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88-428: Over 100 students are involved in various aspects of the magazine, including writing, editorial, production, art, multimedia, website, and business. It currently has more than 2,000 subscribers around the world. Article topics covered by Yale Scientific Magazine include disciplines in science, mathematics , and engineering , at Yale and beyond. The magazine presents and promotes achievements, knowledge, and activities in

176-591: 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

264-411: A bicycle for the competition. They were then assigned tasks in every aspect of the magazine’s operation, and were graded on a point system. The point total and general quality of the heeler’s work were the criteria used in judging them as a perspective member. If a member won several heeling competitions, they would be entitled to a “charm.” Board membership was granted upon the attainment of a charm, which

352-408: A fortnightly magazine which, we trust, will adequately fill the obvious place in the undergraduate world for an illustrated that will portray campus life as the camera records it.” The Graphic was well-received at first, but within a few years it became clear that there was no variety to be found in subject matter, though the names of the students were changing. In addition, the quality and quantity of

440-614: 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

528-669: 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)

616-493: A lecture/demonstration series started in 2004 targeted at elementary/middle schoolers, and Resonance, an annual science conference for high schoolers. Synapse hosted virtual events in 2020 and 2021, including science seminars, professor lecture series, and a scholarship contest. In 2015, YSM launched its blog page, The Scope , which aims to present topics and breakthroughs in science in a simpler, more interesting, and more personal manner. Mathematics Mathematics

704-404: 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

792-422: 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

880-402: 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

968-535: 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

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1056-591: A prominent feature. One year later the Yale Engineering Association (YEA) was founded on December 4, 1914, at a meeting attended by 40 alumni. Membership was open to any Yale graduate although “the association naturally appeals more strongly to those who are engaged in engineering pursuits, transportation or manufacturing." Prior to the founding of YEA, alumni organizations primarily consisted of groups organized by class year or geographic designation. A circular outlining purposes and objectives

1144-609: A representative undergraduate periodical in the institution would be consistent with the progress along other lines.” One of its main purposes was to be a comfortable medium in which Sheff students could develop their writing skills, something many Sheff graduates had complained to not have done in their undergraduate years. Senior members of the Sheffield Class of 1895 sought the advice of literary instructors, and certain Sheff faculty, and subsequently formed YSM. At its founding,

1232-411: 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

1320-424: 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

1408-418: 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

1496-477: 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

1584-703: 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

1672-664: Is flat " and "a field is always a ring ". Yale Science %26 Engineering Association The Yale Science & Engineering Association ( YSEA ) is the Yale University alumni organization focused on science, technology, engineering, and math (STEM). Founded in 1914 as the Yale Engineering Association, YSEA is one of the oldest university alumni organizations in the world. YSEA supports undergraduate research and entrepreneurship at Yale College and recognizes outstanding service, accomplishment and scholarship in STEM through

1760-471: 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

1848-403: 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

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1936-513: 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

2024-407: 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

2112-493: 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

2200-695: Is largely supported by the Yale Science & Engineering Association , which provides a Yale alumni readership base and strategic partnerships in addition to financial support. In recent years, the magazine has extended operations to other modes of scientific communication, including outreach (Synapse), an online blog (The Scope), as well as webinars. Synapse is the outreach team of YSM . Synapse regularly hosts competitions, conferences and events that are usually targeted at children and teenagers, to cultivate and support interest in science and journalism. The flagship programs of Synapse include Science on Saturdays,

2288-586: 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

2376-404: 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,

2464-1192: 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

2552-547: 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

2640-433: 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

2728-567: 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

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2816-418: 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,

2904-405: 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

2992-508: 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

3080-586: 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

3168-768: 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

3256-511: 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

3344-536: 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

3432-446: 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

3520-400: 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

3608-405: 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

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3696-532: 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

3784-637: 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 ,

3872-492: The Sheff, its contents were fluff to everyone else. The Board of the twentieth volume changed the name to Yale Sheffield Monthly, solidifying the magazine’s altered focus. The arrogance and self-interest of the staff was clearly reflected in the contents of the magazine over the next few years. It all came to a self-defeating end, however, when the Monthly shut down after its twenty-fourth volume in 1918, due to lack of support from

