You see Saturn's rings. She sees hidden number theory. - Harvard Gazette

"To find equations that predict real-world systems such as planetary motion, DeMarco researches sequences of numbers that are generated recursively. Perhaps the most best-known example is the Fibonacci sequence, a linear recursion in which each number is the sum of the two numbers that came before it, starting with 0 and 1. Visual representations of the Fibonacci sequences appear in the natural world - for example, in the scales of pine cones, in pineapple fruitlets, and in the structure of nautilus shells."

""It turns out there's a lot of hidden number theory in the planets' very motion, for example, in the structure of the rings around Saturn," explained DeMarco, Radcliffe Alumnae Professor at Harvard Radcliffe Institute and a professor of mathematics in the Harvard Faculty of Arts and Sciences. There are places asteroids simply cannot be, she went on, because of the underlying number theory that "prohibits certain behavior.""

Dynamical systems reveal number-theoretic constraints that shape celestial behavior, producing gaps in the asteroid belt and structured ring patterns. Recursive numerical sequences, both linear and nonlinear, model real-world processes and can encode geometric features seen in nature. The Fibonacci sequence exemplifies how simple linear recursion underlies spirals and phyllotaxis in pine cones, pineapples, and nautilus shells. More complex nonlinear recursions appear in chaotic systems such as planetary motion, weather, and population dynamics. Studying how numerical interactions force geometry illuminates when and where certain behaviors are prohibited, connecting abstract mathematics with observable physical patterns.

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