Alikhan Dadaev

Von Neumann published over 150 papers in his life: about 60 in pure mathematics, 60 in applied mathematics, 20 in physics, and the remainder on special mathematical subjects or non-mathematical ones. His last work, an unfinished manuscript written while he was in the hospital, was later published in book form as The Computer and the Brain.

His analysis of the structure of self-replication preceded the discovery of the structure of DNA. In a shortlist of facts about his life he submitted to the National Academy of Sciences, he wrote, "The part of my work I consider most essential is that on quantum mechanics, which developed in Göttingen in 1926, and subsequently in Berlin in 1927–1929. Also, my work on various forms of operator theory, Berlin 1930 and Princeton 1935–1939; on the ergodic theorem, Princeton, 1931–1932."

During World War II, von Neumann worked on the Manhattan Project with theoretical physicist Edward Teller, mathematician Stanislaw Ulam and others, problem-solving key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb. He developed the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon and coined the term "kiloton" (of TNT) as a measure of the explosive force generated. After the war, he served on the General Advisory Committee of the United States Atomic Energy Commission, and consulted for organizations including the United States Air Force, the Army's Ballistic Research Laboratory, the Armed Forces Special Weapons Project, and the Lawrence Livermore National Laboratory. As a Hungarian émigré, concerned that the Soviets would achieve nuclear superiority, he designed and promoted the policy of mutually assured destruction to limit the arms race.

John von Neumann, original name János Neumann, (born December 28, 1903, Budapest, Hungary—died February 8, 1957, Washington, D.C., U.S.), Hungarian-born American mathematician. As an adult, he appended von to his surname; the hereditary title had been granted his father in 1913. Von Neumann grew from child prodigy to one of the world’s foremost mathematicians by his mid-twenties. Important work in set theory inaugurated a career that touched nearly every major branch of mathematics. Von Neumann’s gift for applied mathematics took his work in directions that influenced quantum theory, automata theory, economics, and defense planning. Von Neumann pioneered game theory and, along with Alan Turing and Claude Shannon, was one of the conceptual inventors of the stored-program digital computer.

René Descartes, (born March 31, 1596, La Haye, Touraine, France—died February 11, 1650, Stockholm, Sweden), French mathematician, scientist, and philosopher. Because he was one of the first to abandon Scholastic Aristotelianism, because he formulated the first modern version of mind-body dualism, from which stems the mind-body problem, and because he promoted the development of a new science grounded in observation and experiment, he is generally regarded as the founder of modern philosophy. Applying an original system of methodical doubt, he dismissed apparent knowledge derived from authority, the senses, and reason and erected new epistemic foundations on the basis of the intuition that, when he is thinking, he exists; this he expressed in the dictum “I think, therefore I am” (best known in its Latin formulation, “Cogito, ergo sum,” though originally written in French, “Je pense, donc je suis”). He developed a metaphysical dualism that distinguishes radically between mind, the essence of which is thinking, and matter, the essence of which is extension in three dimensions. Descartes’s metaphysics is rationalist, based on the postulation of innate ideas of mind, matter, and God, but his physics and physiology, based on sensory experience, are mechanistic and empiricist.

Zu Chongzhi ( 429–500 AD) was a Chinese astronomer, mathematician, politician, inventor, and writer during the Liu Song and Southern Qi dynasties. He was most notable for calculating pi as between 3.1415926 and 3.1415927, a record in accuracy which would not be surpassed for over 800 years.

Like his grandfather and father, Zu Chongzhi was a state functionary. About 462 he submitted a memorandum to the throne that criticized the current calendar, the Yuanjia (created by He Chengtian [370–447]), and proposed a new calendar system that would provide a more precise number of lunations per year and take into consideration the precession of the equinoxes. His calendar, the Daming calendar, was finally adopted in 510 through the efforts of his son, Zu Geng.

