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History of Mathematics: Evergreen Journey from Stone Age to AI

History of Mathematics: Evergreen Journey from Stone Age to AI Click to Read From Beginning  Post - 14 ....Continuation From Post - 13 Click to Read Previous Post CHAPTER 7   Mathematics in the 21st Century   The 21st century has witnessed profound achievements in mathematics, particularly in complexity theory, chaos theory, and the development of artificial intelligence. Mathematicians and scientists have unraveled the intricacies of complex systems, revealing the underlying order within chaos. Simultaneously, AI technologies have advanced at an astonishing pace, with mathematics serving as the foundation for machine learning, deep learning, and data-driven decision-making. This century has been characterized by the exploration of complex systems, the understanding of chaotic phenomena, and the integration of mathematical principles into AI technologies. In this comprehensive exploration, we will delve into these pivotal areas of mathematical achievement in the 21st century, w

History of Mathematics: Evergreen Journey From Stone Age to AI

 Evergreen Journey of Mathematics: From Stone Age to AI Click to Read From Beginning  Post -13 ....Continued From Post - 12 Click to Read Previous Post Non-Euclidean Geometries: Beyond Euclidean Space: The development of non-Euclidean geometries challenged the long-standing assumption that Euclidean geometry was the only valid system for describing the properties of space. Mathematicians like J├ínos Bolyai, Nikolai Lobachevsky, and Bernhard Riemann explored geometries that departed from Euclid's axioms, opening up new avenues of mathematical exploration. Hyperbolic geometry, developed independently by Bolyai and Lobachevsky, proposed a geometry in which the parallel postulate does not hold. In hyperbolic space, the sum of angles in a triangle is less than 180 degrees, and an infinite number of parallel lines can pass through a point not on a given line. Non-Euclidean Geometry Riemannian geometry, formulated by Bernhard Riemann, introduced the concept of curved spaces, challenging t