Mathematician in the context of Frigyes Riesz

Alfred North Whitehead OM FRS FBA (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He created the philosophical school known as process philosophy, which has been applied in a wide variety of disciplines, including ecology, theology, education, physics, biology, economics, and psychology.

In his early career Whitehead wrote primarily on mathematics, logic, and physics. He wrote the three-volume Principia Mathematica (1910–1913), with his former student Bertrand Russell. Principia Mathematica is considered one of the twentieth century's most important works in mathematical logic, and placed 23rd in a list of the top 100 English-language nonfiction books of the twentieth century by Modern Library.

Euclid (/ˈjuːklɪd/; Ancient Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.

Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria.

Hipparchus (/hɪˈpɑːrkəs/; Greek: Ἵππαρχος, Hípparkhos; c. 190 – c. 120 BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC.

Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians and by Meton of Athens (fifth century BC), Timocharis, Aristyllus, Aristarchus of Samos, and Eratosthenes, among others.

Claudius Ptolemy (/ˈtɒləmi/; Ancient Greek: Πτολεμαῖος, Ptolemaios; Latin: Claudius Ptolemaeus; c. 100 – 160s/170s AD), better known mononymously as Ptolemy, was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine, Islamic, and Western European science. The first was his astronomical treatise now known as the Almagest, originally entitled Mathēmatikḗ Syntaxis (Μαθηματικὴ Σύνταξις, Mathēmatikḗ Syntaxis, lit. 'Mathematical Treatise'). The second is the Geography, which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatika (Αποτελεσματικά, 'On the Effects') but more commonly known as the Tetrábiblos (from the Koine Greek meaning 'four books'; Latin: Quadripartitum).

The Catholic Church promoted his work, which included the only mathematically sound geocentric model of the Solar System, and unlike most Greek mathematicians, Ptolemy's writings (foremost the Almagest) never ceased to be copied or commented upon, both in late antiquity and in the Middle Ages. However, it is likely that only a few truly mastered the mathematics necessary to understand his works, as evidenced particularly by the many abridged and watered-down introductions to Ptolemy's astronomy that were popular among the Arabs and Byzantines. His work on epicycles is now seen as a very complex theoretical model built in order to explain a false tenet based on faith.

Apollonius of Perga (Ancient Greek: Ἀπολλώνιος ὁ Περγαῖος Apollṓnios ho Pergaîos; c. 240 BC – c. 190 BC) was an ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the earlier contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors Euclid and Archimedes, Apollonius is generally considered among the greatest mathematicians of antiquity.

Aside from geometry, Apollonius worked on numerous other topics, including astronomy. Most of this work has not survived, where exceptions are typically fragments referenced by other authors like Pappus of Alexandria. His hypothesis of eccentric orbits to explain the apparently aberrant motion of the planets, commonly believed until the Middle Ages, was superseded during the Renaissance. The Apollonius crater on the Moon is named in his honor.

Theon of Alexandria (/ˌθiːən, -ɒn/; Ancient Greek: Θέων ὁ Ἀλεξανδρεύς; c. AD 335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's Elements and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.

Hypatia (born c. 350–370 – March 415 AD) was a Neoplatonist philosopher, astronomer, and mathematician who lived in Alexandria, at that time in the province of Egypt and a major city of the Eastern Roman Empire. In Alexandria, Hypatia was a prominent thinker who taught subjects including philosophy and astronomy, and in her lifetime was renowned as a great teacher and a wise counselor. Not the only fourth century Alexandrian female mathematician, Hypatia was preceded by Pandrosion. However, Hypatia is the first female mathematician whose life is reasonably well recorded. She wrote a commentary on Diophantus's thirteen-volume Arithmetica, which may survive in part, having been interpolated into Diophantus's original text, and another commentary on Apollonius of Perga's treatise on conic sections, which has not survived. Many modern scholars also believe that Hypatia may have edited the surviving text of Ptolemy's Almagest, based on the title of her father Theon's commentary on Book III of the Almagest.