Li Chunfeng (602–670) called Zu Chongzhi the best mathematician ever and gave him credit for three approximations of π: 22/7, 355/113, and the interval 3.1415926 < π < 3.1415927; the third result remained the best in the world until improved by the Arab mathematician al-Kashi (flourished c. 1400). Zu also worked on the mathematical theory of music and metrology, and he constructed several devices, such as a semilegendary “south-pointing carriage” (most likely a mechanical device that kept a pointer in a fixed position); the carriage was topped by a symbolic figure that, once properly aligned, would always point to the south. None of his writings has survived.

Avogadro died exactly one month before his 80th birthday, which was also a day before Nikola Tesla was born. Like some great scientists before him, this physics professor studied religion and law before opting for science. And just like his compatriot, Alessandro Volta, who cashed-in on what eluded Luigi Galvani, Avogadro explored facts which Joseph Louis Gay-Lussac overlooked, alongside those that stumped John Dalton. This resulted in his contributions to Molecular Theory. His famous hypothesis (sometimes called law) propelled Physical Chemistry to loftier heights. This is noteworthy because the terms “atom” and “molecule” were used interchangeably in his era. Avogadro was indeed the person who fostered the term “molecule”. His works were so ahead of their time that his contemporaries showed little interest in them. Notwithstanding, they ushered-in our contemporary age of Particle Physics. It was after André-Marie Ampère rediscovered few of them, that scientists gave them second thoughts. Organic Chemistry experiments, which Auguste Laurent and Charles-Frédéric Gerhardt subsequently conducted, supported Avogadro’s claim that (at constant temperature and pressure) equal volumes of all gases contain equal numbers of molecules. However, he was already deceased, when (in 1860) Stanislao Cannizzaro reenacted and detailed the greatness of his research. They not only helped to determine atomic and molecular masses, but reconciled Dalton’s and Gay-Lussac’s postulations. Several years would elapse before the depths of his accomplishments were fully appreciated: and they consolidated his status as a founder of Molecular Theory. The Avogadrite mineral, and 139-kilometer-wide Avogadro lunar crater, are dedicated to him.

Edward Jenner (17 May 1749 – 26 January 1823) was a British physician and scientist who pioneered the concept of vaccines including creating the smallpox vaccine, the world's first ever vaccine. The terms vaccine and vaccination are derived from Variolae vaccinae ('smallpox of the cow'), the term devised by Jenner to denote cowpox. He used it in 1798 in the long title of his Inquiry into the Variolae vaccinae known as the Cow Pox, in which he described the protective effect of cowpox against smallpox.

In the West, Jenner is often called "the father of immunology", and his work is said to have "saved more lives than the work of any other human". In Jenner's time, smallpox killed around 10% of the population, with the number as high as 20% in towns and cities where infection spread more easily. In 1821, he was appointed physician to King George IV, and was also made mayor of Berkeley and justice of the peace. A member of the Royal Society, in the field of zoology he was among the first to describe the brood parasitism of the cuckoo (Aristotle also noted this behavior in History of Animals). In 2002, Jenner was named in the BBC's list of the 100 Greatest Britons.

As the top math-guru of his era, Brahmagupta journeyed into astronomy and trigonometry: trying to evaluate the periodic positions of heavenly bodies. He was a pacesetter too: introducing some of the earliest known symbolical expressions in his treatises on Geometry, Arithmetic and Algebra (similar to what Diophantus did three centuries prior). Most of his works did not survive, but those that did showed that he was obsessed with quadrilaterals. This explains why some contemporary theorems (such as the formula for the area of a cyclic quad), are named after him. But even more noteworthy is that Brahmagupta is credited (alongside: Liu Hui, Zhang Cang, etc.) with depicting decimals, zero and negative numbers as useful mathematical entities. These are evidenced in his book, titled: Brahmasphutasiddhanta. And a century after his demise, the astronomer, Muhammad Al-Fazari, safeguarded this work by translating it into Arabic. It was a copy of this translation that Muhammad Al-Khwarizmi used to learn the decimals. He then used the acquired knowledge to publish his Al-Jam wal-tafriq bi hisal-al-Hind (which means: Addition and Subtraction based on Indian Arithmetic). This book by Al-Khwarizmi was later translated into Latin (as Algorithmi de numero Indorum), and was sold throughout Europe. Thus, Brahmagupta taught Europeans (and the wider world) the decimal system. His reputation as a mathematician is such that few people realized how profoundly versed he was in astronomy. I am impressed by how his exegesis, Khandakhadyaka, beautifully and eloquently augmented Aryabhata’s Ardharatrikapaksa. Several concepts and theorems are named after Brahmagupta.

