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117-562: Animal Liberation Press Offices relay anonymous communiques , photos, and videos to the media about direct action undertaken by the Animal Liberation Front (ALF), Animal Rights Militia (ARM), Revolutionary Cells – Animal Liberation Brigade , Justice Department , and other leaderless resistance within the animal liberation movement . It states that it will "explain and seek to justify any action, whatever it may be", so long as it appears to have been carried out "with

234-492: A generic drug . Infringers could be liable for the total loss of potential sales (implying that everyone who buys a counterfeit product would have bought the real thing). It applies to unintentional use of copyright material. It puts the onus on website owners to ensure they comply with laws across several territories. It has been negotiated secretively and outside established international trade bodies, despite EU criticisms. The history of anonymous expression in political dissent

351-424: A riot . This perceived anonymity can be compromised by technologies such as photography . Groupthink behavior and conformity are also considered to be an established effect of internet anonymity. Anonymity also permits highly trained professionals such as judges to freely express themselves regarding the strategies they employ to perform their jobs objectively. Anonymous commercial transactions can protect

468-591: A set whose elements are unspecified, of operations acting on the elements of the set, and rules that these operations must follow. The scope of algebra thus grew to include the study of algebraic structures. This object of algebra was called modern algebra or abstract algebra , as established by the influence and works of Emmy Noether . Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics. Their study became autonomous parts of algebra, and include: The study of types of algebraic structures as mathematical objects

585-744: A "central and pivotal figure" in the ALF. The first press office was founded in the UK in October 1991. Media relations were originally handled by the Animal Liberation Front Supporters Group , but a new ALF press office was created to receive claims of responsibility anonymously, in order to avoid charges of conspiracy. The name was changed again, this time to the Animal Liberation Press Office, after

702-518: A collective voice". Guardian considers that "people will often speak more honestly if they are allowed to speak anonymously" . According to Ross Eaman, in his book The A to Z of Journalism , until the mid-19th century, most writers in Great Britain, especially the less well known, did not sign their names to their work in newspapers, magazines and reviews. Most commentary on the Internet

819-493: A conversation) capitalized on a fascination with anonymity. Apps like Yik Yak , Secret and Whisper let people share things anonymously or quasi-anonymously whereas Random let the user to explore the web anonymously. Some email providers, like Tuta also offer the ability to create anonymous email accounts which do not require any personal information from the account holder. Other sites, however, including Facebook and Google+ , ask users to sign in with their legal names. In

936-402: A crime. Anonymity may also be created unintentionally, through the loss of identifying information due to the passage of time or a destructive event. In certain situations, however, it may be illegal to remain anonymous. For example, 24 of the U.S. states have "stop and identify" statutes that require persons detained to self-identify when requested by a law enforcement officer, when the person

1053-421: A fictional collaboration by people who had never previously met and did not know who had recruited them. The anonymous purchase of a gun or knife to be used in a crime helps prevent linking an abandoned weapon to the identity of the perpetrator. There are two aspects, one, giving to a large charitable organization obscures the beneficiary of a donation from the benefactor, the other is giving anonymously to obscure

1170-501: A field or area of interest normally dominated by males (as by the famous science fiction author James Tiptree, Jr who was actually a woman named Alice Bradley Sheldon, and likely JT LeRoy ). Some seem to want to avoid the "limelight" of popularity and to live private lives, such as Thomas Pynchon , J. D. Salinger , De Onbekende Beeldhouwer (an anonymous sculptor whose exhibited work in Amsterdam attracted strong attention in

1287-614: A foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature or—in modern mathematics—purely abstract entities that are stipulated to have certain properties, called axioms . Mathematics uses pure reason to prove properties of objects, a proof consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems , axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of

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1404-669: A fruitful interaction between mathematics and science , to the benefit of both. Mathematical discoveries continue to be made to this very day. According to Mikhail B. Sevryuk, in the January ;2006 issue of the Bulletin of the American Mathematical Society , "The number of papers and books included in the Mathematical Reviews (MR) database since 1940 (the first year of operation of MR)

1521-404: A group attempts to remain anonymous, for various reasons such as adding an element of mystique to themselves or their work, attempting to avoid what is known as the " cult of personality " or hero worship (in which the charisma , good looks, wealth or other unrelated or mildly related aspects of the people is the main reason for interest in their work, rather than the work itself) or to break into

1638-411: A hidden identity is assumed. Suppose that only Alice, Bob, and Carol have keys to a bank safe and that, one day, contents of the safe go missing (lock not violated). Without additional information, we cannot know for sure whether it was Alice, Bob or Carol who emptied the safe. Notably, each element in {Alice, Bob, Carol} could be the perpetrator with a probability of 1. However, as long as none of them

1755-404: A mathematical problem. In turn, the axiomatic method allows for the study of various geometries obtained either by changing the axioms or by considering properties that do not change under specific transformations of the space . Today's subareas of geometry include: Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were

