Nicolaus Copernicus (February 19, 1473 – May 24, 1543) was the astronomer who formulated the first modern heliocentric theory of the solar system. His epochal book, De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), is often conceived as the starting point of modern astronomy, as well as a central and defining epiphany in all the history of science.
Among the great polymaths of the Scientific Revolution, Copernicus was a mathematician, astronomer, jurist, physician, classical scholar, Catholic cleric, governor, administrator, military leader, diplomat and economist. Amid Copernicus' extensive responsibilities, astronomy figured as little more than an avocation.
While the heliocentric theory had been formulated
Greek and Muslim savants centuries before Copernicus, his reiteration
sun (rather than the Earth) is at the center of the solar system is
among the most important landmarks in the history of western science.
Galileo Galilei (15 February 15, 1564 – January 8,1642), commonly known as Galileo, was an Italian physicist, mathematician, astronomer and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the "father of modern observational astronomy", the "father of modern physics", the "father of science", and "the Father of Modern Science". Stephen Hawking says, "Galileo, perhaps more than any other single person, was responsible for the birth of modern science."
The motion of uniformly accelerated objects, taught in nearly all high school and introductory college physics courses, was studied by Galileo as the subject of kinematics. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter (named the Galilean moons in his honour), and the observation and analysis of sunspots. Galileo also worked in applied science and technology, inventing an improved military compass and other instruments.
Johannes Kepler (December 27, 1571 – November 15, 1630) was a German Lutheran mathematician, astronomer and astrologer, and a key figure in the 17th century astronomical revolution. He is best known for his eponymous laws of planetary motion, codified by later astronomers based on his works Astronomia nova, Harmonice Mundi, and Epitome of Copernican Astronomy. Before Kepler, planets' paths were computed by combinations of the circular motions of the celestial orbs. After Kepler, astronomers shifted their attention from orbs to orbits—paths that could be represented mathematically as an ellipse. Kepler's laws also provided one of the foundations for Isaac Newton's theory of universal gravitation.
During his career Kepler was a mathematics teacher at a Graz seminary school (later the University of Graz, Austria), an assistant to Tycho Brahe, the court mathematician to Emperor Rudolf II, a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. He also did fundamental work in the field of optics and helped to legitimize the telescopic discoveries of his contemporary Galileo Galilei.
Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of the more prestigious discipline of philosophy). Kepler also incorporated religious arguments and reasoning into his work, motivated by the religious conviction that God had created the world according to an intelligible plan which was accessible through the natural light of reason. Kepler described his new astronomy as "celestial physics," as "an excursion into Aristotle's Metaphysics," and as "a supplement to Aristotle's On the Heavens," transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics.
Sir Isaac Newton, (January 4, 1643 – March 31, 1727) was an English physicist, mathematician, astronomer, natural philosopher, and alchemist, regarded by many as the greatest figure in the history of science. His treatise Philosophiae Naturalis Principia Mathematica, published in 1687, described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics. By demonstrating consistency between Kepler's laws of planetary motion and this system, he was the first to show that the motion of objects on Earth and of celestial bodies are governed by the same set of natural laws. The unifying and predictive power of his laws was central to the scientific revolution, the advancement of heliocentrism, and the broader acceptance of the notion that rational investigation can reveal the inner workings of nature.
In mechanics, Newton also markedly enunciated the principles of conservation of momentum and angular momentum. In optics, he invented the reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into a visible spectrum. Newton notably argued that light is composed of particles. He also formulated an empirical law of cooling, studied the speed of sound, and proposed a theory of the origin of stars. In mathematics, Newton shares the credit with Gottfried Leibniz for the development of calculus. He also demonstrated the generalized binomial theorem, developed the so-called "Newton's method" for approximating the zeroes of a function, and contributed to the study of power series.
Gottfried Wilhelm Leibniz (also Leibnitz or von Leibniz (July 1,1646 – November 14, 1716) was a German polymath of Sorbian origin, who wrote mostly in Latin and French.
Educated in law and philosophy, and serving as factotum to two major German noble houses (one becoming the British royal family while he served it), Leibniz played a major role in the European politics and diplomacy of his day. He occupies an equally large place in both the history of philosophy and the history of mathematics. He invented calculus independently of Newton, and his notation is the one in general use since. He also invented the binary system, foundation of virtually all modern computer architectures. In philosophy, he is most remembered for optimism, i.e., his conclusion that our universe is, in a restricted sense, the best possible one God could have made. He was, along with René Descartes and Baruch Spinoza, one of the three great 17th century rationalists, but his philosophy also both looks back to the Scholastic tradition and anticipates modern logic and analysis.
Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in biology, medicine, geology, probability theory, psychology, and information science. He also wrote on politics, law, ethics, theology, history, and philology, even occasional verse. His contributions to this vast array of subjects are scattered in journals and in tens of thousands of letters and unpublished manuscripts. To date, there is no complete edition of Leibniz's writings, and a complete account of his accomplishments is not yet possible.
Leonhard Euler (April 15, 1707 – September 7, 1783) was a Swiss mathematician and physicist, who spent most of his life in Russia and Germany.
Euler made important discoveries in fields as diverse as calculus, and topology. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also renowned for his work in mechanics, optics, and astronomy.
Euler is considered to be the preeminent mathematician of the 18th century and one of the greatest of all time. He is also one of the most prolific; his collected works fill 60–80 quarto volumes. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is a master for us all".
Euler was featured on the sixth series of the Swiss 10-franc banknote and on numerous Swiss, German, and Russian postage stamps. The asteroid 2002 Euler was named in his honor. He is also commemorated by the Lutheran Church on their Calendar of Saints on May 24.
Carl Friedrich Gauss (April 30,1777 – 23 February 23, 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. Sometimes known as "the prince of mathematicians" and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians.
Gauss was a child prodigy, of whom there are many anecdotes pertaining to his astounding precocity while a mere toddler, and made his first ground-breaking mathematical discoveries while still a teenager. He completed Disquisitiones Arithmeticae, his magnum opus, at the age of twenty-one (1798), though it would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.