3960-629: The Sheffield Scientific School, and especially on the Board of Editors.” Sheff Dean Charles H. Warren expressed confidence that YSM would “serve as a medium through which the scientific work which is being done in the various departments of the University will be brought to the attention of a larger audience, receive a wider recognition, and awaken a greater interest in this important field of Yale’s intellectual life. Since 1927,

4048-634: The YSEA Annual Awards. YSEA was founded “to advance the interest of Engineering at Yale and prompt the better acquaintanceship and fellowship of Yale Engineers.” YSEA supports secondary school STEM education through its affiliations with FIRST Robotics and the International Science & Engineering Fair. YSEA is a sponsor of the Yale Scientific Magazine , the nation's oldest college science publication and

4136-589: The Yale Engineering Association was held in November 1915 in New Haven, CT. At the meeting several well-established industry professionals were elected to leadership positions. Edwin M. Herr, of Westinghouse Electric & Mfg. Company was elected president. Harry N. Covell, works manager of the Lidgerwood Mfg. Co., was elected vice-president and Richard T. Dana, a New York City-based consulting engineer,

4224-563: The Yale Scientific Monthly was unique for the diverse range of subjects within the sciences it covered. Its first four articles were: “The Sheffield Scientific School,” a history; “Diameters of Stepped Pulleys”; “Something About Bacteria”, and “Some Landmarks in the Life of Chemistry.” The magazine’s policy was to publish both student and faculty articles. Yale undergraduates performed all editorial and managerial work. The cost of

4312-583: 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

4400-473: The college and the Sheff, military officers, and political figures, such as the U.S. Surgeon General and the Secretary of Health. Yale Students ran all of the editorial and managerial affairs of the magazine and wrote news briefs and editorials. This gradually changed, and by the later 1960s, students were writing all the articles and still running the other operations. The foci of the articles has varied with

4488-511: 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,

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4576-399: 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

4664-569: 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

4752-631: The dinner given at the Yale Club of New York (at the time located at 30 West 44th Street , the current home of the Penn Club of New York ). Professor Lester Paige Breckenridge, head of the Sheffield Scientific School , presided. At the dinner, plans were hatched to form a permanent Yale engineering alumni organization. A committee was appointed to consider the formation of a Yale Engineering Society, with an annual reunion to be

4840-516: The elucidation of the DNA double helix by Watson and Crick, and other emerging techniques. In the late 1960s and early to mid-1970s, YSM concentrated on sciences related to the Vietnam War and in other heated social issues. This pathway culminated with the exploratory microanalytical studies in the natural sciences encountered in the last decade or so. Today, Yale Scientific Magazine strives to narrow

4928-418: The estimation of Sheff students. The staff consisted of members of the Sheff who had “heeled” the magazine. “Heeling” was one of Old Blue’s [Yale’s] many traditions that have long since vanished from practice into lore. Common among many organizations, heeling competitions were held periodically as a means of determining staff members. Heelers were told to purchase a Yale Co-op Heeler’s Notebook, and rent or buy

5016-428: 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

5104-482: The first issue was $ 0.30, and a year’s subscription was $ 2.50. The magazine’s stated address was simply: “Yale Scientific Monthly, New Haven, Conn.” For 18 years, the Monthly was an opportunity for young scientists at the Sheffield Scientific School to act as journalists. In the process they kept the rest of the Yale community informed about important and interesting developments in all scientific departments at Yale, and in

5192-567: 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",

5280-409: The general scientific community. It was of a high quality, and served as a model for the development of college science magazines at other institutions. As a serious scientific journal, YSM’s success was marginalized. Yale College students were seldom to read scientific works to relax. Sheff men needed escapes from and not supplements to their science-packed schedules. Nonetheless, it continued to rise in

5368-497: The gulf between the sciences and humanities at Yale, particularly by making science done at Yale accessible to a non-technical audience across campus and nationwide. True to its founding philosophy, the Yale Scientific Magazine has remained a platform for budding scientists to develop the art of written communication, and for non-scientists to learn about the cutting edge of science at Yale. Yale Scientific Magazine

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5456-491: 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

