The Birthday of August Möbius (1790)

August Möbius discovered the Möbius strip (non‑orientable surface) and the Möbius function μ(n) in number theory. μ(n) = 0 if n has a squared prime factor, else (–1)ᵏ where k is number of prime factors. Möbius inversion: g(n) = Σ_{d|n} f(d) ⇔ f(n) = Σ_{d|n} μ(d) g(n/d). This is a cornerstone of multiplicative number theory, used in the proof of the prime number theorem. The Möbius function also appears in the Riemann hypothesis (Mertens conjecture). Möbius’s strip is topology; his μ is arithmetic.