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Mathematician Nikolai Ivanovich Lobachevsky is renowned for his groundbreaking work in non-Euclidean geometry. He challenged the centuries-old Euclidean axioms, proposing that parallel lines could diverge and that the sum of angles in a triangle could be less than 180 degrees. Lobachevsky's groundbreaking ideas laid the foundation for modern geometry and its applications in fields such as physics and cosmology.