👉 The mounting math in recent years, particularly in the realms of machine learning and theoretical computer science, has seen exponential growth in complexity and scale. Initially, many problems were tractable with polynomial or even sub-exponential algorithms, but as models have grown in size and the data they process has increased exponentially, these problems have become intractable with classical methods. For instance, training deep neural networks now often requires vast amounts of computational resources and time, pushing the boundaries of what was previously considered feasible. Moreover, the theoretical underpinnings have evolved to address these challenges, with new complexity classes like PSPACE-hard and beyond emerging to categorize problems that are even harder than NP-complete. This trend not only highlights the limitations of existing algorithms but also drives innovation, leading to breakthroughs in areas like quantum computing and novel algorithmic paradigms that promise to revolutionize how we approach computationally intensive tasks.
