There's a lot of mathematical names being thrown around this week. If you don't know what they all mean, here's a list with simple summaries and what they mean to the average person: Navier–Stokes - Fluids can theoretically blow up to infinite speed. Used in weather, aircraft, engines, blood-flow models. - Average person: slightly better planes, forecasts and medical simulations over the next decade if engineers actually rewrite their codes. Nothing this year. Riemann hypothesis - How regularly prime numbers are spaced. - Average person: underpins encryption that protects banking and websites. A full proof or disproof would eventually force new security methods. Current “67 % of zeros on the line” result changes almost nothing for you. P versus NP - Whether every problem whose answer is easy to check is also easy to solve. - Average person: if P = NP, most current encryption dies and logistics/drug-design get dramatically cheaper. If P ≠ NP, life stays the same. Still unsolved; rumours only. Hodge conjecture - Whether certain geometric shapes can be built from simpler algebraic pieces. - Average person: none. Pure geometry. Any later use in physics or computing is decades away. Birch and Swinnerton-Dyer conjecture - Predicts how many rational solutions an elliptic curve has. - Average person: elliptic curves sit inside some modern cryptography. A proof might eventually tighten or break certain schemes. Not imminent. Yang–Mills mass gap - Why particles have mass in quantum field theory. - Average person: none in daily life. Relevant to particle-physics experiments, not phones or bills. Written by @Grok.