1872-422: A mathematical statement that is taken to be true without need of proof. If a mathematical statement has yet to be proven (or disproven), it is termed a conjecture . Through a series of rigorous arguments employing deductive reasoning , a statement that is proven to be true becomes a theorem. A specialized theorem that is mainly used to prove another theorem is called a lemma . A proven instance that forms part of

1989-402: A more general finding is termed a corollary . Numerous technical terms used in mathematics are neologisms , such as polynomial and homeomorphism . Other technical terms are words of the common language that are used in an accurate meaning that may differ slightly from their common meaning. For example, in mathematics, " or " means "one, the other or both", while, in common language, it

2106-668: A need to honor the remains of soldiers for whom identification is impossible. In many countries, such a memorial is named the Tomb of the Unknown Soldier . Most modern newspapers and magazines attribute their articles to individual editors, or to news agencies . An exception is the Markker weekly The Economist . All British newspapers run their leaders, or editorials , anonymously. The Economist fully adopts this policy, saying "Many hands write The Economist , but it speaks with

2223-493: A negative side of anonymity: The border between illegal and legal but offensive use is not very sharp, and varies depending on the law in each country. Anonymous (used as a mass noun) is a loosely associated international network of activist and hacktivist entities. A website nominally associated with the group describes it as "an internet gathering" with "a very loose and decentralized command structure that operates on ideas rather than directives". The group became known for

2340-413: A person may desire a long-term relationship (such as a reputation) with another party without necessarily disclosing personally identifying information to that party. In this case, it may be useful for the person to establish a unique identifier, called a pseudonym . Examples of pseudonyms are pen names , nicknames , credit card numbers , student numbers, bank account numbers, etc. A pseudonym enables

2457-412: A person might choose to withhold their identity. Acts of charity have been performed anonymously when benefactors do not wish to be acknowledged. A person who feels threatened might attempt to mitigate that threat through anonymity. A witness to a crime might seek to avoid retribution, for example, by anonymously calling a crime tipline. Criminals might proceed anonymously to conceal their participation in

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2574-535: A population mean with a given level of confidence. Because of its use of optimization , the mathematical theory of statistics overlaps with other decision sciences , such as operations research , control theory , and mathematical economics . Computational mathematics is the study of mathematical problems that are typically too large for human, numerical capacity. Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory ; numerical analysis broadly includes

2691-453: A predetermined route through the anonymizing network. Each router sees the immediate previous router as the origin and the immediate next router as the destination. Thus, no router ever knows both the true origin and destination of the packet. This makes these services more secure than centralized anonymizing services (where a central point of knowledge exists). Sites such as Chatroulette , Omegle , and Tinder (which pair up random users for

2808-421: A prior negative experience during which they did not maintain an anonymous presence. Such experiences include stalking, releasing private information by an opposing school political group, or tricking an individual into traveling to another country for a job that did not exist. Participants in this study stated that they were able to avoid their previous problems by using false identification online. David Chaum

2925-507: A protection against legal prosecution. For example, when committing unlawful actions, many criminals attempt to avoid identification by the means of obscuring/covering their faces with scarves or masks , and wear gloves or other hand coverings in order to not leave any fingerprints . In organized crime , groups of criminals may collaborate on a certain project without revealing to each other their names or other personally identifiable information. The movie The Thomas Crown Affair depicted

3042-459: A purchase on a customer's behalf. When purchasing taboo goods and services, anonymity makes many potential consumers more comfortable with or more willing to engage in the transaction. Many loyalty programs use cards that personally identify the consumer engaging in each transaction (possibly for later solicitation, or for redemption or security purposes), or that act as a numerical pseudonym , for use in data mining . Anonymity can also be used as

3159-411: A separate branch of mathematics until the seventeenth century. At the end of the 19th century, the foundational crisis in mathematics and the resulting systematization of the axiomatic method led to an explosion of new areas of mathematics. The 2020 Mathematics Subject Classification contains no less than sixty-three first-level areas. Some of these areas correspond to the older division, as

3276-402: A series of well-publicized publicity stunts and distributed denial-of-service (DDoS) attacks on government, religious, and corporate websites. An image commonly associated with Anonymous is the "man without a head" represents leaderless organization and anonymity. Anonymity is perceived as a right by many, especially the anonymity in the internet communications. The partial right for anonymity

3393-643: A shield from the tyranny of the majority. . . . It thus exemplifies the purpose behind the Bill of Rights and of the First Amendment in particular: to protect unpopular individuals from retaliation . . . at the hand of an intolerant society." However, anonymous online speech is not without limits. It is clearly demonstrated in a case from 2008, one in which the defendant stated on a law-school discussion board that two women should be raped, an anonymous poster's comments may extend beyond free speech protections. In

