National Classics Week Packet National Classics Week Packet | Page 8

Math

In 1960 , the physicist Eugene Wigner published a paper titled “ The Unreasonable Effectiveness of Mathematics in the Natural Sciences ,” in which he discusses how certain topics in pure mathematics can surprisingly be used in applied mathematics .

One such topic is prime factorization . This is the process of decomposing a number into the product of its prime factors . As an example , 864 can be rewritten as 2^5 × 3^3 .

An early mathematician dedicated to studying prime factorization was Eratosthenes , an ancient Greek scholar who lived during the third century BC . You might recognize him for his famous Sieve of Eratosthenes , a method for determining a list of prime numbers from a table of integers . This method was first documented and attributed to Eratosthenes in the Introduction to Arithmetic by Nichomachus of Gerasa , who lived in the first century AD .

The method for the Sieve is rather simple and can be expanded to as large a number as needed . The result is achieved by repeatedly marking multiples of prime numbers as composite until only prime numbers are left . Starting with 2 ( which is prime ), one would mark off 4 , 6 , 8 , and so on as they are all divisible by 2 .