Quaternions and applications

In 1805 a truly remarkable mathematician was born in Dublin, Ireland. This man eventually became one of the most influential mathematicians of the 19th century. He was Sir William Hamilton. This childhood prodigy would have a profound influence on many fields of mathematics and physical sciences. In this paper his greatest legacy is going to be explored: that of quaternions. Hamilton believed that his invention of the quaternion; a hypercomplex set of numbers representing space-time; held the key to the future of mathematical physics. Although Hamilton's belief in his invention never wavered, it was not until the middle of this century that his achievement was recognized as having true merit, with the advent of quantum mechanics and special relativity. Although quaternions hasn't and probably never will become the predominant mathematical method of physics; his early work and the invention of quaternions influenced and fostered the modern vectorial calculus we use today. In these and many other fields Hamilton's works still influence today and most certainly will into the next century.