Antoine Lavoisier, in full Antoine-Laurent Lavoisier, (born August 26, 1743, Paris, France—died May 8, 1794, Paris), prominent French chemist and leading figure in the 18th-century chemical revolution who developed an experimentally based theory of the chemical reactivity of oxygen and coauthored the modern system for naming chemical substances. Having also served as a leading financier and public administrator before the French Revolution, he was executed with other financiers during the Terror.

It is generally accepted that Lavoisier's great accomplishments in chemistry stem largely from his changing the science from a qualitative to a quantitative one. Lavoisier is most noted for his discovery of the role oxygen plays in combustion. He recognized and named oxygen (1778) and hydrogen (1783), and opposed the phlogiston theory. Lavoisier helped construct the metric system, wrote the first extensive list of elements, and helped to reform chemical nomenclature. He predicted the existence of silicon (1787) and discovered that, although matter may change its form or shape, its mass always remains the same.

Emmy Noether, in full Amalie Emmy Noether, (born March 23, 1882, Erlangen, Germany—died April 14, 1935, Bryn Mawr, Pennsylvania, U.S.), German mathematician whose innovations in higher algebra gained her recognition as the most creative abstract algebraist of modern times.

Noether was certified to teach English and French in schools for girls in 1900, but she instead chose to study mathematics at the University of Erlangen (now University of Erlangen-Nürnberg). At that time, women were only allowed to audit classes with the permission of the instructor. She spent the winter of 1903–04 auditing classes at the University of Göttingen taught by mathematicians David Hilbert, Felix Klein, and Hermann Minkowski and astronomer Karl Schwarzschild. She returned to Erlangen in 1904 when women were allowed to be full students there. She received a Ph.D. degree from Erlangen in 1907, with a dissertation on algebraic invariants. She remained at Erlangen, where she worked without pay on her own research and assisting her father, mathematician Max Noether (1844–1921).

In 1915 Noether was invited to Göttingen by Hilbert and Klein and soon used her knowledge of invariants helping them to explore the mathematics behind Albert Einstein’s recently published theory of general relativity. Hilbert and Klein persuaded her to remain there despite the vehement objections of some faculty members to a woman teaching at the university. Nevertheless, she could only lecture in classes under Hilbert’s name. In 1918 Noether discovered that if the Lagrangian (a quantity that characterizes a physical system; in mechanics, it is kinetic minus potential energy) does not change when the coordinate system changes, then there is a quantity that is conserved. For example, when the Lagrangian is independent of changes in time, then energy is the conserved quantity. This relation between what are known as the symmetries of a physical system and its conservation laws is known as Noether’s theorem and has proven to be a key result in theoretical physics. She won formal admission as an academic lecturer in 1919.

The appearance of “Moduln in nichtkommutativen Bereichen, insbesondere aus Differential- und Differenzenausdrücken” (1920; “Concerning Moduli in Noncommutative Fields, Particularly in Differential and Difference Terms”), written in collaboration with a Göttingen colleague, Werner Schmeidler, and published in Mathematische Zeitschrift, marked the first notice of Noether as an extraordinary mathematician. For the next six years her investigations centred on the general theory of ideals (special subsets of rings), for which her residual theorem is an important part. On an axiomatic basis she developed a general theory of ideals for all cases. Her abstract theory helped draw together many important mathematical developments.

