Transformation of biological species from one to another through many generations was a radical thesis proposed by Jean-Baptiste Lamarck in 1809 and forcefully opposed by Charles Lyell in 1832. Lyell, with Carl Linnaeus and others, believed that species, once created, have distinguishing characters in common that remain the same and never vary. In the Origin of Species in 1859 Charles Darwin supported and extended the thesis of Lamarck and contradicted the reactionary antithesis of Lyell. The debate between "transformationists" and "punctuationists" extends to the present day. The "Modern Synthesis" of evolution in the mid-19th century was at best a partial synthesis, with "quantum evolution" proposed to describe and explain rapid shifts of species from one equilibrium state to another. J. B. S. Haldane calculated very slow rates of evolutionary change from the fossil record and raised the possibility of micromutation as an alternative to natural selection to explain long-term evolution. The challenge before us is reconciliation of the Lamarck-Darwin thesis of slow gradual change in species with the Lyell-Linnaeus antithesis involving mysterious origins followed by stasis.