#womenscreativity

t A paper posted on February 10 left the math world by turns stunned, delighted and ready to welcome a bold new talent into its midst. Its author was Hannah Cairo, just 17 at the time. She had solved a 40-year-old mystery about how functions behave, called the Mizohata-Takeuchi conjecture.

“We were all shocked, absolutely. I don’t remember ever seeing anything like that,” said Itamar Oliveira of the University of Birmingham, who has spent the past two years trying to prove that the conjecture was true. In her paper, Cairo showed that it’s false. The result defies mathematicians’ usual intuitions about what functions can and cannot do.

British aerodynamicist Hermann Glauert’s original 1935 model helped determine how much power a wind turbine could theoretically produce. But while the equation gave an upper limit to power, it left out crucial forces that turbines face every day—like the strong wind pushing against the blades and the pressure that causes them to bend. Tyagi’s work solves this shortfall, making it easier to design turbines that are not only efficient but also strong enough to withstand these forces over time.

Tyagi’s breakthrough came by applying calculus of variations, a tool often used to solve complex optimization problems. Her refined method builds on Glauert’s model but goes further. It calculates exact values for both the force pushing on the rotor (thrust) and the torque that causes blades to twist (bending moment). These new integrals work across the full range of tip speed ratios—how fast blade tips move compared to wind speed—which is vital for modern turbine design.