Kolmogorov Complexity Theorem

The Kolmogorov Complexity Theorem states that most strings of data cannot be compressed into a shorter description than themselves, meaning they are inherently complex. In other words, there's a limit to how much you can simplify or summarize to describe a random piece of data. For example, a random string like "010101..." doesn't have a shorter pattern, so its simplest description is just itself. Conversely, highly ordered data like "aaaaaa" can be described very briefly. This theorem highlights the idea that some data is fundamentally complex and can't be easily summarized or reduced.