Solving the World's Hardest Magic Square

Ethan Brown does the most impressive magic square. I don’t know anyone else in the world who can do what he does.
— Dr. Arthur Benjamin, Mathemagician
I was at breakfast with Ethan and his family, and he whipped out one of his magic square cards. He blew my mind right there! I still don’t know how he does it.
— Jay Novella, Skeptics Guide to the Universe

Though most audiences with an intermediate mathematical understanding will be able to follow this talk, it is best suited for crowds at mathematics conventions. Ethan starts this 15 minute presentation in performance mode; he energetically and humorously shows the audience his magic square. Any general audience will be wondering "how did he do it?" but any mathematically minded audience will think, "how is that mathematically possible?". Ethan then reveals his technique, going through many magic square algorithms and touching upon some combinatorics and linear algebra concepts during this explanation.

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Performing my magic square for Penn Jilette, Teller, Jason Segel, and Will Shortz

Ethan’s magic square is nothing short of amazing. The only drawback is that it makes me painfully aware that Ethan is much smarter than I am.
— Joey Styles, World Wrestling Entertainment