From 1927 Noether concentrated on noncommutative algebras (algebras in which the order in which numbers are multiplied affects the answer), their linear transformations, and their application to commutative number fields. She built up the theory of noncommutative algebras in a newly unified and purely conceptual way. In collaboration with Helmut Hasse and Richard Brauer, she investigated the structure of noncommutative algebras and their application to commutative fields by means of cross product (a form of multiplication used between two vectors). Important papers from this period are “Hyperkomplexe Grössen und Darstellungstheorie” (1929; “Hypercomplex Number Systems and Their Representation”) and “Nichtkommutative Algebra” (1933; “Noncommutative Algebra”).

In addition to research and teaching, Noether helped edit the Mathematische Annalen. From 1930 to 1933 she was the centre of the strongest mathematical activity at Göttingen. The extent and significance of her work cannot be accurately judged from her papers. Much of her work appeared in the publications of students and colleagues; many times a suggestion or even a casual remark revealed her great insight and stimulated another to complete and perfect some idea.

When the Nazis came to power in Germany in 1933, Noether and many other Jewish professors at Göttingen were dismissed. In October she left for the United States to become a visiting professor of mathematics at Bryn Mawr College and to lecture and conduct research at the Institute for Advanced Study in Princeton, New Jersey. She died suddenly of complications from an operation on an ovarian cyst. Einstein wrote shortly after her death that “Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.”

Gregor Johann Mendel was a meteorologist, mathematician, biologist, Augustinian friar and abbot of St. Thomas' Abbey in Brno, Margraviate of Moravia. Mendel was born in a German-speaking family in the Silesian part of the Austrian Empire (today's Czech Republic) and gained posthumous recognition as the founder of the modern science of genetics. Though farmers had known for millennia that crossbreeding of animals and plants could favor certain desirable traits, Mendel's pea plant experiments conducted between 1856 and 1863 established many of the rules of heredity, now referred to as the laws of Mendelian inheritance.

Mendel worked with seven characteristics of pea plants: plant height, pod shape and color, seed shape and color, and flower position and color. Taking seed color as an example, Mendel showed that when a true-breeding yellow pea and a true-breeding green pea were cross-bred their offspring always produced yellow seeds. However, in the next generation, the green peas reappeared at a ratio of 1 green to 3 yellow. To explain this phenomenon, Mendel coined the terms "recessive" and "dominant" in reference to certain traits. In the preceding example, the green trait, which seems to have vanished in the first filial generation, is recessive and the yellow is dominant. He published his work in 1866, demonstrating the actions of invisible "factors"—now called genes—in predictably determining the traits of an organism.

The profound significance of Mendel's work was not recognized until the turn of the 20th century (more than three decades later) with the rediscovery of his laws. Erich von Tschermak, Hugo de Vries and Carl Correns independently verified several of Mendel's experimental findings in 1900, ushering in the modern age of genetics.

Zhu Shijie, Wade-Giles Chu Shih-Chieh, (flourished 1300, China), Chinese mathematician who stood at the pinnacle of traditional Chinese mathematics. Zhu is also known for having unified the southern and northern Chinese mathematical traditions.

Little is known of Zhu’s life except that he was probably a native of the present Beijing area and that he traveled throughout the country as an itinerant teacher during the last 30 years of the 13th century.

Zhu’s fame rests primarily on two publications, Suanxue qimeng (1299; “Introduction to Mathematical Science”) and Siyuan yujian (1303; “Precious Mirror of Four Elements”). The former is an introductory mathematics textbook, proceeding from elementary arithmetic to algebraic calculations. Through its layout and progression it clearly testifies to the author’s didactic concern. Following the southern Chinese tradition of mathematics, this book contains many rules and problems presented in the form of verses to facilitate their memorization. This practical orientation, together with the introduction of contemporary data in commercial problems, suggests that mathematics had begun to reach beyond the confines of mandarin society. This book was also read in Korea and Japan; it played a central role in the development of the wasan (“Japanese calculation”) tradition.

