What, if anything, does sports gear have in common with the field of mathematics? And, even more to the point, what role did a Swiss mathematician living in the 1700s play in the creation of the decidedly modern, 21st-century football helmet?

Actually, quite a bit.

Last month, there was news about the launch this spring of a “revolutionary” new helmet, designed to absorb impact forces more effectively.

Revolutionary maybe, but inventors of this cutting-edge headgear drew, at least, some of their inspiration from the 18^{th} century master of mathematical sciences—the mathematician and physicist Leonhard Euler (1707–1783).

In fact, some of the principles he formulated still form the basis of structural engineering. For instance, in 1757, he derived the Euler buckling formula, which allowed engineers to design compression elements.

Perhaps not as well known to the general public as Isaac Newton, Euler is nevertheless considered to be one of the founders of pure mathematics, as well as an important contributor to modern analytic geometry, trigonometry, calculus, differential equations, number theory, and notational systems. With over 880 books and papers to his name, he is still among the most prolific writers of mathematics in history.

Among his accomplishments is also the eponymous Euler’s Identity theorem (e^{iπ} + 1 = 0), which the late physicist Richard Feynman called “the most remarkable formula in mathematics.”

Numerous other concepts were named after him as well: Euler’s constant, Euler’s polyhedron formula, the Euler line of a triangle, Euler’s equations of motion, Eulerian graphs, Euler’s pentagonal formula for partitions, and many others.

Add to the line-up a concussion-resistant helmet, and Euler’s legacy is truly multi-disciplinary.

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