Beck was born in Schnenectady, New York to a family of English descent. He graduated from Union College at the age of 16 and the Columbia University College of Physicians and Surgeons with a M.D. at the age of 20 before going into practice in Albany in 1811. In 1815 he was appointed professor of the institutes of medicine, and lecturer on medical jurisprudence in the College of Physicians and Surgeons of Western New York, at Fairfield. He served as the Principal of The Albany Academy from 1817 to 1848, where he encouraged the future curator of the Smithsonian Institution, Joseph Henry, to enroll as a student and later serve as a professor of mathematics and natural philosophy in 1826. Also during this time, he was a professor of medical jurisprudence at Fairfield Medical College from 1826 until 1836, and professor of materia medica in that institution from 1836 till 1840, and at Albany Medical College from 1840 util 1854. In 1823, while secretary of the Society for the Promotion of Useful Arts (SPUA), he founded the Albany Lyceum of Natural History, which focused on the preservation of mineral and botanical specimens collected in New York State surveys. The following year, SPUA and the Albany Lyceum of Natural History merged to form the Albany Institute; Stephen Van Rensselaer III was appointed its President and Beck was appointed its Vice President. He was chosen President of the New York State Medical Society in 1829, and became a manager of the state lunatic asylum before becoming President of the Board of Managers in 1854. During his service, he collected statistics on deaf-mutes, which influenced the legislature to pass laws for the education of the mentally ill. In addition, from 1849 to 1853 he edited the American Journal of Insanity. His principal work was Elements of Medical Jurisprudence; the first edition was printed in 1823, a seventh edition was issued in London in 1842, and a tenth in Albany in 1850. Dr. Beck also contributed to numerous scientific journals during his lifetime.