The Carolinum Zürich is the predecessor educational institution of the theological faculty of the University of Zürich, established in 1525. As building, it is part of the former cloister of the Grossmünster Chorherrenstift in Zürich, Switzerland. Grossmünster and Carolinum are listed in the Swiss inventory of cultural property of national and regional significance as a Class A object. An institutionalized academic education in Zürich dates back to the medieval collegiate and city schools. In the late European Middle Ages, a Carolinum associated to the Grossmünster priory and its canons was mentioned. On occasion of the Reformation in Zürich, it became an important rule for the training of prospective Protestant theologians; as other educational institutions, it is named after Charlemagne. The reformer Huldrich Zwingli initiated the transformation of the former Latin school Prophezey or Prophezei into a training center for reformed theologians, by a Zürich city's council mandate on 29 September 1523 AD.
The weekday lectures were free of charge for the interested people in urban and rural areas of the city republic of Zürich, by well-learned men. Heinrich Bullinger's Schola Tigurina may have influenced the education in many other institutions beginning in 1559. Bullinger's Schola Tigurina merged in the 18th century to the theological faculty and the upper secondary school in the Carolinum been; the financing of the chairs professorships was depending on the benefices of the secularized canons of the former Grossmünster priory. In addition to theological subjects and Classical languages, in 1541 the natural history department and in 1731 a political science chair was created, in 1782 the surgical institute to train medical doctors. After the abolition of the Chorherrenstift congregation in 1832, the building was sold to the Canton of Zürich. In 1849 the structures were demolished and replaced by Gustav Albert Wegmann's building; the Grossmünsterplatz schoolhouse of the girls' gymnasium, an urban high school for girls, was established in 1875 and located in the building until 1976, when the Theological faculty of the University of Zürich moved in.
The present University of Zürich bases on the Carolinum and uses its former logo, the silhouette of the Grossmünster church. The university claims to be established in the tradition of the canons of the Carolinum's institutions. Theodor Bibliander, faculty Johann Jakob Bodmer, faculty Heinrich Bullinger, faculty Conrad Gessner, faculty Konrad Pellikan, faculty Josias Simmler, faculty Peter Martyr Vermigli, faculty The building is located at Kirchgasse 9 at the Grossmünsterplatz square – attached to the Grossmünster church on its eastern side – in the southeast of the Neumarkt northwesternly of the Münsterhof squares in Zürich; the cloister of the former Chorherrenstift Grossmünster, the chapter of Augustinian canons, dates from the late 12th century and was part of the canons, dissolved in 1832, making way for the girls' school. The cloister was dismantled and integrated into the new building those reconstruction was based on the original elements of the architecture, but includes numerous interpretations by the architect.
The cloister is home to a permanent exhibition on Zwingli and other important people in the Reformation era. The cloister was renewed in 2009, its sandstone elements were cleaned, the interior garden redesigned in corporation with the ProSpecieRara foundation; the compilation of the cultural and historical ornamental plants is inspired by the natural scientist and polymath Conrad Gessner who found his final resting place in the cloister. Gessner dealt inter alia with the elements of teaching, therefore the renewed courtyard garden is dedicated to the thema earth, fire and air, cultural-historical ornamental plants in the four beds, analogous to the Gessner-Garten in the Old Botananical Garden. After the abolition of the Chorherrenstift congregation in 1832, to 1849 the structures were demolished and replaced by Wegmann's building in the Romanesque Revival style; the as of today faculty building was built according to the drafts Gustav Albert Wegmann from 1843 to 1849. The cloister was dismantled during the demolition, supplemented with many new parts and integrated into the new building in 1851.
The Grossmünster church building is owned by the Canton of Zürich, the annex building being the former cloister, however, is in the property of the city of Zürich. It is leased to the Theological faculty of the University of Zürich since 1976. Grossmünster and Carolinum are listed in the Swiss inventory of cultural property of national and regional significance as a Class A object of national importance. Daniel Gutscher: Das Grossmünster in Zürich. Eine baugeschichtliche Monographie. Beiträge zur Kunstgeschichte der Schweiz, Volume 5. Redaction by Catherine Courtiau, Stefan Biffiger, Gian-Willi Vonesch. Gesellschaft für Schweizerische Kunstgeschichte Stäfa, Bern 1983, ISBN 3-85717-017-4. UZH Theologische Fakultät Sebastian Brändli: Universität Zürich in German and Italian in the online Historical Dictionary of Switzerland, 28 January 2013
ETH Zurich is a science, technology and mathematics university in the city of Zürich, Switzerland. Like its sister institution EPFL, it is an integral part of the Swiss Federal Institutes of Technology Domain, directly subordinate to Switzerland's Federal Department of Economic Affairs and Research; the school was founded by the Swiss Federal Government in 1854 with the stated mission to educate engineers and scientists, serve as a national center of excellence in science and technology and provide a hub for interaction between the scientific community and industry. In the 2019 edition of the QS World University Rankings ETH Zurich is ranked 7th in the world, is ranked 10th in the world by the Times Higher Education World Rankings 2018. In the 2019 QS World University Rankings by subject it is ranked 3rd in the world for engineering and technology, 1st for Earth & Marine Science; as of August 2018, 32 Nobel laureates, 4 Fields Medalists, 1 Turing Award winner have been affiliated with the Institute, including Albert Einstein.
