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Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist. He is best known for his theory of relativity and specifically mass–energy equivalence, expressed by the equation E = mc2. Einstein received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect."

Einstein's many contributions to physics include his special theory of relativity, which reconciled mechanics with electromagnetism, and his general theory of relativity, a new theory of gravitation which added the principle of equivalence to the principle of relativity. His other contributions include the founding of relativistic cosmology with a cosmological constant, the first post-Newtonian expansions for the perihelion advance of mercury and frame-dragging, the deflection of light by gravity and gravitational lensing, an explanation for capillary action, the first fluctuation dissipation theorem which explaned the Brownian movement of molecules, the photon theory and wave-particle duality from the thermodynamic properties of light, the quantum theory of atomic motion in solids, zero point energy, the semiclassical version of the Schrodinger equation, relations for atomic transition probabilities which predicted stimulated emission, the quantum theory of a monatomic gas which predicted Bose-Einstein condensation, the EPR paradox, and a program for a unified field theory by the geometrization of physics.

Einstein published over 300 scientific works and over 150 non-scientific works. In 1999 Time magazine named him the "Person of the Century", and according to Einstein biographer Don Howard, "to the scientifically literate and the public at large, Einstein is synonymous with genius.

Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and the explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.

Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere inscribed within a cylinder. Archimedes had proven that the sphere has two thirds of the volume and surface area of the cylinder (including the bases of the latter), and regarded this as the greatest of his mathematical achievements.

Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. AD 530 by Isidore of Miletus, while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results

Einstein's many contributions to physics include his special theory of relativity, which reconciled mechanics with electromagnetism, and his general theory of relativity, a new theory of gravitation which added the principle of equivalence to the principle of relativity. His other contributions include the founding of relativistic cosmology with a cosmological constant, the first post-Newtonian expansions for the perihelion advance of mercury and frame-dragging, the deflection of light by gravity and gravitational lensing, an explanation for capillary action, the first fluctuation dissipation theorem which explaned the Brownian movement of molecules, the photon theory and wave-particle duality from the thermodynamic properties of light, the quantum theory of atomic motion in solids, zero point energy, the semiclassical version of the Schrodinger equation, relations for atomic transition probabilities which predicted stimulated emission, the quantum theory of a monatomic gas which predicted Bose-Einstein condensation, the EPR paradox, and a program for a unified field theory by the geometrization of physics.

Einstein published over 300 scientific works and over 150 non-scientific works. In 1999 Time magazine named him the "Person of the Century", and according to Einstein biographer Don Howard, "to the scientifically literate and the public at large, Einstein is synonymous with genius.

Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and the explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.

Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere inscribed within a cylinder. Archimedes had proven that the sphere has two thirds of the volume and surface area of the cylinder (including the bases of the latter), and regarded this as the greatest of his mathematical achievements.

Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. AD 530 by Isidore of Miletus, while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results