2 May 1737: The British Prime Minister William (Petty) FitzMaurice the Earl of Shelburne was born in Dublin on this day. 

I was born in Dublin in the house of Dr. Hort, then Bishop of Kilmore, afterwards Archbishop of Tuam, in Bride Street, Dublin, who married my mother's sister. I spent the four first years of my life in the remotest part of the south of Ireland, under the government of an old grandfather who reigned, or rather tyrannised, equally over his own family and the neighbouring country, as if it was his family, in the same manner as I suppose his ancestors, Lords of Kerry, had done for generations since the time of Henry II., who granted to our family 100,000 acres in those remote parts in consideration of their services against the Irish, with the title of Barons of Kerry.

Edmond George Petty-Fitzmaurice

Life of William, Earl of Shelburne/Volume 1/Chapter 1 - Wikisource, the free online library

According to his own account, when he entered Oxford in 1755, he had "both everything to learn and everything to unlearn".

He left Oxford in 1757 without taking a Degree & he then served in British Army during Seven Years War. He fought in the expedition to Rochefort in France and saw action at the battles of Minden and Kloster Kamp in Germany where he distinguished himself in action. He was a senior Whig who was the Home Secretary in 1782 and then Prime Minister from July 1782 to April 1783. It was Shelburne's ministry that concluded the peace treaty with the American states, after Rockingham's acknowledgement of the colonies' independence. Shelburne faced opposition from Charles James Fox and Lord North and in March 1783 tendered his resignation, which was accepted. He retired to his estates and never held office again. 

He continued to hold a seat in the House of Lords until his death in 1805. His tenure as PM was of a short duration but he succeeded in securing peace with America and this feat remains his most notable legacy.

‘The 45-year-old ex-premier remained active in Parliament for more than two decades, but not even Pitt, formerly his protégé, wished (or could afford to) offer him major office, especially after Lord Lansdowne (as Shelburne became in November 1784) proved conciliatory to the French revolutionaries and to domestic extra-parliamentary opposition. Lansdowne died in London on 7 May 1805.’

https://history.blog.gov.uk/2015/08/26/william-petty-2nd-earl-of-shelburne-whig-1782-1783/

As for Ireland he had some pronounced views on the value of a Union between Ireland and Britain but he realised that the removal of impediments to the participation of Catholics in political affairs was a political necessity - something though that was not achieved in his lifetime.

'There were many contradictions in Shelburne's character. Although he was one of the most talented politicians of his day, his self-destructive tendencies sabotaged his career. He was unpredictable, autocratic, bad-tempered, and suffered from unpredictable mood swings that made him appear insincere and untrustworthy. Disliked for being ‘un-English’, he became the most despised and unpopular figure in British public life. Samuel Johnson praised him for being ‘a man of abilities and information’ but recognised that he ‘acted like himself, that is, unlike anybody else’...

Many people have struggled to understand Shelburne's unpopularity and the contempt with which his contemporaries regarded him. Benjamin Disraeli considered him to be ‘the ablest and most accomplished statesman of the eighteenth century’ (G.E.C., Peerage, 438), and credited him with many of the younger Pitt's successes. Historians have found little evidence of his notorious duplicity but many examples of his inconsistency.'

https://www.dib.ie/biography/petty-william-a7304

There are a number of landmarks in Dublin that bear the name Shelburne or a variation of it. One of Dublin’s most famous hotels is apparently named after him.

Recent genealogical research would indicate that Catherine, Duchess of Cambridge, (Kate Middleton) is a distant descendant.