3510-424: A single unknown , which were called algebraic equations (a term still in use, although it may be ambiguous). During the 19th century, mathematicians began to use variables to represent things other than numbers (such as matrices , modular integers , and geometric transformations ), on which generalizations of arithmetic operations are often valid. The concept of algebraic structure addresses this, consisting of

3627-425: A soapbox for disruptive conversational behavior. The term " troll " is sometimes used to refer to those who engage in such disruptive behavior. Relative anonymity is often enjoyed in large crowds. Different people have different psychological and philosophical reactions to this development, especially as a modern phenomenon. This anonymity is an important factor in crowd psychology , and behavior in situations such as

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3744-410: A specific city designation, is traditionally used by scholars in the humanities to refer to an ancient writer whose name is not known, or to a manuscript of their work. Many such writers have left valuable historical or literary records: an incomplete list of such Anonymi is at Anonymus . In the history of art , many painting workshops can be identified by their characteristic style and discussed and

3861-421: A specific individual (because other people could be using that customer's connection, especially if the customer is a public resource, such as a library), but it provides regional information and serves as powerful circumstantial evidence. Anonymizing services such as I2P and Tor address the issue of IP tracking. In short, they work by encrypting packets within multiple layers of encryption. The packet follows

3978-418: A statistical action, such as using a procedure in, for example, parameter estimation , hypothesis testing , and selecting the best . In these traditional areas of mathematical statistics , a statistical-decision problem is formulated by minimizing an objective function , like expected loss or cost , under specific constraints. For example, designing a survey often involves minimizing the cost of estimating

4095-477: A wide expansion of mathematical logic, with subareas such as model theory (modeling some logical theories inside other theories), proof theory , type theory , computability theory and computational complexity theory . Although these aspects of mathematical logic were introduced before the rise of computers , their use in compiler design, formal verification , program analysis , proof assistants and other aspects of computer science , contributed in turn to

4212-703: Is Fermat's Last Theorem . This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles , who used tools including scheme theory from algebraic geometry , category theory , and homological algebra . Another example is Goldbach's conjecture , which asserts that every even integer greater than 2 is the sum of two prime numbers . Stated in 1742 by Christian Goldbach , it remains unproven despite considerable effort. Number theory includes several subareas, including analytic number theory , algebraic number theory , geometry of numbers (method oriented), diophantine equations , and transcendence theory (problem oriented). Geometry

4329-423: Is a potential risk, which is expected to grow as analytic techniques improve and computing power and text corpora grow. Authors may resist such identification by practicing adversarial stylometry . When it is necessary to refer to someone who is anonymous, it is typically necessary to create a type of pseudo-identification for that person. In literature, the most common way to state that the identity of an author

4446-507: Is both long and with important effect, as in the Letters of Junius or Voltaire 's Candide , or scurrilous as in pasquinades . In the tradition of anonymous British political criticism, The Federalist Papers were anonymously authored by three of America's Founding Fathers . Without the public discourse on the controversial contents of the U.S. Constitution , ratification would likely have taken much longer as individuals worked through

4563-463: Is called the Godfathers of anonymity and he has a claim to be one of the great visionaries of contemporary science. In the early 1980s, while a computer scientist at Berkeley, Chaum predicted the world in which computer networks would make mass surveillance a possibility. As Dr. Joss Wright explains: "David Chaum was very ahead of his time. He predicted in the early 1980s concerns that would arise on

4680-403: Is commonly used for advanced parts. Analysis is further subdivided into real analysis , where variables represent real numbers , and complex analysis , where variables represent complex numbers . Analysis includes many subareas shared by other areas of mathematics which include: Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example

4797-513: Is defined by the set of all similar objects and the properties that these objects must have. For example, in Peano arithmetic , the natural numbers are defined by "zero is a number", "each number has a unique successor", "each number but zero has a unique predecessor", and some rules of reasoning. This mathematical abstraction from reality is embodied in the modern philosophy of formalism , as founded by David Hilbert around 1910. The "nature" of

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4914-407: Is either ambiguous or means "one or the other but not both" (in mathematics, the latter is called " exclusive or "). Finally, many mathematical terms are common words that are used with a completely different meaning. This may lead to sentences that are correct and true mathematical assertions, but appear to be nonsense to people who do not have the required background. For example, "every free module

5031-503: Is essentially done anonymously, using unidentifiable pseudonyms. However this has been widely discredited in a study by the University of Birmingham, which found that the number of people who use the internet anonymously is statistically the same as the number of people who use the internet to interact with friends or known contacts. While these usernames can take on an identity of their own, they are sometimes separated and anonymous from

5148-493: Is in Babylonian mathematics that elementary arithmetic ( addition , subtraction , multiplication , and division ) first appear in the archaeological record. The Babylonians also possessed a place-value system and used a sexagesimal numeral system which is still in use today for measuring angles and time. In the 6th century BC, Greek mathematics began to emerge as a distinct discipline and some Ancient Greeks such as

