Geometry and number theory are related in several ways, including:
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This area of number theory uses geometry to study algebraic numbers. It involves studying lattices, which are repeating sets of points in a plane or higher dimensions.
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This field of mathematics studies polynomial equations with multiple unknowns and their solutions in real, rational, or complex numbers. It's closely related to number theory, and understanding the geometry of varieties defined by polynomial equations is important for studying their integral solutions.
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This area of mathematics applies algebraic geometry techniques to number theory problems. It's centered around Diophantine geometry, which studies the rational points of algebraic varieties.
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This geometric object was developed around 2010 by Fargues and Jean-Marc Fontaine. In 2014, Fargues and Scholze adapted the curve to Scholze's theory, collapsing the boundary between numbers and geometry.
