Conclusion

Without exaggeration, this was the busiest summer of my life thus far. When I entered this project, I had no idea of what to expect. To repeat my earlier point, the term “math research” sounds almost oxymoronic, what is there to research about numbers? What I didn’t realize at the time was just how fast possibilities can blow up. What may seem manageable with “only” a million cases to test by computer can jump well out of the range of feasibility with the addition of one more variable to consider, so it’s not possible to simply have a computer to try all your theories. Most of my time was spent on how to narrow down the search space for our theories, bringing it down from 2^50 to 2^30 to a few hundred billion to a few hundred million, from something solvable in decades to something solvable in days or hours.

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Post 3: The method

In the previous post, I laid out two routes that we explored over the course of our project: reverse-engineering an existing graph to find a similar graph that corresponds to a generalized quadrangle, and assuming the existence of an ovoid in order to adapt an existing search method. I’ll go over what I did for each of these, and I’ll start out by mentioning that all my code is available in my GitHub repository, which I’ll link at the end. Like my last post, I will be leaving out some of the more technical details that complicate the explanation without offering any important context or information in return.

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Post 2: The math of quadrangles

In this section, I’ll try to explain the mathematical ideas behind my project topic. But to keep things readable (this is a blog post, not a textbook), I’m going to sacrifice some thoroughness in favor of clarity. That is to say, I’m going to gloss over a lot of details so you don’t need a math degree to read this.

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Post 1: Where have I been?

So, I started my research on June 10. This, my first blog post, was written (is being written?) on July 3. That makes it… 23 days since I started. The question now becomes, “Where in the world have you been?”

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