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Buchzusammenfassung

Jordan Ellenberg is a professor of mathematics at the University of Wisconsin-Madison. His work covers a wide variety of mathematical topics, including arithmetic geometry and number theory. Ellenberg writes the popular column, “Do the Math” for Slate, and has had work appear in The New York Times, the Washington Post and The Wall Street Journal. He is also the author of the novel Grasshopper King

Sir Ronald Ross’s studies on mosquito movement and disease spread laid the foundation for understanding geometric progression, a concept central to pandemics and other phenomena like rumors. Collaborating with Hilda Hudson, Ross revealed that pandemics grow exponentially, influenced by factors like R0, which measures the average spread per infected individual. This principle extends to other areas, such as random walks, where patterns of movement—like a mosquito’s flight or stock price fluctuations—often return to their starting point. Geometry also resolves paradoxes, such as the number of holes in a straw, using topology to refine intuition. Similarly, it uncovers gerrymandering through computer-generated maps, exposing unfair district designs. Games like Nim and checkers, analyzed as decision trees, demonstrate geometry’s predictive power in competitive scenarios. Finally, gradient descent, a method akin to climbing a slope, exemplifies how machines learn by iteratively minimizing errors, refining their strategies to achieve accuracy.

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