5265-528: Is legally protected to various degrees in different jurisdictions. The tradition of anonymous speech is older than the United States. Founders Alexander Hamilton , James Madison , and John Jay wrote The Federalist Papers under the pseudonym "Publius" and "the Federal Farmer" spoke up in rebuttal. The US Supreme Court has repeatedly recognized rights to speak anonymously derived from

5382-586: Is mostly used for numerical calculations . Number theory dates back to ancient Babylon and probably China . Two prominent early number theorists were Euclid of ancient Greece and Diophantus of Alexandria. The modern study of number theory in its abstract form is largely attributed to Pierre de Fermat and Leonhard Euler . The field came to full fruition with the contributions of Adrien-Marie Legendre and Carl Friedrich Gauss . Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example

5499-494: Is no way to trace their source and it can be disseminated widely. "Cyberbullying, as opposed to general bullying, is still a widely-debated area of Internet freedom in several states. Though Internet anonymity can provide a harmful environment through which people can hurt others, anonymity can allow for a much safer and relaxed internet experience. In a study conducted at Carnegie Mellon University, 15 out of 44 participants stated that they choose to be anonymous online because of

5616-404: Is not sufficient to verify by measurement that, say, two lengths are equal; their equality must be proven via reasoning from previously accepted results ( theorems ) and a few basic statements. The basic statements are not subject to proof because they are self-evident ( postulates ), or are part of the definition of the subject of study ( axioms ). This principle, foundational for all mathematics,

5733-1192: 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." Mathematical notation is widely used in science and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. This notation consists of symbols used for representing operations , unspecified numbers, relations and any other mathematical objects, and then assembling them into expressions and formulas. More precisely, numbers and other mathematical objects are represented by symbols called variables, which are generally Latin or Greek letters, and often include subscripts . Operation and relations are generally represented by specific symbols or glyphs , such as + ( plus ), × ( multiplication ), ∫ {\textstyle \int } ( integral ), = ( equal ), and < ( less than ). All these symbols are generally grouped according to specific rules to form expressions and formulas. Normally, expressions and formulas do not appear alone, but are included in sentences of

5850-547: Is often held to be Archimedes ( c.  287  – c.  212 BC ) of Syracuse . He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series , in a manner not too dissimilar from modern calculus. Other notable achievements of Greek mathematics are conic sections ( Apollonius of Perga , 3rd century BC), trigonometry ( Hipparchus of Nicaea , 2nd century BC), and

5967-433: Is one of the oldest branches of mathematics. It started with empirical recipes concerning shapes, such as lines , angles and circles , which were developed mainly for the needs of surveying and architecture , but has since blossomed out into many other subfields. A fundamental innovation was the ancient Greeks' introduction of the concept of proofs , which require that every assertion must be proved . For example, it

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6084-435: Is reasonably suspected of committing a crime. The term "anonymous message" typically refers to a message that does not reveal its sender. In many countries, anonymous letters are protected by law and must be delivered as regular letters. In mathematics , in reference to an arbitrary element (e.g., a human, an object, a computer ), within a well-defined set (called the "anonymity set"), "anonymity" of that element refers to

6201-567: Is sometimes mistranslated as a condemnation of mathematicians. The apparent plural form in English goes back to the Latin neuter plural mathematica ( Cicero ), based on the Greek plural ta mathēmatiká ( τὰ μαθηματικά ) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after

6318-418: Is the purpose of universal algebra and category theory . The latter applies to every mathematical structure (not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects such as topological spaces ; this particular area of application is called algebraic topology . Calculus, formerly called infinitesimal calculus,

6435-405: Is the set of all integers. Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply. Algorithms —especially their implementation and computational complexity —play a major role in discrete mathematics. The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of

6552-508: Is true regarding number theory (the modern name for higher arithmetic ) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly considered part of geometry. Algebra and calculus do not appear as first-level areas but are respectively split into several first-level areas. Other first-level areas emerged during the 20th century or had not previously been considered as mathematics, such as mathematical logic and foundations . Number theory began with

6669-597: Is unknown is to refer to them as simply "Anonymous". This is usually the case with older texts in which the author is long dead and unable to claim authorship of a work. When the work claims to be that of some famous author the pseudonymous author is identified as "Pseudo-", as in Pseudo-Dionysius the Areopagite , an author claiming—and long believed—to be Dionysius the Areopagite , an early Christian convert. Anonymus , in its Latin spelling, generally with

6786-586: The Babylonians and Egyptians began using arithmetic, algebra, and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The oldest mathematical texts from Mesopotamia and Egypt are from 2000 to 1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical concept after basic arithmetic and geometry. It

6903-744: The First Amendment. The pressure on anonymous communication has grown substantially after the 2001 terrorist attack on the World Trade Center and the subsequent new political climate. Although it is still difficult to oversee their exact implications, measures such as the US Patriot Act , the European Cybercrime Convention and the European Union rules on data retention are only few of

