Number theory is the study of whole numbers. It is one of the oldest academic disciplines.
Some of the questions in number theory are relatively easy to understand.
- Can every even integer greater than two be expressed as the sum of two primes?
- Which integers can be the area of a right-angled triangle with integer length sides?
- Are there infinitely many prime numbers p such that p+2 is also prime?
People are sometimes surprised that there is anything left to answer in mathematics. Yet, even seemingly simple questions, such as those above, have remained unanswered for centuries.
One of the most appealing features of number theory is that this apparent simplicity gives rise to lots of different and beautiful ideas. Number theory is not all equations; it is full of symmetry, structure, and unforeseen connections to other branches of mathematics. It also plays a crucial role in the real world: numbers are the language of computers, and how we store, transmit, and encrypt those numbers is of fundamental importance to modern life.