Writing a Proof in Verse -- with ChatGPT3

     Academician Punya Mishra (from Arizona State) is active in integrating various topics and learning patterns.  Back in 2020, at this link I featured his poem, "The Mathematical i"  -- and Mishra has recently shared with me some of his explorations with poetry created by artificial intelligence.

     Back in 2010, Mishra wrote a fascinating poem (The Infinity of Primes")  -- a poem that is also a proof -- which begins with these stanzas:

     Over numbers and their combinations if you sit and mull
     You will find that not one of them is uninteresting and dull.
     But it is a certain class of figures that most attention stirs
     Yes, I am speaking of those special ones, the prime numbers.

     Prime numbers are interesting, the mathematician posits,
     ‘Cos they make up all the others, the so-called composites.
     Here’s an imperfect analogy, a simple little working rule,
     Consider the prime to be an atom, then a composite’s a molecule. 

                        . . .               Mishra's complete 17-stanza poem is available here.

Mishra recently explored the the ability of ChatGPT3 to create a proof of the infinity of the set of primes;  The stanzas below offer a start of a proof-attempt; its completion and two other attempts are available at this link.

Poetically exploring the the invention of "i"

     Today's posting features work by Punya Mishra, professor and administrator at Arizona State University -- a writer who offers explanations of mathematical concepts in his poems, explanations that can appeal to students!   Mishra's website features several mathy poems and in our email correspondence he said that "The Mathematical i" is his favorite.  Here are are several stanzas:

from  The Mathematical i     by Punya Mishra

       The negative numbers were full of dismay
       We have no roots, they were heard to  say
       What, they went on, would be the fruit
       of trying to find our square root?

       Matters seem to be getting out of hand
       Since the negatives have taken a stand,
       On the fact that positives have two roots, while they have none.
       They plead, would it have killed anybody to give us just one?
       The square roots of 4 are + and – 2! As for -4 ?  How unfair,
       He has none! None at all. Do the math gods even care?