7020-768: The Golden Age of Islam , especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra . Other achievements of the Islamic period include advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarizmi , Omar Khayyam and Sharaf al-Dīn al-Ṭūsī . The Greek and Arabic mathematical texts were in turn translated to Latin during

7137-511: The Pythagoreans appeared to have considered it a subject in its own right. Around 300 BC, Euclid organized mathematical knowledge by way of postulates and first principles, which evolved into the axiomatic method that is used in mathematics today, consisting of definition, axiom, theorem, and proof. His book, Elements , is widely considered the most successful and influential textbook of all time. The greatest mathematician of antiquity

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7254-536: The Renaissance , mathematics was divided into two main areas: arithmetic , regarding the manipulation of numbers, and geometry , regarding the study of shapes. Some types of pseudoscience , such as numerology and astrology , were not then clearly distinguished from mathematics. During the Renaissance, two more areas appeared. Mathematical notation led to algebra which, roughly speaking, consists of

7371-626: The University of Texas, El Paso . The current press officers are: In October 2006, the distinction between the British Animal Liberation Press Office and the ALF was questioned when a High Court judge ruled that Robin Webb was bound by an injunction banning protests at Oxford University . Webb had argued that he was a journalist and not a member of the ALF or its supporters group. According to The Guardian ,

7488-446: The controversy over Cantor's set theory . In the same period, various areas of mathematics concluded the former intuitive definitions of the basic mathematical objects were insufficient for ensuring mathematical rigour . This became the foundational crisis of mathematics. It was eventually solved in mainstream mathematics by systematizing the axiomatic method inside a formalized set theory . Roughly speaking, each mathematical object

7605-400: The 17th century, when René Descartes introduced what is now called Cartesian coordinates . This constituted a major change of paradigm : Instead of defining real numbers as lengths of line segments (see number line ), it allowed the representation of points using their coordinates , which are numbers. Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry

7722-469: The 1980s and 1990s ), and by DJ duo Daft Punk (1993-2021). For street artist Banksy , "anonymity is vital to him because graffiti is illegal". Anonymity has been used in music by avant-garde ensemble The Residents , Jandek (until 2004), costumed comedy rock band The Radioactive Chicken Heads , and DJs Deadmau5 (1998–present) and Marshmello (2015–present). This is frequently applied in fiction, from The Lone Ranger , Superman , and Batman , where

7839-405: The 19th century, mathematicians discovered non-Euclidean geometries , which do not follow the parallel postulate . By questioning that postulate's truth, this discovery has been viewed as joining Russell's paradox in revealing the foundational crisis of mathematics . This aspect of the crisis was solved by systematizing the axiomatic method, and adopting that the truth of the chosen axioms is not

7956-532: The 20th century. The P versus NP problem , which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult problems. Discrete mathematics includes: The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. Before this period, sets were not considered to be mathematical objects, and logic , although used for mathematical proofs, belonged to philosophy and

8073-494: The European Union. Japan was on 4 October 2012 the first to ratify the treaty. It creates an international regime for imposing civil and criminal penalties on Internet counterfeiting and copyright infringement. Although ACTA is intentionally vague, leaving signatories to draw precise rules themselves, critics say it could mean innocent travellers having their laptops searched for unlicensed music, or being jailed for carrying

8190-427: The Internet is accessed, it is accessed from a particular IP address, and the data traffic patterns to and from IP addresses can be intercepted, monitored, and analysed, even if the content of that traffic is encrypted. This address can be mapped to a particular Internet Service Provider (ISP), and this ISP can then provide information about what customer that IP address was leased to. This does not necessarily implicate

8307-637: The Middle Ages and made available in Europe. During the early modern period , mathematics began to develop at an accelerating pace in Western Europe , with innovations that revolutionized mathematics, such as the introduction of variables and symbolic notation by François Viète (1540–1603), the introduction of logarithms by John Napier in 1614, which greatly simplified numerical calculations, especially for astronomy and marine navigation ,

8424-528: The United States, disclosure of identity is required to be able to vote , though the secret ballot prevents disclosure of individual voting patterns. In airports in most countries, passengers are not allowed to board flights unless they have identified themselves to airline or transportation security personnel, typically in the form of the presentation of an identification card . On the other hand, some policies and procedures require anonymity. Stylometric identification of anonymous authors by writing style

8541-480: The actual author. According to the University of Stockholm this is creating more freedom of expression, and less accountability. Misplaced Pages is collaboratively written mostly by authors using either unidentifiable pseudonyms or IP address identifiers, although many Misplaced Pages editors use their real names instead of pseudonyms. However, the Internet was not designed for anonymity: IP addresses serve as virtual mailing addresses, which means that any time any resource on

8658-455: The appropriateness of anonymous organizational communication varies depending on the use, with organizational surveys or assessments typically perceived as highly appropriate and firing perceived as highly inappropriate. Anonymity use and appropriateness have also been found to be significantly related to the quality of relationships with key others at work. With few perceived negative consequences, anonymous or semi-anonymous forums often provide

