P = NP: Exploring Algorithms, Learning, and the Abstract Mathematical Universe

This paper presents an informal, amateur proof of P = NP, combining theoretical ideas and personal insights without the constraints of formal academic conventions.

Disclaimer: I feel completely drained from this work and just want to share it. While I can try to explain the concept, I don’t have the mental capacity for much more and plan to disengage or reduce engagement from the topic. Thank you for your understanding.

Abstract

The traditional concept of an algorithm is incomplete, as it overlooks the origin and broader context of how algorithms are created. Algorithms are developed by entities—such as AI, Turing machines, humans, animals, or other agents—interacting with the abstract/mathematical universe. We explore the idea of the abstract/mathematical universe through various real-life and pop culture examples. We discuss the impact of the process of outside learning on algorithms and their complexities. Next, we illustrate how the process of learning interacts with the abstract/mathematical universe to address the P vs NP dilemma and resolve the challenge of theoretically demonstrating the existence of polynomial algorithms, ultimately leading to the conclusion that P=NP.

The concept of abstract/mathematical universe:

This universe encompasses an infinite expanse of mathematics, concepts, and alternative universes, including imaginary physics and imaginary scenarios. For humans, it influences nearly all aspects of life: science, engineering, software, hardware, tasks, sports, entertainment, games, anime, music, art, algorithms, languages, technology, food, stories, comics and beyond. Within this universe, variables and structures like "story length" or "music genre" can be freely defined, giving rise to an overwhelming range of possibilities. For example, there are countless ways to complete an unfinished work at any point, whether it's a musical composition, a show, or something else. How many different variations of basketball or any other sport can you create? There’s an endless universe of possibilities and variables to explore.

Navigating this abstract universe without a clear direction or purpose is equivalent to solving an incomputable function. Humans and animals solve this challenge by defining finite domains, focusing only on what they need or desire within those constrai...

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