Tamarkin was born in Chernigov, Russian Empire (now Chernihiv, Ukraine), to a wealthy Jewish family.
He shares a common ancestor with the Van Leer family, sometimes spelled Von Löhr or Valar.
He died later that year in Bethesda, Maryland, a suburb of Washington, D.C.[3] Tamarkin's work spanned a number of areas, including number theory, integral equations, Fourier series, complex analysis, moment problem, boundary value problem and differential equations.
He was a proponent and a founding co-editor of the Mathematical Reviews (which was based at Brown at that time), together with Otto Neugebauer and William Feller.
He had over twenty doctoral students at Brown, including Dorothy Lewis Bernstein, Nelson Dunford, George Forsythe, Margaret Gurney and Derrick Lehmer.