5544-400: 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

5632-414: The literary works gradually decreased. Within five years of the publication’s beginning, it had become defunct. The name change proved an insufficient guise for the continued low quality of the content. No trace of the original Scientific Monthly was seen for three years. In 1926, the Sheff senior class decided to revive the magazine in the manner in which it was originally intended, as a magazine devoted to

5720-504: The magazine has stayed continuously in print, with few major changes in format. ("The" in the title was eliminated since 1952.) The content of the magazine, however, has changed to reflect the times. From 1927 until the mid 1960s, the majority of the feature articles were solicited from Yale faculty members rather than students. Many articles were also written by the chief executives of large-scale technical and engineering companies. There were also articles written by presidents of Yale, deans of

5808-409: 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

5896-711: The material they printed and joined forces with the beleaguered Yale Courant, the school’s first illustrated periodical (1865). By February 1919, the Yale Graphic was being published from the basement of Sheffield’s Byers Hall by former staff of the Sheffield Monthly and of the Courant. In its first issue, Chairman L. Staples explained: “With this issue, the Yale Sheffield Monthly and The Yale Courant erstwhile rivals, unite to publish The Graphic

5984-400: 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

6072-536: 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

6160-521: 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

6248-903: The premier science publication at Yale. The Yale Science & Engineering Association, Inc. traces its origin to the 34th annual meeting of the American Society of Mechanical Engineers (ASME) held December 2–5, 1913 in New York City at the Engineering Societies’ Building . On the final evening of the ASME annual meeting, seven colleges ( Stevens Institute of Technology , Worcester Polytechnic Institute , Polytechnic Institute of Brooklyn , Yale University , Kentucky State University , Brown University , and Cornell University ) held alumni reunions at various locations throughout New York City. Twenty-nine Yale alumni attended

6336-658: 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

6424-432: The ring of campus controversies unless they shall lead to significant steps in the development of the school.” The magazine was received surprisingly well, and 75% of graduate and Sheff students had subscribed by the time the first issue was printed, with a circulation of 1,900 magazines. Yale President James Rowland Angell commented that “The Yale Scientific Magazine is an admirable achievement which reflects great credit on

6512-468: The sciences at Yale. In 1927, this plan became a reality with the first issue of The Yale Scientific Magazine. In the first pages of the issue, there is a statement from the editors describing the magazine, and its new role at Yale: “The Yale Scientific Magazine, while published in the interest of science and engineering within the Sheffield Scientific School, will include accounts of the scientific accomplishments of Yale graduates. It will not cast its hat into

6600-473: The sciences, medicine , and engineering at the University. In October 1894, the senior class of Yale’s Sheffield Scientific School (or the “Sheff”) published the first issue of the Yale Scientific Monthly. The Monthly was founded in response to “the rapid growth of the Scientific School, and the important position it was attaining in the affairs of the University", such that "the establishment of

6688-473: The student body. On its demise, a writer for the Yale Daily News wrote that “the purpose and scope of the Sheffield Monthly was never fully understood” and its “quality was never what it should have been.” The editors of the Monthly realized their error in documenting collegiate opinions and social activities in a publication intended for scientific writing. They aligned their stated editorial focus with

6776-657: 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

6864-568: 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

6952-672: 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,

7040-418: The times, and reflects Yale’s contribution to the sciences. The late 1920s and the 1930s concentrated on applied physics and engineering. The following decade was dominated by war-related sciences. The 1950s saw a revival of the applied physical sciences, culminating in the feverish space race. The 1950s also served as a prelude to the burst of biological studies in the 1960s, fueled by Jonas Salk’s polio vaccine,

7128-487: 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

7216-508: 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

7304-399: Was also awarded to select students who consistently contributed quality works to YSM. The editorial board of the nineteenth volume of the Monthly took an unexpected step by beginning to record the affairs of Sheff students, sports, and societies, as well as printing lengthy student editorials. The move was disastrous. While the publication remained of interest to its writers and readers within

7392-474: Was distributed to Yale graduates. Interest among Sheffield Scientific School alumni was high; membership neared 500 at the end of September 1915, two months before the first official meeting. Prior to its official founding in 1914, alumni and faculty of the Sheffield Scientific School had been interested in creating an organization devoted to the welfare of the Sheffield School. The first meeting of

7480-462: 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

7568-414: 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"

7656-437: 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

7744-571: 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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