Abraham Lincoln used geometry to make better arguments. Google uses geometry to hide or promote websites. And U.S. political parties use it to tip elections in their favor. In his new book Shape, mathematician Jordan Ellenberg exposes the geometric underpinnings of logic, science, and politics. A former child prodigy who aced the SATs at age 12, Ellenberg argues that clever use of math and geometry is helping corrupt American democracy, but mathematicians might still be able to save it.