"Real math is just different."

This is the reason often given by highly-accomplished students when they decide not to pursue a major in math. And they're right - the style of the textbooks, lectures and homework is unlike anything they've been exposed to before. And most professors are not dedicated to seeing the world from the students' perspective and bridging the gap. We want to give students the introduction to higher math that we always wanted, and we believe this introduction is accessible even to children. Our introduction is ...

+ unlike traditional college courses

Advanced college math courses tend to assume the student is somehow already acquainted with the culture in which the subject was produced. The courses focus on rigor and abstraction, without motivating why anyone would value such things in the first place. In our courses, we put students in the position to observe the phenomena behind each theorem, just like the first mathematicians who stumbled upon it. By doing so, students see for themselves why the phenomena was worth describing so carefully.

+ unlike curricula focused on problem solving

The communities which use such curricula tend to value speed and are highly competitive. Whether or not you share these values, you still might ask: Is that what professional mathematicians value? The answer is no. Research mathematics is highly collaborative, and mathematicians can spend years, decades or even a lifetime thinking about a problem - with most of their time spent in the dark. In our courses, we work together to explore the ideas proposed by students. This yields many dead ends with no guarantee of success, but this makes the successes all the sweeter (an experience unlike solving a human-designed contest problem). And in the process students learn much more than math - they gain insight into what it's actually like to be a research mathematician and they learn how to share their technical ideas in a convincing and respectful manner.

Also, the curricula of such communities often consists of an erratic sequence of topics and techniques, without any story weaving them together. In our courses, we connect the material to major themes running through mathematics, so students see the subject not as a disconnected set of topics, but as different parts of a whole.

+ unlike coding schools

Coding schools tend to focus on contrived questions (e.g. Can you make the robot dance?). In our classes, students learn how just a few lines of Python code allows them to quickly get answers to their own questions. They see that learning to code is like strapping on an iron-man suit for mathematicians - it enhances their own skill to notice patterns and formulate and test conjectures. With skill in coding, they can accomplish in 10 minutes what took great mathematicians months with pencil and paper. And even if coding isn't their passion, they will still get to observe what a powerful tool it is, and collaborate with others using a different toolkit.