Number theory is the second large field of mathematics that comes to us from the pythagoreans via euclid. Number theory is the mathematical study of the natural numbers, the positive whole numbers such as 2, 17, and 123. International journal of mathematical science education, vol. The systematic study of number theory was initiated around 300b.
Arche, and that the substance of the entire universe is identified with numbers. Greek number theory greek mathematics from 500 bce to 500 ce this second edition is organized by subject matter. Euclid drew attention to the primes by proving that there are infinitely many of them. One form of philosophical theory is a metatheory or metatheory. A metatheory is a theory whose subject matter is some other theory or set of theories.
As we have noted, adding successive counting numbers or positive integers generates triangular numbers and adding successive odd positive integers generates square numbers or. The ancient greeks studied squares, triangular numbers, primes and perfect numbers. Introduction to number theory lecture notes adam boocher 20145, edited by andrew ranicki 20156 december 4, 2015 1 introduction 21. Number theory or arithmetic or higher arithmetic in older usage is a branch of pure mathematics devoted primarily to the study of the integers and integervalued functions. This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. Euclid stated the fundamental theorem of arithmetic. It grew out of undergraduate courses that the author taught at harvard, uc san diego, and the university of washington. Pdf algebraic number theory, 2nd edition by richard a. Despite their ubiquity and apparent sim plicity, the natural integers are chockfull of beautiful ideas and open problems. Number theory introduction the greek concept of number greek number theory was exclusively interested in natural numbers. The pythagorean theorem led mathematicians to the study of squares and sums of squares. German mathematician carl friedrich gauss 17771855 said, mathematics is the queen of the sciencesand number theory is the queen of mathematics. Number is conceived not as a mental abstraction but something which exists in and composes all things. Greek number theory greek mathematics from 500 bce to.