Mathematician, Educator. He received national acclaim for his ability in mathematics especially geometry, an advanced branch of mathematics that is concerned with the size and shape of objects relative to space. He was one of the nine members of Thomas H. Huxley's, X-Club, a group of scientists that met monthly to share ideas. He was the recipient of the Royal Society's Royal Medal in 1883. Born the youngest of four sons of Thomas and Hannah Oates Hirst, Archer, as he was called, had a financial secured childhood from his grandfather's inheritance and attended excellent schools. In 1844 his father was killed in an accident as a result his mother placed him in trade school; he began as an apprentice engineer. At the age of 15, he started recording in a diary and did this for the rest of his life describing every lecture he attended. As an apprentice, his first task was to work as a surveyor on the proposed railroad line from Halifax to Keighley. His supervisor was John Tyndell. Becoming long-time friends, it was Tyndell that encouraged him to obtain a higher education by reading books and training. In 1884, he enrolled at the Halifax Mechanics Institute but in a short time, turned back to mathematics. After obtaining a monetary inheritance after his mother's death, he followed Tyndell to the University of Marburg in Germany. At first his major was mathematics, physics and chemistry under Robert Bunsen but eventually focused on mathematics receiving a PhD Degree in July 1852. After graduation, he traveled about Germany, France, and Austria listening to lectures given by noted scientists and mathematicians, especially Jakob Steiner. He returned to England in 1852 obtaining a teaching position at Queenwood College after Tyndell's resignation. At the end of 1854, he married Anna Martin. When she became ill with tuberculosis, he resigned his position in 1856 to care for her in the south of France in hope for a cure, but she died in Paris in July 1857. During this time, he was able to finish and publish two papers on mathematics and attend lectures. In August 1858 he traveled to Italy where he became friends with Luigi Cremona of the prestigious Italian school of Algebraic Geometry. Through the years they exchanged correspondence, which, years later, 84 letters from Hirst to Cremona were published. In the summer of 1859 he returned to England and obtained a teaching position at University College School. The following year, he was nominated for a fellowship at the Royal Society and elected as a fellow in 1861. In 1864, he resigned his position at University College School to concentrate on his research. Later that year, he was a founding member, along with Tyndell, of the X-Club, which had an aim to promote science in England. He was elected to the Council of the Royal Society becoming a prominent figure in British Science, which was confirmed by becoming a major figure in forming the London Mathematical Society on November 7, 1864. He became professor of physics at the University College in London in 1865, and a fellow of the Royal Astronomical Society in 1866 as well as being appointed General Secretary of the British Association for the Advancement of Science. In 1867 he accepted the chairman of the mathematics at the University College in London, serving on the organization's executive board for twenty years. In 1869 in the support of women's education, he gave a successful course of twenty-four lectures on the “Element of Geometry” to a group of sixty from the Ladies Educational Association of London. The course syllabus was published becoming a staple tool for teaching. In March 1870, to allow time for research, he requested to be Assistant Registrar of the University College. In January 1871, he founded and was the first president of the Association for the Improvement of Geometrical Teaching, which was involved in reforming the mathematics curriculum in all schools. This was a turning point in teaching mathematics. In 1873 he was appointed as the first Director of Studies at the Royal Naval College in Greenwich. His research had been mainly geometrical, especially expanding Cremona's work. “For his researches in pure mathematics,” he received the Royal Medal in 1883 before resigning from Greenwich at the age of 53. At this point, his health started to decline as he was diagnosed with renal calculi, a stomach tumor, cancer of the prostate, and depression from the death of his brother. On January 18, 1892, his last entry to his diary was made, and four weeks later, he died during a influenza epidemic. To his credit, he published and edited numerous papers, along with translating others from German to English, but he burnt many of his notebooks. A tall, straight-back man, he was described as having a devoted passion for mathematics, a Victorian English gentleman who was well-mannered and kind, very patient, and had a love for the simple things in life.