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Helen Maria Bayly (1804-1869) was the wife of Irish mathematician William Rowan Hamilton. They married in 1833. Little appears to be known of Bayly other than in connection to Hamilton.

Bayly was born in County Tipperary, the daughter of Rev Henry Bayly, the rector of Nenagh, into what was described as an 'old' family. She met Hamilton at Dunsink Hill near Dublin, which was the site of an observatory, where Hamilton resided. It is thought that Bayly may have been visiting her sister at the time . She married Hamilton in Ballinaclough parish church in 1833, and they spent their honeymoon at Bayly Farm, the Bayly family home. It is widely reported that Hamilton spent most of his time during the honeymoon perfecting his theory of rays, though Bayly's occupation goes unrecorded. Bayly Farm remains standing, and offers bed and breakfast accommodation.

Early commentators were critical of the match, asserting that Bayly lacked the wifely qualities required to manage Hamilton's tempestuous character. Alexander MacFarlane, in 1916, wrote:

:"The kind of wife which Hamilton needed was one who could govern him, and efficiently supervise all domestic matters; but the wife he chose was, from weakness of body and mind, incapable of doing it."

Bayly's attempts at domestic order may have been impeded, to some extent, by Hamilton's character. For example, concerning his study

:any invasion of the domestics, with a view to tidying up, would throw the mathematician, as we are informed, into a good honest thundering passion.

In the early years of their marriage, their home was described as

:a centre to which his high and various endowments of its occupant have attracted, not only the scientific stranger, but numbers from a wide circle, whose moral and intellectual tendencies have been of a congenial nature

Hamilton described Bayly as "not at all brilliant".

Bayly had three children with Hamilton: two sons, William and Archibald, and one daughter, also named Helen. The younger Helen went on to marry Archdeacon Patrick O'Regan.

The nature of Bayly's marriage, particularly in later years, is a subject of some controversy amongst biographers. Many comment on her repeated absences from the family home, leaving their children in the care of her husband, though the circumstances surrounding these absences are unclear. They seem in part to be due to Bayly caring for her ailing mother. Those who have studied Hamilton's private papers often claim that the marriage was close, evidenced in letters Bayly received from her husband during her sickness and absence. During one of her periods of absence, a sister-in-law took charge of their family home.

Bayly's absences from the public society of her husband (due, in part, to her illnesses and caring duties) were a matter for discussion amongst his colleagues. She was described by one as an "abstract idea".

During one of her absences, Bayly's husband initiated correspondence with a former love, Catherine Disney, which came to a head when Disney confessed to her own husband. Friends of Hamilton are reported to have suspected that Bayly long knew that she was not Hamilton's primary focus of romantic attention. Disney left her husband as a result of the confession, though they were never officially separated, and Hamilton continued the correspondence, often through other members of the Disney family. Disney unsuccessfully attempted suicide. Around this time, Hamilton took to drink, as Bayly's absences became more extended. Contemporaries of Hamilton saw this addiction as evidence of a lack of Bayly's regulation of Hamilton. Later, Hamilton continued to write to Disney's family even after Catherine's death. One of his letters was discovered by Bayly, which led to an argument.

Bayly accompanied her husband when he made the famous discovery of the multiplication of quaternions. According to a letter Hamilton wrote to their eldest son:

:your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind

Hamilton died in 1865. Bayly outlived her husband by four years. She received many letters of condolence from prominent mathematicians and astronomers.