The Sporadic Nature of Big Numbers - Data Structures in Mathematics

Explore the destabilizing nature of large numbers in mathematics through this 32-minute video lecture. Delve into the complexity of arithmetical expressions and how they break down when dealing with increasingly large numbers. Learn about mathematical expressions, theorems related to number complexity, and the proportions of numbers with specific complexities. Investigate the probability of compressing complexity and gain insights into the true nature of natural numbers. Challenge your understanding of arithmetic and number theory as you uncover the limitations of our knowledge when it comes to extremely large numbers.

Destabilizing arithmetic with big numbers
What is the complexity of an arithmetical expression?
Observations about complexity
Mathematical expressions
Theorem
Numbers with digit length
Computing proportions of numbers with a given complexity
Probability that you can compress complexity to half
Nature of natural numbers