Kakeya problem is a beautiful question, and Besicovitch's construction has been really useful in harmonic analysis (Fefferman's The multiplier problem for the b

Kakeya problem is a beautiful question, and Besicovitch's construction has been really useful in harmonic analysis (Fefferman's The multiplier problem for the ball is a classic example). Still, in the eyes of wider public it must appear uncanny, requiring the Amazon truck analogies, etc. Reminds me of Vladimir Arnold's comment on the state of modern number theory (presumably talking about density of primes in arithmetic progressions, he says): why would you even want to add primes, they were born to be multiplied?