Investigating the Limits of Mathematical Knowledge: Insights from Computability and Computer Science
How much of mathematics can ever be truly known? This age-old question is back at the forefront after a recent high-profile lecture at Harvard, where a renowned quantum computing expert explored how the frontiers of computer science, philosophy, and mathematical logic intertwine to define the boundaries of the knowable in mathematics (Harvard Math - Fifth Annual Yip Lecture).
The lecture, titled “How Much Math Is Knowable?”, highlighted that while mathematics is often thought of as the bastion of certainty, the reality is more nuanced and constrained by the very limits of computation itself. The core message: computer science doesn’t just create new tools for mathematicians—it draws the actual lines that define what humanity can, or cannot, ever formally prove or know in mathematics.