Hypatia constructed astrolabes and hydrometers, but did not invent either of these, which were both in use long before she was born. She was tolerant toward Christians and taught many Christian students, including Synesius, the future bishop of Ptolemais. Ancient sources record that Hypatia was widely beloved by pagans and Christians alike and that she established great influence with the political elite in Alexandria. Toward the end of her life, Hypatia advised Orestes, the Roman prefect of Alexandria, who was in the midst of a political feud with Cyril, the bishop of Alexandria. Rumors spread accusing her of preventing Orestes from reconciling with Cyril and, in March 415 AD, she was murdered by a mob of Christians led by a lector named Peter.

Posidonius (/ˌpɒsɪˈdoʊniəs/; Ancient Greek: Ποσειδώνιος Poseidṓnios, "of Poseidon") "of Apameia" (ὁ Ἀπαμεύς) or "of Rhodes" (ὁ Ῥόδιος) (c. 135 – c. 51 BC), was a Greek politician, astronomer, astrologer, geographer, historian, mathematician, and teacher native to Apamea, Syria. He was considered the most learned man of his time and, possibly, of the entire Stoic school. After a period learning Stoic philosophy from Panaetius in Athens, he spent many years in travel and scientific researches in Spain, Africa, Italy, Gaul, Liguria, Sicily and on the eastern shores of the Adriatic. He settled as a teacher at Rhodes where his fame attracted numerous scholars. Next to Panaetius he did most, by writings and personal lectures, to spread Stoicism to the Roman world, and he became well known to many leading men, including Pompey and Cicero.

His works are now lost, but they proved a mine of information to later writers. The titles and subjects of more than twenty of them are known. In common with other Stoics of the middle period, he displayed syncretic tendencies, following not just the earlier Stoics, but making use of the works of Plato and Aristotle. A polymath as well as a philosopher, he took genuine interest in natural science, geography, natural history, mathematics and astronomy. He sought to determine the distance and magnitude of the Sun, to calculate the diameter of the Earth and the influence of the Moon on the tides.

Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet, mathematician, photographer and reluctant Anglican deacon. His most notable works are Alice's Adventures in Wonderland (1865) and its sequel Through the Looking-Glass (1871), some of the most important examples of Victorian literature. He was noted for his facility with word play, logic, and fantasy. His poems Jabberwocky (1871) and The Hunting of the Snark (1876) are classified in the genre of literary nonsense. Some of Alice's nonsensical wonderland logic reflects his published work on mathematical logic.

Carroll came from a family of high-church Anglicans, and pursued his clerical training at Christ Church, Oxford, where he lived for most of his life as a scholar, teacher and (necessarily for his academic fellowship at the time) Anglican deacon. Alice Liddell – a daughter of Henry Liddell, the Dean of Christ Church – is widely identified as the original inspiration for Alice in Wonderland, though Carroll always denied this.

Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (/ælˈkɪndi/; Arabic: أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; Latin: Alkindus; c. 801–873 AD) was an Arab Muslim polymath active as a philosopher, mathematician, physician, and music theorist. Al-Kindi was the first of the Islamic peripatetic philosophers, and is hailed as the "father of Arab philosophy".

Al-Kindi was born in Kufa and educated in Baghdad. He became a prominent figure in the House of Wisdom, and a number of Abbasid Caliphs appointed him to oversee the translation of Greek scientific and philosophical texts into the Arabic language. This contact with "the philosophy of the ancients" (as Hellenistic philosophy was often referred to by Muslim scholars) had a profound effect on him, as he synthesized, adapted and promoted Hellenistic and Peripatetic philosophy in the Muslim world. He subsequently wrote hundreds of original treatises of his own on a range of subjects ranging from metaphysics, ethics, logic and psychology, to medicine, pharmacology, mathematics, astronomy, astrology and optics, and further afield to more practical topics like perfumes, swords, jewels, glass, dyes, zoology, tides, mirrors, meteorology and earthquakes.

Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books Astronomia nova, Harmonice Mundi, and Epitome Astronomiae Copernicanae. The variety and impact of his work made Kepler one of the founders and fathers of modern astronomy, the scientific method, natural science, and modern science. He has been described as the "father of science fiction" for his novel Somnium.

Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein.

Pierre Gassendi (French: [pjɛʁ gasɛ̃di]; also Pierre Gassend, Petrus Gassendi, Petrus Gassendus; 22 January 1592 – 24 October 1655) was a French philosopher, Catholic priest, astronomer, and mathematician. While he held a church position in south-east France, he also spent much time in Paris, where he was a leader of a group of free-thinking intellectuals. He was also an active observational scientist, publishing the first data on the transit of Mercury in 1631. The lunar crater Gassendi is named after him.

He wrote numerous philosophical works, and some of the positions he worked out are considered significant, finding a way between skepticism and dogmatism. Richard Popkin indicates that Gassendi was one of the first thinkers to formulate the modern "scientific outlook", of moderated skepticism and empiricism. He clashed with his contemporary Descartes on the possibility of certain knowledge. His best known intellectual project attempted to reconcile Epicurean atomism with Christianity.

Christiaan Huygens, Lord of Zeelhem, FRS (/ˈhaɪɡənz/ HY-gənz, US also /ˈhɔɪɡənz/ HOY-gənz; Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] ; also spelled Huyghens; Latin: Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution. In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of mathematical parameters, and the first mathematical and mechanistic explanation of an unobservable physical phenomenon.

Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione, completed in 1656 but published posthumously in 1703. In 1659, Huygens derived geometrically the formula in classical mechanics for the centrifugal force in his work De vi Centrifuga, a decade before Isaac Newton. In optics, he is best known for his wave theory of light, which he described in his Traité de la Lumière (1690). His theory of light was initially rejected in favour of Newton's corpuscular theory of light, until Augustin-Jean Fresnel adapted Huygens's principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the Huygens–Fresnel principle.

Sir Isaac Newton (/ˈnjuːtən/ ; 4 January [O.S. 25 December] 1643 – 31 March [O.S. 20 March] 1727) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, author, and inventor. He was a key figure in the Scientific Revolution and the Enlightenment that followed. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, achieved the first great unification in physics and established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, though he developed calculus years before Leibniz. Newton contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science.

In the Principia, Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. He used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System's heliocentricity. Newton solved the two-body problem and introduced the three-body problem. He demonstrated that the motion of objects on Earth and celestial bodies could be accounted for by the same principles. Newton's inference that the Earth is an oblate spheroid was later confirmed by the geodetic measurements of Alexis Clairaut, Charles Marie de La Condamine, and others, convincing most European scientists of the superiority of Newtonian mechanics over earlier systems. He was also the first to calculate the age of Earth by experiment, and described a precursor to the modern wind tunnel. Further, he was the first to provide a quantitative estimate of the solar mass.

Gottfried Wilhelm Leibniz (or Leibnitz; 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics. Leibniz has been called the "last universal genius" due to his vast expertise across fields, which became a rarity after his lifetime with the coming of the Industrial Revolution and the spread of specialized labour. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science.

Leibniz contributed to the field of library science, developing a cataloguing system (at the Herzog August Library in Wolfenbüttel, Germany) that came to serve as a model for many of Europe's largest libraries. His contributions to a wide range of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German.

A geometer is a mathematician whose area of study is the historical aspects that define geometry, instead of the analytical geometric studies conducted by geometricians.

Some notable geometers and their main fields of work, chronologically listed, are:

Hippocrates of Chios (Ancient Greek: Ἱπποκράτης ὁ Χῖος; c. 470 – c. 421 BC) was an ancient Greek mathematician, geometer, and astronomer.

He was born on the isle of Chios, where he was originally a merchant. After some misadventures (he was robbed by either pirates or fraudulent customs officials) he went to Athens, possibly for litigation, where he became a leading mathematician.

The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. The term Archimedean spiral is sometimes used to refer to the more general class of spirals of this type (see below), in contrast to Archimedes' spiral (the specific arithmetic spiral of Archimedes). It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation$${\displaystyle r=b\cdot \theta }$$with real number b. Changing the parameter b controls the distance between loops.

From the above equation, it can thus be stated: position of the particle from point of start is proportional to angle θ as time elapses.