“Precious Mirror” corresponds to the final stage in the generalization of the northern Chinese technique of tian yuan (“method of the celestial unknown”), a kind of algebraic computation performed with counting rods to solve problems. This method, also contained in books written by Li Ye (1192–1279), was developed primarily to calculate the dimensions of simple geometric figures, given their volume or area and some supplementary data. Zhu demonstrated that the method can be applied to a very wide range of problems. As in the method of the celestial unknown, Zhu’s procedure depends heavily on the use of counting rods to represent polynomials and equations. His main improvement lay in the introduction of techniques to eliminate unknown variables between equations.

“Precious Mirror” also contains a diagram known in the West as Blaise Pascal’s triangle, which most likely inspired Zhu’s discovery of an important combinatoric identity.

Abū al-Qāsim al-Zahrāwī, also spelled Abul Kasim, in full Abū al-Qāsim Khalaf ibn ʿAbbās al-Zahrāwī, Latin Albucasis, (born c. 936, near Córdoba [Spain]—died c. 1013), medieval surgeon of Andalusian Spain, whose comprehensive medical text, combining Middle Eastern and Greco-Roman classical teachings, shaped European surgical procedures until the Renaissance.

Abū al-Qāsim was court physician to the Andalusian caliph ʿAbd al-Raḥmān III al-Nāṣir and wrote Al-Taṣrīf li-man ʿajaz ʿan al-taʾālīf, or Al-Taṣrīf (“The Method”), a medical work in 30 parts. While much of the text was based on earlier authorities, especially the Epitomae of the 7th-century Byzantine physician Paul of Aegina, it contained many original observations, including the earliest known description of hemophilia. The last chapter, with its drawings of more than 200 instruments, constitutes the first illustrated independent work on surgery.

Although Al-Taṣrīf was largely ignored by physicians of the eastern parts of the Islamic world, the surgical treatise had tremendous influence in Christian Europe. Translated into Latin in the 12th century by the scholar Gerard of Cremona, it stood for nearly 500 years as the leading textbook on surgery in Europe, preferred for its concise lucidity even to the works of the classic Greek medical authority Galen.

Henri Becquerel, in full Antoine-Henri Becquerel, (born December 15, 1852, Paris, France—died August 25, 1908, Le Croisic), French physicist who discovered radioactivity through his investigations of uranium and other substances. In 1903 he shared the Nobel Prize for Physics with Pierre and Marie Curie.

He was a member of a scientific family extending through several generations, the most notable being his grandfather Antoine-César Becquerel (1788–1878), his father, Alexandre-Edmond Becquerel (1820–91), and his son Jean Becquerel (1878–1953).

Wernher Magnus Maximilian Freiherr von Braun (23 March 1912 – 16 June 1977) was a German-American aerospace engineer and space architect. He was the leading figure in the development of rocket technology in Nazi Germany and a pioneer of rocket and space technology in the United States.

While in his twenties and early thirties, von Braun worked in Nazi Germany's rocket development program. He helped design and co-developed the V-2 rocket at Peenemünde during World War II. Following the war, he was secretly moved to the United States, along with about 1,600 other German scientists, engineers, and technicians, as part of Operation Paperclip. He worked for the United States Army on an intermediate-range ballistic missile program, and he developed the rockets that launched the United States' first space satellite Explorer 1 in 1958.

In 1960, his group was assimilated into NASA, where he served as director of the newly formed Marshall Space Flight Center and as the chief architect of the Saturn V super heavy-lift launch vehicle that propelled the Apollo spacecraft to the Moon. In 1967, von Braun was inducted into the National Academy of Engineering, and in 1975, he received the National Medal of Science. He advocated a human mission to Mars.

Srinivasa Ramanujan, (born December 22, 1887, Erode, India—died April 26, 1920, Kumbakonam), Indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function.

When he was 15 years old, he obtained a copy of George Shoobridge Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics, 2 vol. (1880–86). This collection of thousands of theorems, many presented with only the briefest of proofs and with no material newer than 1860, aroused his genius. Having verified the results in Carr’s book, Ramanujan went beyond it, developing his own theorems and ideas. In 1903 he secured a scholarship to the University of Madras but lost it the following year because he neglected all other studies in pursuit of mathematics.

