Good article. I like this approach to problem solving and learning. I’m just at the start of my math degree (there may be time to change) and the usefulness of inductive reasoning cannot be understated. Mathematical reasoning is why I started my degree in math. Math is a language all of its own. It is the language of the universe. It is a tool. It can be whatever a mathematician chooses math to be, and I find that beautiful. In its purest form, I believe math to be closer to a form of poetry or philosophy than a science. Science has many great uses of math, but science only uses math as a way solve its problems. Math doesn’t have to be about solving problems, but instead expressing new ideas. It is wild to look back in human history and realize that calculus existed as far back as the early 17th-century. Humanity all too often deems itself smarter than our historical counterparts, but is that even a reasonable argument? Do we simply have access to more tools? Math is a form of poetry. Math seeks to find aesthetically pleasing, rational, easy to understand solutions to the fundamental systems we use in day to day life. Math is a universal language to share, tinker with, and discover even the most complex ideas. I believe the power of mathematics lies in the creativity of the mathematicians wielding the sword, and the sheer power held by the abstract ideas we have learned to express in simple notation.