Hypertree divisors on the Grothedieck--Knudsen moduli space of stable rational curves with n marked points were introduced by Castravet and Tevelev to study its birational geometry. These divisors have determinantal equations, which, quite mysteriously, appear in the work of Arkani-Hamed, Bourjaily, Cachazo, Postnikov and Trnka as numerators of scattering amplitudes (also known as S-matrices) for n massless particles in 4-dimensional supersymmetric Yang--Mills theory.  Rather than being a  coincidence, this turns out to be just the tip of the iceberg of amusing relations between geometry of Riemann surfaces and high energy physics. In this talk, directed towards general audience, we will go on a tour of old and new results in algebraic geometry inspired and reinterpreted by scattering amplitudes.