"January 2006 issue of the ""Bulletin of the American Mathematical Society"", ""The number of papers and books included in the ""Mathematical Reviews"" database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."" The word ""mathematics"" comes from Ancient Greek μάθημα (""máthēma""), meaning ""that which is learnt"", ""what one gets to know"", hence also ""study"" and ""science"". The word for ""mathematics"" came to have the narrower and"
"Mathematics Mathematics (from Greek μάθημα ""máthēma"", ""knowledge, study, learning"") includes the study of such topics as quantity, structure, space, and change. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of conjectures by mathematical proofs. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist."
"the other two sides. The ancient mathematical texts are available with the prior mentioned Ancient Egyptians notation and with Plimpton 322 (Babylonian mathematics c. 1900 BC). The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term ""mathematics"" from the ancient Greek ""μάθημα"" (""mathema""), meaning ""subject of instruction"". Plato's influence has been especially strong in mathematics and the sciences. He helped to distinguish between pure and applied mathematics by widening the gap between ""arithmetic"", now called number theory and ""logistic"", now called arithmetic. Greek mathematics greatly refined"
"Science Science (from the Latin word ""scientia"", meaning ""knowledge"") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The earliest roots of science can be traced to Ancient Egypt and Mesopotamia in around 3500 to 3000 BCE. Their contributions to mathematics, astronomy, and medicine entered and shaped Greek natural philosophy of classical antiquity, whereby formal attempts were made to explain events of the physical world based on natural causes. After the fall of the Western Roman Empire, knowledge of Greek conceptions of the world deteriorated in Western Europe during"
"more technical meaning ""mathematical study"" even in Classical times. Its adjective is (""mathēmatikós""), meaning ""related to learning"" or ""studious"", which likewise further came to mean ""mathematical"". In particular, (""mathēmatikḗ tékhnē""), , meant ""the mathematical art"". Similarly, one of the two main schools of thought in Pythagoreanism was known as the ""mathēmatikoi"" (μαθηματικοί)—which at the time meant ""teachers"" rather than ""mathematicians"" in the modern sense. In Latin, and in English until around 1700, the term ""mathematics"" more commonly meant ""astrology"" (or sometimes ""astronomy"") rather than ""mathematics""; the meaning gradually changed to its present one from about 1500 to 1800. This has"
"Greek mathematics Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by culture and language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. The word ""mathematics"" itself derives from the , meaning ""subject of instruction"". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is the key"
"""μάθημα"" (""mathema""), meaning ""subject of instruction"". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. Although they made virtually no contributions to theoretical mathematics, the ancient Romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, creation of lunar and solar calendars, and even arts and crafts. Chinese mathematics made early contributions, including a place value system and the first use of negative numbers. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today"
"Mathetics Mathetics is the science of learning. The term was coined by John Amos Comenius (1592–1670) in his work ""Spicilegium didacticum"", published in 1680. He understood ""Mathetics"" as the opposite of ""Didactics"", the science of teaching. Mathetics considers and uses findings of current interest from pedagogical psychology, neurophysiology and information technology. In 1962, The University of Alabama's Mathetics Foundation began publication of ""The Journal of Mathetics"". However, only two issues were ever printed, the first in January and the second in April. The contents of the first issue included: Seymour Papert, MIT mathematician, educator, and author, explains the rationale behind"
"Arithmetic Arithmetic (from the Greek ἀριθμός ""arithmos"", ""number"" and τική [τέχνη], ""tiké [téchne]"", ""art"") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms ""arithmetic"" and ""higher arithmetic"" were used until the beginning of the 20th century as synonyms for ""number theory"" and are sometimes still used to refer to a wider part of"
"English, the noun ""mathematics"" takes a singular verb. It is often shortened to ""maths"" or, in North America, ""math"". Mathematics has no generally accepted definition. Aristotle defined mathematics as ""the science of quantity"", and this definition prevailed until the 18th century. Galileo Galilei (1564–1642) said, ""The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering"
"History of physics Physics (from the Ancient Greek φύσις ""physis"" meaning ""nature"") is the fundamental branch of science. The primary objects of study are matter and energy. Physics is, in one sense, the oldest and most basic academic pursuit; its discoveries find applications throughout the natural sciences, since matter and energy are the basic constituents of the natural world. The other sciences are generally more limited in their scope and may be considered branches that have split off from physics to become sciences in their own right. Physics today may be divided loosely into classical physics and modern physics. Elements"
