Unlocking the Unsolvable | Gödel Paradox of Incompleteness | An…

Gödel’s theorem of incompleteness, presented by Anushka Dassi and Pinakin Choudhary, revolutionized our understanding of the foundation of mathematics, shook its limits of concreteness, and shattered the dreams of complete and consistent proof. So, what is it? Was it a bunch of hefty equations, axioms, theorems, and bulky Greek symbols compiled into one blob of mathematical tragedy? No. In fact, its simplicity is a derision of the fragility of mathematics. 1 Line. 4 words. At the core of what broke mathematics. “This statement is False.” This presentation is part of the Paradox Festival organized by @Databased_IISc and @iiscacm-w under the guidance of Prof. Pandurangan and Kotak AI ML Center on 14th May 2023. Editing Credits - Agastasya Gaur To access the presentation, click here - https://drive.google.com/file/d/1D7vcA4F2eyBLVUCb6BQKQgh-IS6RjeSL/view?usp=sharing 0:00 Introduction 0:52 This Statement is False 2:19 Non Euclidean Geometries, Cantor's Infinities 2:55 Formalists 3:58 Russell's Paradox 4:29 Self Referencing Paradoxes in Logic 5:22 A Formal System 6:24 First Incompleteness Theorem 7:34 Elementary Arithmetic 9:01 Theories not formulated in the language of Arithmetic 10:35 The Special One... 12:42 Infinite Regression 13:41 And this can go on forever... 14:15 The Catch... 15:59 Slide Title