cool math is complex
haiku's beauty is simple
math makes poetry
An Exploration of Communicating Math Concepts Through Haiku
by Anaya Willabus

First, about Haiku…

lined five seven fivecounting words in syllables
illuminates finds

In the 13th century, haiku made up the first part of Japanese oral poems called renga,
which were a hundred stanzas long and also accounted for syllables. Haiku became an
independent art form around 300 years later.
Constrained to 3 lines written in a 5/7/5 syllable count, the focus of a haiku is on
simplicity, directness, and the capacity to offer the reader a digestible sense ofunderstanding. These traits make haiku a great tool for attempting to express
complex math topics with brevity and clarity.

Goldbach’s Conjecture
wholes greater than two
equal sums ought to exist
when adding two primes
Goldbach’s Conjecture, created by Christian Goldbach in 1742, states that every eveninteger greater than 2 is equal to the sum of two prime numbers. It was partially provennearly 200 years later by a mathematician named Ivan Matveyevich Vinogradov who foundthat every even integer is the sum of at most six primes. Then, more progress was made byChen Jing Run in 1973 as he proved that every even integer greater than 2 is the sum of aprime plus a number with no more than two prime factors. However, the conjecture
remains unproven for all numbers which it would apply to.

Collatz Conjecture (The 3x+1 Problem)
multiply, add, halve
a possibly endless loop
Collatz gives one four two
In the 1930s, Lothar Collatz conjectured that when starting with any positive integer, if you
follow the process of multiplying by 3 and adding 1 if it's odd, and dividing by 2 if it's even,all values will eventually lead to 1 then hit a loop of 1, 4, 2 for infinity. Manymathematicians consider this problem a waste of time to attempt to solve because we areunable to test it out on all of the infinite integers that the rule would apply to.
Mathematician Terence Tao got the closest to solving it as a proof, finding that it isguaranteed to work for almost all numbers, by creating a weighted sample of numbers andconfirming that the theory applied.

Gödel's Incompleteness Theoremsalways limited
nothing proven doubtlessly true
there is no ending
Kurt Gödel’s Incompleteness Theorems are strongly related to the cause of theimpossibility behind many famous unsolved math problems, such as Goldbach’s Conjecture
and the Collatz Conjecture. The first states that there is no set of rules that is capable ofproving all possible truths about a set of numbers. The second states that a formal systemcannot prove itself consistent if it is in fact true. This theorem is paradoxical since it assertsthat for something to be true, it must also be false.Sources--“Haiku” https://poets.org/glossary/haiku“Goldbach’s Conjecture”
https://primes.utm.edu/glossary/page.php?sort=GoldbachConjecture“Goldbach Conjecture” https://www.britannica.com/science/Goldbach-conjecture“Mathematician Proves Huge Result on ‘Dangerous’ Problem”
https://www.quantamagazine.org/mathematician-proves-huge-result-on-dangerous-prob
lem-20191211/“Gödel’s Incompleteness Theorems”
https://plato.stanford.edu/entries/goedel-incompleteness/#SecIncThe“The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus duSautoy” https://youtu.be/I4pQbo5MQOs