8775-583: The beginnings of algebra (Diophantus, 3rd century AD). The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics . Other notable developments of Indian mathematics include the modern definition and approximation of sine and cosine , and an early form of infinite series . During

8892-481: The benefactor both from the beneficiary and from everyone else. Anonymous charity has long been a widespread and durable moral precept of many ethical and religious systems, as well as being in practice a widespread human activity. A benefactor may not wish to establish any relationship with the beneficiary, particularly if the beneficiary is perceived as being unsavory. Benefactors may not wish to identify themselves as capable of giving. A benefactor may wish to improve

9009-416: The case of Google+, this requirement led to a controversy known as the nymwars . The prevalence of cyberbullying is often attributed to relative Internet anonymity, due to the fact that potential offenders are able to mask their identities and prevent themselves from being caught. A principal in a high school stated that comments made on these anonymous site are "especially vicious and hurtful since there

9126-547: The case, a Connecticut federal court must apply a standard to decide whether the poster's identity should be revealed. There are several tests, however, that the court could apply when considering this issue. The right to internet anonymity is also covered by European legislation that recognizes the fundamental right to data protection , freedom of expression , freedom of impression. The European Union Charter of Fundamental Rights recognizes in Article. 8 (Title II: "Freedoms")

9243-511: The concept of a proof and its associated mathematical rigour first appeared in Greek mathematics , most notably in Euclid 's Elements . Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions ), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new fields. Since then,

9360-399: The current language, where expressions play the role of noun phrases and formulas play the role of clauses . Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and how they interact. It is based on rigorous definitions that provide a standard foundation for communication. An axiom or postulate is

9477-569: The derived expression mathēmatikḗ tékhnē ( μαθηματικὴ τέχνη ), meaning ' mathematical science ' . It entered the English language during the Late Middle English period through French and Latin. Similarly, one of the two main schools of thought in Pythagoreanism was known as the mathēmatikoi (μαθηματικοί)—which at the time meant "learners" rather than "mathematicians" in the modern sense. The Pythagoreans were likely

9594-428: The expansion of these logical theories. The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially probability theory . Statisticians generate data with random sampling or randomized experiments . Statistical theory studies decision problems such as minimizing the risk ( expected loss ) of

9711-567: The first to constrain the use of the word to just the study of arithmetic and geometry. By the time of Aristotle (384–322 BC) this meaning was fully established. In Latin and 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 change has resulted in several mistranslations: For example, Saint Augustine 's warning that Christians should beware of mathematici , meaning "astrologers",

9828-481: The immediate circle of Sandro Botticelli . In legal cases, a popularly accepted name to use when it is determined that an individual needs to maintain anonymity is " John Doe ". This name is often modified to "Jane Doe" when the anonymity-seeker is female. The same names are also commonly used when the identification of a dead person is not known. The semi-acronym Unsub is used as law enforcement slang for "Unknown Subject of an Investigation". The military often feels

9945-491: The interaction between mathematical innovations and scientific discoveries has led to a correlated increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method , which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than sixty first-level areas of mathematics. Before

10062-852: The internet 15 or 20 years later." There are some people though that consider anonymity in internet being a danger for our society as a whole. David Davenport, an assistant professor in the Computer Engineering Department of Bilkent University in Ankara, Turkey, considers that by allowing anonymous Net communication, the fabric of our society is at risk. "Accountability requires those responsible for any misconduct be identified and brought to justice. However, if people remain anonymous, by definition, they cannot be identified, making it impossible to hold them accountable." he says. As A. Michael Froomkin says: "The regulation of anonymous and pseudonymous communications promises to be one of

10179-400: The introduction of coordinates by René Descartes (1596–1650) for reducing geometry to algebra, and the development of calculus by Isaac Newton (1643–1727) and Gottfried Leibniz (1646–1716). Leonhard Euler (1707–1783), the most notable mathematician of the 18th century, unified these innovations into a single corpus with a standardized terminology, and completed them with the discovery and

10296-686: The introduction of the Terrorism Act 2000 , in order to avoid police attention, and to reflect that the office issues statements on behalf of a number of activist groups, not just the ALF. Robin Webb, formerly a member of the RSPCA ruling council, runs the office in the UK. The press office in North America , also known as NAALPO, was co-founded in 1994, and re-opened in December 2004, by Steven Best , an associate professor of philosophy at

10413-453: The issues. The United States Declaration of Independence , however, was not anonymous. If it had been unsigned, it might well have been less effective. John Perry Barlow , Joichi Ito , and other U.S. bloggers express a very strong support for anonymous editing as one of the basic requirements of open politics as conducted on the Internet. Anonymity is directly related to the concept of obscurantism or pseudonymity , where an artist or