"who greatly enjoys learning and studying. The shift in meaning for ""mathema"" is likely a result of the rapid categorization during the time of Plato and Aristotle of their ""mathemata"" in terms of education: arithmetic, geometry, astronomy, and music (the quadrivium), which the Greeks found to create a ""natural grouping"" of mathematical (in the modern usage; ""doctrina mathematica"" in the ancient usage) precepts. In a philosophical dialogue, King James first penned the character Philomathes to debate on arguments of whether the ancient religious concepts of witchcraft should be punished in a politically fueled Christian society. The arguments King James poses"
"evidence. Examples of issues that have involved the politicization of science include the global warming controversy, health effects of pesticides, and health effects of tobacco. Publications Resources Science Science (from the Latin word ""scientia"", meaning ""knowledge"") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The earliest roots of science can be traced to Ancient Egypt and Mesopotamia in around 3500 to 3000 BCE. Their contributions to mathematics, astronomy, and medicine entered and shaped Greek natural philosophy of classical antiquity, whereby formal attempts were made to explain events of"
"mathematics and mathematicians with strong autobiographical elements. Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, and change. One of the earliest known mathematicians was Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known"
"Mechanics Mechanics (Greek ) is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The scientific discipline has its origins in Ancient Greece with the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, and Newton laid the foundation for what is now known as classical mechanics. It is a branch of classical physics that deals with particles that are either at rest or are moving"
"1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the ""Millennium Prize Problems"", was published in 2000. Only one of them, the Riemann hypothesis, duplicates one of Hilbert's problems. A solution to any of these problems carries a $1 million reward. Mathematics Mathematics (from Greek μάθημα ""máthēma"", ""knowledge, study, learning"") includes the study of such topics as quantity, structure, space, and change. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity"
"Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, and change. One of the earliest known mathematicians was Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c."
"the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. Greek mathematics was much more sophisticated than the mathematics that had been developed by earlier cultures. All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them. Greek mathematics is thought to have begun"
"astronomy and to formulate calendars and record time. The most ancient mathematical texts available are from Mesopotamia and Egypt - ""Plimpton 322"" (Babylonian c. 1900 BC), the ""Rhind Mathematical Papyrus"" (Egyptian c. 2000–1800 BC) and the ""Moscow Mathematical Papyrus"" (Egyptian c. 1890 BC). All of these texts mention the so-called Pythagorean triples and so, by inference, the Pythagorean theorem, seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. The study of mathematics as a ""demonstrative discipline"" begins in the 6th century BC with the Pythagoreans, who coined the term ""mathematics"" from the ancient Greek"
"in a given formal system without needing to be derived using the rules of the system. The German mathematician Carl Friedrich Gauss referred to mathematics as ""the Queen of the Sciences"". More recently, Marcus du Sautoy has called mathematics ""the Queen of Science ... the main driving force behind scientific discovery"". In the original Latin ""Regina Scientiarum"", as well as in German ""Königin der Wissenschaften"", the word corresponding to ""science"" means a ""field of knowledge"", and this was the original meaning of ""science"" in English, also; mathematics is in this sense a field of knowledge. The specialization restricting the meaning"
"Definitions of mathematics Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All are controversial. Aristotle defined mathematics as: The science of quantity. In Aristotle's classification of the sciences, discrete quantities were studied by arithmetic, continuous quantities by geometry. Auguste Comte's definition tried to explain the role of mathematics in coordinating phenomena in all other fields: The science of indirect measurement. The ""indirectness"" in Comte's definition refers to determining quantities that cannot be measured directly, such as the distance to planets or the size of atoms, by means of their"
"Physics Physics (from , from ""phýsis"" ""nature"") is the natural science that studies matter and its motion and behavior through space and time and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves. Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural"
"(from the Greek γῆ, gê, ""earth"" and λόγος, logos, ""study"") is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which they change. Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 17th century. The 19th century saw breakthroughs occur after observing networks developed across several countries. After the development of the computer in the latter half of the 20th century, breakthroughs in weather forecasting were achieved. Space science or Astronomy is the"