Ramanujan continued his work, without employment and living in the poorest circumstances. After marrying in 1909 he began a search for permanent employment that culminated in an interview with a government official, Ramachandra Rao. Impressed by Ramanujan’s mathematical prowess, Rao supported his research for a time, but Ramanujan, unwilling to exist on charity, obtained a clerical post with the Madras Port Trust.

In 1911 Ramanujan published the first of his papers in the Journal of the Indian Mathematical Society. His genius slowly gained recognition, and in 1913 he began a correspondence with the British mathematician Godfrey H. Hardy that led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge. Overcoming his religious objections, Ramanujan traveled to England in 1914, where Hardy tutored him and collaborated with him in some research.

Ramanujan’s knowledge of mathematics (most of which he had worked out for himself) was startling. Although he was almost completely unaware of modern developments in mathematics, his mastery of continued fractions was unequaled by any living mathematician. He worked out the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his own theory of divergent series, in which he found a value for the sum of such series using a technique he invented that came to be called Ramanujan summation. On the other hand, he knew nothing of doubly periodic functions, the classical theory of quadratic forms, or Cauchy’s theorem, and he had only the most nebulous idea of what constitutes a mathematical proof. Though brilliant, many of his theorems on the theory of prime numbers were wrong.

In England Ramanujan made further advances, especially in the partition of numbers (the number of ways that a positive integer can be expressed as the sum of positive integers; e.g., 4 can be expressed as 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1). His papers were published in English and European journals, and in 1918 he was elected to the Royal Society of London. In 1917 Ramanujan had contracted tuberculosis, but his condition improved sufficiently for him to return to India in 1919. He died the following year, generally unknown to the world at large but recognized by mathematicians as a phenomenal genius, without peer since Leonhard Euler (1707–83) and Carl Jacobi (1804–51). Ramanujan left behind three notebooks and a sheaf of pages (also called the “lost notebook”) containing many unpublished results that mathematicians continued to verify long after his death.

Pierre-Simon, marquis de Laplace was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Mécanique céleste (Celestial Mechanics) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace.

Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origin of the Solar System and was one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse.

Laplace is remembered as one of the greatest scientists of all time. Sometimes referred to as the French Newton or Newton of France, he has been described as possessing a phenomenal natural mathematical faculty superior to that of any of his contemporaries. He was Napoleon's examiner when Napoleon attended the École Militaire in Paris in 1784. Laplace became a count of the Empire in 1806 and was named a marquis in 1817, after the Bourbon Restoration.

Robert Boyle, (born January 25, 1627, Lismore Castle, County Waterford, Ireland—died December 31, 1691, London, England), Anglo-Irish natural philosopher and theological writer, a preeminent figure of 17th-century intellectual culture. He was best known as a natural philosopher, particularly in the field of chemistry, but his scientific work covered many areas including hydrostatics, physics, medicine, earth sciences, natural history, and alchemy. His prolific output also included Christian devotional and ethical essays and theological tracts on biblical language, the limits of reason, and the role of the natural philosopher as a Christian. He sponsored many religious missions as well as the translation of the Scriptures into several languages. In 1660 he helped found the Royal Society of London.

Muhammad ibn Muhammad ibn al-Hasan al-Tūsī better known as Nasir al-Din al-Tusi or simply Tusi was a Persian polymath, architect, philosopher, physician, scientist, and theologian. Nasir al-Din al-Tusi was a well published author, writing on subjects of math, engineering, prose, and mysticism. Additionally, al-Tusi made several scientific advancements. In astronomy, al-Tusi created very accurate tables of planetary motion, an updated planetary model, and critiques of Ptolemaic astronomy. He also made strides in logic, mathematics but especially trigonometry, biology, and chemistry. Nasir al-Din al-Tusi left behind a great legacy as well. Some consider Tusi one of the greatest scientists of medieval Islam, since he is often considered the creator of trigonometry as a mathematical discipline in its own right. The Muslim scholar Ibn Khaldun (1332–1406) considered Tusi to be the greatest of the later Persian scholars. There is also reason to believe that he may have influenced Copernican heliocentrism.