#polynomialequations — Public Fediverse posts

"Why study Diophantine equations?" 😂 Oh, because figuring out integer solutions to polynomial equations is the high-stakes drama of the math world! Who needs Hollywood when you have mathematicians revealing hidden structures like they're uncovering a Da Vinci code? 🎭🔍
https://hidden-phenomena.com/articles/modular #DiophantineEquations #MathDrama #IntegerSolutions #HiddenStructures #PolynomialEquations #HackerNews #ngated

Fernando Rosas (unfortunately not on Mastodon) asked on bsky:

"Has anyone figured out what exactly is the relation between the ideas of feedback, recurrence, and self-reference?"

A really interesting question.

He pointed to this paper for ideas: https://arxiv.org/abs/1711.02456
"Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos"

I did some desk research and found this cool paper:
https://arxiv.org/abs/1112.2141
"Resolving Gödel's Incompleteness Myth: Polynomial Equations and Dynamical Systems for Algebraic Logic"
that argues there is no essential incompleteness in formal reasoning systems if you look closely enough (using a more elaborate formalism based on polynomial equations to represent and evaluate logical proposition).

I wonder if analogous construction could be created for related theorems like the halting problem in computability theory.

#DynamicalSystems #IncompletenessTheorem #PolynomialEquations #HaltingProblem #Undecidability #SelfReference #Recurrence