The article explores the complex world of modular forms, mathematical functions with symmetrical properties that fill the upper half of the complex plane. It discusses how these forms, first studied in depth by German mathematician Erich Hecke, can be used to solve problems like determining the number of ways an integer can be expressed as the sum of four squares. The article also highlights the role of modular forms in generating functions, which are used in mathematics and physics to encode questions of interest.
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