10530-790: The judge described Webb as a "central and pivotal figure [in the ALF]," and concluded that "the press office was not a neutral reporting exercise or even simply a vehicle for apologists for the ALF, but a vital part of the ALF's strategy." In contrast, the North American press office claims: If the Press Office had any direct dealings with the underground, knew who the members of underground groups were, or were members ourselves, law enforcement would not hesitate to charge and imprison us. The Press Office frequently receives communiques anonymously from these underground groups, and passes them along to

10647-851: The latter is used to refer to both (in general, a situation where the legal identity of the person is disguised). Anonymity may reduce the accountability one perceives to have for their actions, and removes the impact these actions might otherwise have on their reputation. This can have dramatic effects, both useful and harmful to various parties involved. Thus, it may be used for psychological tactics involving any respective party to purport or support or discredit any sort of activity or belief. In conversational settings, anonymity may allow people to reveal personal history and feelings without fear of later embarrassment. Electronic conversational media can provide physical isolation, in addition to anonymity. This prevents physical retaliation for remarks, and prevents negative or taboo behavior or discussion from tarnishing

10764-409: The manipulation of numbers , that is, natural numbers ( N ) , {\displaystyle (\mathbb {N} ),} and later expanded to integers ( Z ) {\displaystyle (\mathbb {Z} )} and rational numbers ( Q ) . {\displaystyle (\mathbb {Q} ).} Number theory was once called arithmetic, but nowadays this term

10881-417: The media, but has no personal knowledge of who sends them or from where they are sent. Anonymity An important example for anonymity being not only protected, but enforced by law is the vote in free elections. In many other situations (like conversation between strangers, buying some product or service in a shop), anonymity is traditionally accepted as natural. There are also various situations in which

10998-543: The most important and contentious Internet-related issues of the next decade". Anonymity and pseudonymity can be used for good and bad purposes. And anonymity can in many cases be desirable for one person and not desirable for another person. A company may, for example, not like an employee to divulge information about improper practices within the company, but society as a whole may find it important that such improper practices are publicly exposed. Good purposes of anonymity and pseudonymity: There has always, however, also been

11115-400: The natural numbers, there are theorems that are true (that is provable in a stronger system), but not provable inside the system. This approach to the foundations of mathematics was challenged during the first half of the 20th century by mathematicians led by Brouwer , who promoted intuitionistic logic , which explicitly lacks the law of excluded middle . These problems and debates led to

11232-536: The objects defined this way is a philosophical problem that mathematicians leave to philosophers, even if many mathematicians have opinions on this nature, and use their opinion—sometimes called "intuition"—to guide their study and proofs. The approach allows considering "logics" (that is, sets of allowed deducing rules), theorems, proofs, etc. as mathematical objects, and to prove theorems about them. For example, Gödel's incompleteness theorems assert, roughly speaking that, in every consistent formal system that contains

11349-407: The other party to link different messages from the same person and, thereby, to establish a long-term relationship. Pseudonyms are widely used in social networks and other virtual communication, although recently some important service providers like Google try to discourage pseudonymity. Someone using a pseudonym would be strictly considered to be using "pseudonymity" not "anonymity", but sometimes

11466-521: The pattern of physics and metaphysics , inherited from Greek. In English, the noun mathematics takes a singular verb. It is often shortened to maths or, in North America, math . In addition to recognizing how to count physical objects, prehistoric peoples may have also known how to count abstract quantities, like time—days, seasons, or years. Evidence for more complex mathematics does not appear until around 3000  BC , when

11583-457: The privacy of consumers. Some consumers prefer to use cash when buying everyday goods (like groceries or tools), to prevent sellers from aggregating information or soliciting them in the future. Credit cards are linked to a person's name, and can be used to discover other information, such as postal address, phone number, etc. The ecash system was developed to allow secure anonymous transactions. Another example would be Enymity, which actually makes

11700-658: The proof of numerous theorems. Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Gauss , who made numerous contributions to fields such as algebra, analysis, differential geometry , matrix theory , number theory, and statistics . In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems , which show in part that any consistent axiomatic system—if powerful enough to describe arithmetic—will contain true propositions that cannot be proved. Mathematics has since been greatly extended, and there has been

11817-467: The property of that element of not being identifiable within this set. If it is not identifiable, then the element is said to be "anonymous". The word anonymous was borrowed into English around 1600 from the Late Latin word "anonymus", from Ancient Greek ᾰ̓νώνῠμος (anṓnumos, "without name"), from ᾰ̓ν- (an-, "un-") with ὄνῠμᾰ (ónuma), Aeolic and Doric dialectal form of ὄνομᾰ (ónoma, "name"). Sometimes

11934-449: The reputation of the speaker. This can be beneficial when discussing very private matters, or taboo subjects or expressing views or revealing facts that may put someone in physical, financial, or legal danger (such as illegal activity, or unpopular, or outlawed political views). In work settings, the three most common forms of anonymous communication are traditional suggestion boxes, written feedback, and Caller ID blocking. Additionally,

