**William Rowan Hamilton** was an Irish astronomer and mathematician who discovered the quaternions.

- By the age of five, William had already learned Latin, Greek, and Hebrew.
- William soon mastered additional languages but a turning point came in his life at the age of 12 when he met the American Zerah Colburn.
- Colburn could perform amazing mental arithmetical feats and Hamilton joined in competitions of arithmetical ability with him.
- It appears that losing to Colburn sparked Hamilton's interest in mathematics.
- Hamilton's introduction to mathematics came at the age of 13 when he studied Clairaut's Algebra, a task made somewhat easier as Hamilton was fluent in French by this time.
- Hamilton entered Trinity College, Dublin at the age of 18 and in his first year he obtained an 'optime' in Classics, a distinction only awarded once in 20 years.
- Unfortunately, as he had three years left at Trinity College, Hamilton was not in a position to propose marriage.
- However Hamilton was making remarkable progress for an undergraduate and submitted his first paper to the Royal Irish Academy before the end of 1824, which was entitled On Caustics.
- He was affluent and could offer more to Catherine than Hamilton.
- In his next set of exams William was given a 'bene' instead of the usual 'valde bene' due to the fact that he was so distraught at losing Catherine.
- In 1826 Hamilton received an 'optime' in both science and Classics, which was unheard of, while in his final year as an undergraduate he presented a memoir Theory of Systems of Rays to the Royal Irish Academy.
- It is in this paper that Hamilton introduced the characteristic function for optics.
- Hamilton's finals examiner, Boyton, persuaded him to apply for the post of Royal Astronomer at Dunsink observatory even although there had already been six applicants, one of whom was George Biddell Airy.
- Later in 1827 the board appointed Hamilton Andrews' Professor of Astronomy in Trinity College while he was still an undergraduate aged twenty-one years.
- This appointment brought a great deal of controversy as Hamilton did not have much experience in observing.
- His predecessor, Professor Brinkley, who had become a bishop, did not think that it had been the correct decision for Hamilton to accept the post and implied that it would have been prudent for him to have waited for a fellowship.
- It turned out that Hamilton had made an poor choice as he lost interest in astronomy and spend all time on mathematics.
- Hamilton liked to compare the two, suggesting that mathematical language was as artistic as poetry.
- Hamilton took on a pupil by the name of Adare.
- They were a bad influence on each other as Adare's eyesight started to present problems as he was doing too much observing, while at the same time Hamilton became ill due to overwork.
- It was on this occasion that Hamilton met Lady Campbell, who was to become one of his favourite confidants.
- William also took the opportunity to visit Catherine, as she was living relatively nearby, which she then reciprocated by coming to the observatory.
- Hamilton was so nervous in her presence that he broke the eyepiece of the telescope whilst trying to give her a demonstration.
- Hamilton thought this was her way of discouraging him tactfully and so he ceased to pursue her.
- Catherine aside, Hamilton seemed quite fickle when it came to relationships with women.
- William told Aubrey that she was "not at all brilliant" and, unfortunately, the marriage was fated from the start.
- They spent their honeymoon at Bayly Farm and Hamilton worked on his third supplement to his Theory of Systems of Rays for the duration.
- In 1832 Hamilton published this third supplement to Theory of Systems of Rays which is essentially a treatise on the characteristic function applied to optics.
- This Lloyd did two months later and this theoretical prediction brought great fame to Hamilton.
- On 4 November 1833 Hamilton read a paper to the Royal Irish Academy expressing complex numbers as algebraic couples, or ordered pairs of real numbers.
- In this paper Hamilton gave his first statement of the characteristic function applied to dynamics and wrote a second paper on the topic the following year.
- Hamilton presented his arguments with great economy, as usual, and his approach was entirely different from that now commonly presented in textbooks describing the method.
- In the two essays on dynamics Hamilton first applied the characteristic function VVV to dynamics just as he had in optics, the characteristic function being the action of the system in moving from its initial to its final point in configuration space.
- For conservative systems, the total energy HHH was constant along any real path but varied if the initial and final points were varied, and so the characteristic function in dynamics became a function of the 6n coordinates of initial and final position (for nnn particles) and the Hamiltonian HHH.
- The year 1834 was the one in which Hamilton and Helen had a son, William Edwin.
- Helen then left Dunsink for nine months leaving Hamilton to fight the loneliness by throwing himself into his work even more.
- In 1835 Hamilton published Algebra as the Science of Pure Time which were inspired by his study of Kant and presented to a meeting of the British Association for the Advancement of Science.
- Hamilton was knighted in 1835 and that year his second son, Archibald Henry, was born but the next few years did not bring him much happiness.
- Hamilton felt this discovery would revolutionise mathematical physics and he spent the rest of his life working on quaternions.
- Shortly after Hamilton's discovery of the quaternions his personal life started to prey on his mind again.
- In 1845, Thomas Disney visited Hamilton at the observatory and brought Catherine with him.
- This must have upset William as his alcohol dependency took a turn for the worse.
- The following year Catherine began writing to Hamilton, which cannot have helped at this time of depression.
- Hamilton wrote to Barlow and informed him that they would never hear from him again.
- Hamilton persisted in his correspondence to Catherine, which he sent through her relatives.
- It is no surprise that Hamilton gave in to alcohol immediately after this, but he threw himself into his work and began writing his Lectures on Quaternions.
- Perhaps Hamilton's lack of skill as a teacher showed up in this work.
- Hamilton went straight to Catherine and gave her a copy of Lectures on Quaternions.
- Determined to produce a work of lasting quality, Hamilton began to write another book Elements of Quaternions which he estimated would be 400 pages long and take 2 years to write.
- The title suggests that Hamilton modelled his work on Euclid's Elements and indeed this was the case.
- Not everyone found Hamilton's quaternions the answer to everything they had been looking for.
- Hamilton died from a severe attack of gout shortly after receiving the news that he had been elected the first foreign member of the National Academy of Sciences of the USA.

Born 4 August 1805, Dublin, Ireland. Died 2 September 1865, Dublin, Ireland.

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