Born in an Irish Catholic family in Cork, Mathew was educated at the largely Protestant Trinity College, Dublin, before joining the English bar.

The Temperance campaigner Father Theobald Mathew was his uncle, and it was largely due to his representations that the nephew, after receiving his early education at a private school at Cork, was sent at the age of fifteen to Trinity College, Dublin, an unusual step at that period for a member of a Catholic family.

In the meantime he found scope for his debating and argumentative powers at the Hardwicke Society, of which he was one of the founders; and the humour and sarcasm which never forsook him brought him into prominence at the social gatherings of the Home Circuit mess.

He had a strong natural aptitude for the practical side of law, and from the outset of his career at the bar he showed impatience of technicalities and determination to get at the real points at issue.

His services were in especial demand at the now defunct Guildhall sittings, where the heavy City special jury cases were tried, and after the way was cleared by Arthur Cohen being made a Queen's Counsel in 1874, Mathew and Charles Bowen were invariably retained by one side or the other; but in spite of his vast practice as a junior, Mathew steadily refrained from applying to become a QC: a weak and rather harsh voice may have rendered him distrustful of his powers as a leader.

On the criminal side, though his previous experience in that branch of the profession was small, he showed acuteness and broad common sense, with occasionally, as was observed, a slight leaning to the prisoner.

He had always held strong views on the question of costs and of legal procedure, and shortly before his elevation to the bench he had served on a royal commission appointed to inquire into the former subject.

Shortly after the return of the Liberal Party to office in August 1892, Mathew was made chairman of a royal commission appointed to inquire into the case of the evicted tenants in Ireland, with especial reference to their reinstatement and resettlement.

In his new capacity he displayed all his old qualities of accuracy, common sense, and vigour, but he deprecated elaborate arguments and voluminous citation of authorities, the 'old umbrellas of the law,' as he used to call them.

An ardent radical and a devout Roman Catholic, he maintained the happiest relations with many who were vehemently opposed to him in religion and politics; on circuit he was always a welcome visitor at the houses of the dignitaries of the Church of England.