"Mathematicism Mathematicism is any opinion, viewpoint, school of thought, or philosophy that states that everything can be described/defined/modelled ultimately by mathematics, or that the universe and reality (both material and mental/spiritual) are fundamentally/fully/only mathematical, i.e. that 'everything is mathematics' necessitating the ideas of logic, reason, mind, and spirit. Mathematicism is a form of rationalist idealist or mentalist/spiritualist monism). The idea started in the West with ancient Greece's Pythagoreanism, and continued in other rationalist idealist schools of thought such as Platonism. The term 'mathematicism' has additional meanings among Cartesian idealist philosophers and mathematicians, such as describing the ability and process to"
"Muses In ancient Greek religion and mythology, the Muses (Ancient Greek: Μοῦσαι, ""Moũsai"") are the inspirational goddesses of literature, science, and the arts. They are considered the source of the knowledge embodied in the poetry, lyric songs, and myths that were related orally for centuries in these ancient cultures. In current English usage, ""muse"" can refer in general to a person who inspires an artist, musician, or writer. The word ""Muses"" (, ""Moũsai"") perhaps came from the o-grade of the Proto-Indo-European root *""men-"" (""to think"") or from root *""men-"" (""to tower, mountain"") since all the most important cult-centres of the"
"study reality mathematically. Mathematicism includes (but is not limited to) the following (chronological order): Mathematicism Mathematicism is any opinion, viewpoint, school of thought, or philosophy that states that everything can be described/defined/modelled ultimately by mathematics, or that the universe and reality (both material and mental/spiritual) are fundamentally/fully/only mathematical, i.e. that 'everything is mathematics' necessitating the ideas of logic, reason, mind, and spirit. Mathematicism is a form of rationalist idealist or mentalist/spiritualist monism). The idea started in the West with ancient Greece's Pythagoreanism, and continued in other rationalist idealist schools of thought such as Platonism. The term 'mathematicism' has additional meanings"
"the term ""mathetics"" in Chapter 5 (A Word for Learning) of his book, ""The Children's Machine"". The origin of the word, according to Papert, is not from ""mathematics,"" but from the Greek, ""mathēmatikos"", which means ""disposed to learn."" He feels this word (or one like it) should become as much part of the vocabulary about education as is the word pedagogy or instructional design. In Chapter 6 of ""The Children's Machine"", Papert mentions six case studies, and all six have their own accompanying learning moral and they all continue his discussion of his views of mathetics. Case study 2 looks"
"that continues through the present day. This symbolic system was in use by medieval Indian mathematicians and in Europe since the middle of the 17th century, and has continued to develop in the contemporary era. The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, the focus here, the investigation into the mathematical methods and notation of the past. Although the history commences with that of the Ionian schools, there is no doubt that those Ancient Greeks who paid attention to it were largely indebted to the previous"
"mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language. The word ""proof"" comes from the Latin ""probare"" meaning ""to test"". Related modern words are the English ""probe"", ""probation"", and ""probability"", the Spanish ""probar"" (to smell or taste, or (lesser use) touch or test), Italian ""provare"" (to try), and the German ""probieren"" (to try). The early use of ""probity"" was in the presentation of legal evidence. A person of authority, such as a nobleman, was said to have probity,"
"and the analysis of experiments, and theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies (also known as applied physics or engineering physics). The study and practice of physics is based on an intellectual ladder of discoveries and insights from ancient times to the present. Many mathematical and physical ideas used today found their earliest expression in ancient Greek culture, for example in the work of Euclid, Thales of Miletus, Archimedes and Aristarchus. Roots also emerged in ancient"
"Geometry Geometry (from the ; ""geo-"" ""earth"", ""-metron"" ""measurement"") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of formal mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid's ""Elements"","
"as part of the four ""cyclical exercises"" (ἐγκύκλια μαθήματα) that preceded the Latin quadrivium and science today based on mathematics, established mainly among Greeks in southern Italy (at Taranto and Crotone). Greek anachoretes of the early Middle Ages did still follow this education. The Calabrian Cassiodorus founded Vivarium where he translated Greek texts (science, theology and the Bible), and John of Damascus who learnt Greek from a Calabrian monk Kosmas, a slave in the household of his privileged father at Damascus, mentioned mathematics as part of the speculative philosophy. According to him philosophy was divided into theory (theology, physiology, mathematics)"
"mathematics generally lagged behind Greek literature, and there is very little known about Greek mathematics from this period—nearly all of which was passed down through later authors, beginning in the mid-4th century BC. Historians traditionally place the beginning of Greek mathematics proper to the age of Thales of Miletus (ca. 624–548 BC). Little is known about the life and work of Thales, so little indeed that his date of birth and death are estimated from the eclipse of 585 BC, which probably occurred while he was in his prime. Despite this, it is generally agreed that Thales is the first"