered weak and weary
Over many a lengthy text of theorems whose proofs to find.
Drawing useful lemmas from thence, by the problem’s antecedents
Showed I then by abstract nonsense that the converse was implied.
“’Tis unfortunate,” I muttered “it’s the converse that’s implied”
As the proof escaped my mind.
Dealing with this foul equation, foiled by obscure notation
Still I saw no sound causation from the left to right hand side.
With this cursed reverse inclusion all I’d need to do was use one
Of the claims I hadn’t proven; they could prove the ones I had.
But unfairly used conclusions that can prove the left hand side—
“Tis it’s converse that I need.
‘Tis but vaguely I remember, it was sometime past September
And by all my class’s members every method had been tried.
Staring at the sheet unblinking, feeling all my chances shrinking,
Near despairing, always thinking “Can I prove the other side?
Is the statement even true that sat upon the right hand side?”
For it still my skills defied.
Midnight passed as time grew longer, certainty grew ever stronger
That the proof was wrong and wronger, for no true proof could I find.
Each as failed as its successor, my attempts were ever lesser
“I must ask the class’ professor what theorem may be applied.
“On the morrow I shall ask him if with success this may be tried.
For my brain’s so liquefied.
“Problem!” said I “Unsolvable! Problem which might be possible!
If solution may be found or count’rexample be espied!
I was up til seven a.m. with all manner of mental mayhem.
By every tactic and stratagem just the converse was implied.
Is this possible, professor? Was a false proof there assigned?”
Quoth the teacher then, “I lied.”