Higher mathematics isn’t about performing fancy calculations — it’s rare to find a calculation that requires some higher mathematical tools that can’t be done m

Higher mathematics isn’t about performing fancy calculations — it’s rare to find a calculation that requires some higher mathematical tools that can’t be done more simply using elementary methods. So it’s no wonder people aren’t explicitly using higher mathematics everyday. Instead, higher mathematics allows you to add powerful new features to your mental models, and reason about these features accurately and effectively. A key example: the Fourier transform. Understanding a signal in terms of its frequency components is immensely valuable for understanding how periodic phenomena work, and since periodic systems are ubiquitous, this often leads to concrete insights into concrete problems. With this more sophisticated understanding of the problem, you can write down a solution that can be implemented with “8th grade algebra and a little programming”. Other similar examples: singular value decomposition, spectral decomposition, probabilistic reasoning (MLE, Bayesian inference). It’s important to equip people with the tools required to build powerful mental models of the world around them, so they can solve hard problems. Higher mathematics offers many such tools.