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Finally, we are excited to start a new column: How Euler Could Have Done It. In the first installment, frequent contributor Alexander Aycock explores how Euler’s work in analytic number theory could have been assembled into a direct proof of the
functional equation for the Riemann zeta-function.

In our Articles & Notes section, Shigeki Matsutani examines Euler's original derivation for the elastica equation, in which we see how Euler anticipated Emmy Noether's theorem on the translational symmetry of elastica.

Sylvio Bistafa presents an article-translation for "Dilucidationes de resistentia fluidorum" (E276) where Euler critiques Newton and d'Alembert's fluid resistance theories. After surveying the key contributions of this work, Bistafa gives a translation produced in conversation with ChatGPT.

In Julian Schennach's translation of Euler’s "Subsidium calculi sinuum" (E246), Euler uses de Moivre's formula to derive a collection of trigonometric identities and infinite series expressions.

Jonathan David Evans presents a translation of Euler's sizable 1750 paper "De numeris amicabilibus" (E152), in which Euler introduces the sum-of-divisors function and uses it to find around 60 new pairs of amicable numbers.

Langton also includes a reader’s guide to this work:

In Stacy Langton's translation of "Observationes de seriebus" we find a young Daniel Bernoulli developing a theory of linear recurrence relations to solve polynomial equations numerically and prove an early form of De Moivre's Theorem.