Number theory
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Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers, or defined as generalizations of the integers.
The Plimpton 322 tablet
Leonhard Euler
"Here was a problem, that I, a ten-year-old, could understand, and I knew from that moment that I would never let it go. I had to solve it." —Sir Andrew Wiles about his proof of Fermat's Last Theorem.
Arithmetic
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Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms.
Calculations in mental arithmetic are done exclusively in the mind without relying on external aids.
Abacuses are tools to perform arithmetic operations by moving beads.
Some historians interpret the Ishango bone as one of the earliest arithmetic artifacts.
Image: Vlčí radius