12051-412: The right of everyone to protection of personal data concerning him. The right to privacy is now essentially the individual's right to have and to maintain control over information about him. One of the most controversial international legal acts, regarding this subject is Anti-Counterfeiting Trade Agreement (ACTA) . As of February 2015, the treaty was signed -but not all ratified- by 31 states as well as

12168-454: The signs that the exercise of the right to the anonymous exchange of information is under substantial pressure. An above-mentioned 1995 Supreme Court ruling in McIntyre v. Ohio Elections Commission reads: "(...) protections for anonymous speech are vital to democratic discourse. Allowing dissenters to shield their identities frees them to express critical minority views . . . Anonymity is

12285-434: The sincere intention of furthering animal liberation ." The North American press office also includes a newsletter, prisoner list and merchandise page. The press office's position is that it receives claims of responsibility from anonymous cells , and that its officers "do not engage in illegal activities, nor do they know any individuals who do." In contrast, a British High Court judge described press officer Robin Webb as

12402-657: The study and the manipulation of formulas . Calculus , consisting of the two subfields differential calculus and integral calculus , is the study of continuous functions , which model the typically nonlinear relationships between varying quantities, as represented by variables . This division into four main areas—arithmetic, geometry, algebra, and calculus —endured until the end of the 19th century. Areas such as celestial mechanics and solid mechanics were then studied by mathematicians, but now are considered as belonging to physics. The subject of combinatorics has been studied for much of recorded history, yet did not become

12519-568: The study of approximation and discretization with special focus on rounding errors . Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic- matrix -and- graph theory . Other areas of computational mathematics include computer algebra and symbolic computation . The word mathematics comes from the Ancient Greek word máthēma ( μάθημα ), meaning ' something learned, knowledge, mathematics ' , and

12636-672: The theory under consideration. Mathematics is essential in the natural sciences , engineering , medicine , finance , computer science , and the social sciences . Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation. Some areas of mathematics, such as statistics and game theory , are developed in close correlation with their applications and are often grouped under applied mathematics . Other areas are developed independently from any application (and are therefore called pure mathematics ) but often later find practical applications. Historically,

12753-487: The title of his main treatise . Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified numbers. Variables allow mathematicians to describe the operations that have to be done on the numbers represented using mathematical formulas . Until the 19th century, algebra consisted mainly of the study of linear equations (presently linear algebra ), and polynomial equations in

12870-508: The two main precursors of algebra. Diophantus solved some equations involving unknown natural numbers by deducing new relations until he obtained the solution. Al-Khwarizmi introduced systematic methods for transforming equations, such as moving a term from one side of an equation into the other side. The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in

12987-591: The workshop's output set in chronological order. Sometimes archival research later identifies the name, as when the "Master of Flémalle"—defined by three paintings in the Städelsches Kunstinstitut in Frankfurt — was identified as Robert Campin . The 20th-century art historian Bernard Berenson methodically identified numerous early Renaissance Florentine and Sienese workshops under such sobriquets as "Amico di Sandro" for an anonymous painter in

13104-425: The world, as long as no one knows who did it, out of modesty, wishing to avoid publicity. Another reason for anonymous charity is a benefactor who does not want a charitable organization to pursue them for more donations, sometimes aggressively. Attempts at anonymity are not always met with support from society. Anonymity sometimes clashes with the policies and procedures of governments or private organizations. In

13221-694: Was convicted with 100% certainty, we must hold that the perpetrator remains anonymous and that the attribution of the probability of 1 to one of the players has to remain undecided. Mathematics Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as

13338-462: Was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements . The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane ( plane geometry ) and the three-dimensional Euclidean space . Euclidean geometry was developed without change of methods or scope until

13455-414: Was introduced independently and simultaneously by 17th-century mathematicians Newton and Leibniz . It is fundamentally the study of the relationship of variables that depend on each other. Calculus was expanded in the 18th century by Euler with the introduction of the concept of a function and many other results. Presently, "calculus" refers mainly to the elementary part of this theory, and "analysis"

13572-437: Was not specifically studied by mathematicians. Before Cantor 's study of infinite sets , mathematicians were reluctant to consider actually infinite collections, and considered infinity to be the result of endless enumeration . Cantor's work offended many mathematicians not only by considering actually infinite sets but by showing that this implies different sizes of infinity, per Cantor's diagonal argument . This led to

13689-571: Was split into two new subfields: synthetic geometry , which uses purely geometrical methods, and analytic geometry , which uses coordinates systemically. Analytic geometry allows the study of curves unrelated to circles and lines. Such curves can be defined as the graph of functions , the study of which led to differential geometry . They can also be defined as implicit equations , often polynomial equations (which spawned algebraic geometry ). Analytic geometry also makes it possible to consider Euclidean spaces of higher than three dimensions. In

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