William Rowan Hamilton

A Quaternion Walk

Stone carving in Dublin

through Dublin, Ireland

Hamilton struggled for many years to find rules for multiplication of imaginary numbers in three dimensions in such a way as to be consistent with the properties of abstract algebra. He could not define multiplication of triplets in a manner that would preserve the properties of ordinary complex numbers. In particular, division, the inverse operation of multiplication, failed. He described his difficulties as "metaphysical stumbling blocks."

Thus, his "flash of genius" was based upon many years of futile investigations of triplets of hypercomplex numbers. He suddenly realized that by using four couples of imaginary numbers both the philosophical and algebraic conflicts could be solved. He called his new system quaternions.

This carving is on the wall behind the ivy to your left in the picture of the bridge.

Trinity College Dublin has honored Hamilton in a number of significant ways. His bust is among a collection of great scholars in the Long Room of the Old Library.

The Hamilton Building is one of the newest buildings on campus.

From the notebook in which Hamilton
first entered his ideas on how to formulate quaternions.

See:
<http://www.maths.may.ie/quat.html> .

See pp. 103 -105 for his publication on Quaternions.

For a biography:
Thomas L. Hankins, William Rowan Hamilton,
The Johns Hopkins University Press, 1980.

< http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.html >
< http://www.maths.tcd.ie./pub/HistMath/HistMath.html >