Somewhere on Earth right now, two exactly opposite points share one weather reading
Take any moment in time. Earth's surface is a sphere, and temperature and air pressure both vary continuously across it. Is there any guarantee that two points on exactly opposite sides of the planet, antipodes, ever have identical temperature and identical pressure at the very same instant?
Reveal the answer
Yes, always, guaranteed by the Borsuk-Ulam theorem, proved by Karol Borsuk in 1933 after a conjecture credited to Stanislaw Ulam. The theorem says any continuous function mapping a sphere's surface to the plane must assign the same value to at least one pair of antipodal points, and since temperature and pressure together act as exactly such a function, somewhere on Earth, right now, two points on opposite sides of the globe match on both at once.
— Karol Borsuk, Borsuk-Ulam theorem — Fundamenta Mathematicae, 1933