Summer of Math Exposition

Might be good as a paper on magic squares (idk, I don’t know anything about them), but not as educational material. No fun, just formula after formula, and no reason provided to care about the topic.

While this is fine as a math paper, I don’t think it does a great job in communicating the idea in a manner that would maintain attention, especially of those with minimal knowledge of the subject matter.

1. Written as a math paper in LaTeX is great for proofs but generally not great for communicating to a general audience.

2. The introduction begins immediately with skipping a step. “The following is obtained from empirical observation”… but it is not clear how it is obtained. It could be explained further. Additionally, I seem to be missing something as the paper mentions to take the values as roots of a polynomial. For instance, the first row is [2,7,6] and proceeds to say it is the roots of the polynomial (x+2)(x+7)(x+6). But 2,7,6 are roots of the polynomial (x-2)(x-7)(x-6). The math in the paper seems to follow appropriately so it may be an issue in terminology.

3. I think just overall it’s too much formula and calculations and I think steps should have been taken to communicate why steps are being taken to communicate this in a more captivating matter. The material looks interesting enough that it could be captivating with some nice visualizations.

4. More of a nitpick but numbers are randomly underlined - though I think it may be just formatted as a fraction with no denominator. It’s a good idea to clean up the formatting when submitting the final product.

Anyway overall good idea, and the base of it is interesting. You have the foundation set up and it would be much more memorable with some additional work. However in regards to the guidelines, I unfortunately have to score low.

Motivation: “Is it clear by the end of the introduction why one should care for the topic?”, I don’t think it’s fulfilled. It takes me onto the journey immediately, and I would say the introduction isn’t really an introduction but a start.

Clarity: “Would the explanations make sense for the target audience?” It would make sense to some.

Novelty: “Is there something unique to this entry which would make it worth sharing? It could have its own unique style, or a new way of presenting a common topic, or it could be surfacing an otherwise obscure idea which more people should know about.” I do not think the format itself being a mathematical paper is novel. The idea itself may be novel but I believe there should be an explanation on the importance of this formula and what insight it may give in order to provide novelty to this paper.

Memorability: “Is there a takeaway the audience would easily remember weeks later?” Mostly due to the format of it being a mathematical paper, I do not think this would be memorable.

I don’t want to be too tough, it’s a great job to submit and get something out there! Keep it up!

• Interesting idea to use $ab+ac+bc$ (sum of pair products), but no justification or heuristic arguments are given as to why this expression is useful for finding magic squares. In the first example, 2 7 6 9 5 1 4 3 8, the first and last rows match with each other in sums of pair products, but not with the middle row. Same with the columns. It is not explained why this pattern should hold true for other 3x3 magic squares or how it should generalize to larger sizes.
• Using the polynomial $(x+a)(x+b)(x+c)$ is cumbersome, since we only care about one specific coefficient
• There are too many equations, and they are only referenced with numbers (no names), I have to go back and find each equation when I’m reading
• Did not define what a “valid” magic square is (but I could probably guess from the abstract)

The notations weren’t clear and not consistent, the goals and results weren’t explained clearly. Randomly it switched from algebra containing letters to a calculation containing numbers without explaining which numbers were being substituted. Although the topic was interesting, the presentation was bland.