Royal Medal in the context of "William Rowan Hamilton"

Charles Robert Darwin (/ˈdɑːrwɪn/ DAR-win; 12 February 1809 – 19 April 1882) was an English naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology. His proposition that all species of life have descended from a common ancestor is now generally accepted and considered a fundamental scientific concept. In a joint presentation with Alfred Russel Wallace, he introduced his scientific theory that this branching pattern of evolution resulted from a process he called natural selection, in which the struggle for existence has a similar effect to the artificial selection involved in selective breeding. Darwin has been described as one of the most influential figures in human history and was honoured by burial in Westminster Abbey.

Darwin's early interest in nature led him to neglect his medical education at the University of Edinburgh; instead, he helped Grant to investigate marine invertebrates. His studies at the University of Cambridge's Christ's College from 1828 to 1831 encouraged his passion for natural science. However, it was his five-year voyage on HMS Beagle from 1831 to 1836 that truly established Darwin as an eminent geologist. The observations and theories he developed during his voyage supported Charles Lyell's concept of gradual geological change. Publication of his journal of the voyage made Darwin famous as a popular author. His first scientific work was The Structure and Distribution of Coral Reefs (1842). Along with his work on barnacles, it won him the Royal Medal in 1853.

William Whewell (/ˈhjuːəl/ HEW-əl; 24 May 1794 – 6 March 1866) was an English polymath. He was Master of Trinity College, Cambridge. In his time as a student there, he achieved distinction in both poetry and mathematics.

The breadth of Whewell's endeavours is his most remarkable feature. In a time of increasing specialisation, Whewell belonged in an earlier era when natural philosophers investigated widely. He published work in mechanics, physics, geology, astronomy, and economics, while also composing poetry, writing a Bridgewater Treatise, translating the works of Goethe, and writing sermons and theological tracts. In mathematics, Whewell introduced what is now called the Whewell equation, defining the shape of a curve without reference to an arbitrarily chosen coordinate system. He also organized thousands of volunteers internationally to study ocean tides, in what is now considered one of the first citizen science projects. He received the Royal Medal for this work in 1837.

John Dalton FRS (/ˈdɔːltən/; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist, and meteorologist whose work laid the foundations of modern atomic theory and stoichiometric chemistry. Building on earlier ideas about the indivisibility of matter and his own precise measurements of combining ratios, Dalton proposed that each chemical element consists of identical atoms of characteristic weight, and that compounds are formed when atoms of different elements combine in fixed whole-number proportions. His A New System of Chemical Philosophy (1808) presented a coherent atomic model, supplied relative atomic weights and symbolic notation, and established the quantitative framework that shaped nineteenth-century chemistry and remains the basis of modern chemical thought.

Dalton was also a pioneering meteorologist and physicist, keeping daily weather observations for over fifty years, formulating the first empirical law of partial pressures (later known as Dalton’s Law), and studying the behavior of gases through his work on vapor pressure and gas solubility. His investigations into his own color blindness led to the first scientific description of the condition—still called Daltonism in several languages—and helped establish experimental methods for linking perception with physiology. Elected a Fellow of the Royal Society in 1822 and awarded its Royal Medal in 1826, Dalton became the first British scientist to develop a quantitative atomic theory and one of the key figures in the transition of chemistry from a qualitative to a mathematical science.

The Darwin Medal is one of the medals awarded by the Royal Society for "distinction in evolution, biological diversity and developmental, population and organismal biology".

In 1885, the International Darwin Memorial Fund was transferred to the Royal Society. The fund was devoted for promotion of biological research, and was used to establish the Darwin Medal. The medal was first awarded to Alfred Russel Wallace in 1890 for "his independent origination of the theory of the origin of species by natural selection." The medal commemorates the work of English biologist Charles Darwin (1809–1882). Darwin, most famous for his 1859 book On the Origin of Species, was a fellow of the Royal Society, and had received the Royal Medal in 1853 and the Copley Medal in 1864.

Terence Chi-Shen Tao FAA FRS (born 17 July 1975) is an Australian and American mathematician. He is a Fields medalist and a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing, analytic number theory and the applications of artificial intelligence in mathematics.

Tao was born to Chinese immigrant parents and raised in Adelaide, South Australia. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014, and is a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers, and is widely regarded as one of the greatest living mathematicians.