It is a founding member of the IDEA League and the International Alliance of Research Universities and a member of the CESAER network. ETH was founded on 7 February 1854 by the Swiss Confederation and began giving its first lectures on 16 October 1855 as a polytechnic institute at various sites throughout the city of Zurich, it was composed of six faculties: architecture, civil engineering, mechanical engineering, forestry, an integrated department for the fields of mathematics, natural sciences and social and political sciences. It is locally still known as Polytechnikum, or as Poly, derived from the original name eidgenössische polytechnische Schule, which translates to "federal polytechnic school". ETH is a federal institute; the decision for a new federal university was disputed at the time. In the beginning, both universities were co-located in the buildings of the University of Zürich. From 1905 to 1908, under the presidency of Jérôme Franel, the course program of ETH was restructured to that of a real university and ETH was granted the right to award doctorates.
In 1909 the first doctorates were awarded. In 1911, it was given Eidgenössische Technische Hochschule. In 1924, another reorganization structured the university in 12 departments. However, it now has 16 departments. ETH Zurich, the EPFL, four associated research institutes form the "ETH Domain" with the aim of collaborating on scientific projects. ETH Zurich is ranked among the top universities in the world. Popular rankings place the institution as the best university in continental Europe and ETH Zurich is ranked among the top 1-5 universities in Europe, among the top 3-10 best universities of the world. ETH Zurich has achieved its reputation in the fields of chemistry and physics. There are 32 Nobel Laureates who are associated with ETH; the most recent Nobel Laureate is Richard F. Heck, awarded the Nobel Prize in chemistry in 2010. Albert Einstein is its most famous alumnus. In 2018, the QS World University Rankings placed ETH Zurich at 7th overall in the world. In 2015, ETH was ranked 5th in the world in Engineering and Technology, just behind the Massachusetts Institute of Technology, Stanford University, Cambridge University and National University of Singapore.
In 2015, ETH ranked 6th in the world in Natural Sciences, in 2016 ranked 1st in the world for Earth & Marine Sciences for the second consecutive year. In 2016, Times Higher Education World University Rankings ranked ETH Zurich 9th overall in the world and 8th in the world in the field of Engineering & Technology, just behind the Massachusetts Institute of Technology, Stanford University, California Institute of Technology, Princeton University, Cambridge University, Imperial College London and Oxford University. In a comparison of Swiss universities by swissUP Ranking and in rankings published by CHE comparing the universities of German-speaking countries, ETH Zurich traditionally is ranked first in natural sciences, computer science and engineering sciences. In the survey CHE ExcellenceRanking on the quality of Western European graduate school programmes in the fields biology, chemistry and mathematics, ETH was assessed as one of the three institutions to have excellent graduate programmes in all considered fields, the other two being the Imperial College London and the University of Cambridge.
ETH Zurich had a total budget of 1.885 billion CHF in the year 2017. For Swiss students, ETH is not selective in its undergraduate admission procedures. Like every public university in Switzerland, ETH is obliged to grant admission to every Swiss resident who took the Matura. Applicants from foreign countries are required to take either the reduced entrance exam or the comprehensive entrance exam although some applicants from several European countries are exempted from this rule. An applicant can be admitted to ETH without any verifiable educational records by passing the comprehensive entrance exam; as at all universities in Switzerland, the academic year is divided into two semesters. Examinations are held durin
Karl Moser was an architect from Switzerland. Between 1887 and 1915 he worked together with Robert Curjel in Karlsruhe; some of their works are: Kunsthaus Zurich University of Zurich Basel Badischer Bahnhof St. Paul's Church, Bern St. Anthony's, Basel several Protestant churchesFrom 1915 to 1928 he was professor at ETH Zurich. In 1928 he was president of the newly founded Congrès International d'Architecture Moderne, an organisation, steered prominently by the pioneers of modernism, architects Le Corbusier and Walter Gropius, which championed rational and functionalist architecture, while critiquing the type of revivalist architecture typified by Moser's own work. Indeed, at was at this time that Moser's own work changed radically towards modernism, exemplified in the St. Anthony's in Basel, built in reinforced concrete rather than brick and stone typical for his earlier works, his son Werner M. Moser became a noted architect. Leonardo Benevolo. History of Modern Architecture, Volume 2. MIT Press, 1977 pg. 618
Economics is the social science that studies the production and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents. Microeconomics analyzes basic elements in the economy, including individual agents and markets, their interactions, the outcomes of interactions. Individual agents may include, for example, firms and sellers. Macroeconomics analyzes the entire economy and issues affecting it, including unemployment of resources, economic growth, the public policies that address these issues. See glossary of economics. Other broad distinctions within economics include those between positive economics, describing "what is", normative economics, advocating "what ought to be". Economic analysis can be applied throughout society, in business, health care, government. Economic analysis is sometimes applied to such diverse subjects as crime, the family, politics, social institutions, war and the environment; the discipline was renamed in the late 19th century due to Alfred Marshall, from "political economy" to "economics" as a shorter term for "economic science".
At that time, it became more open to rigorous thinking and made increased use of mathematics, which helped support efforts to have it accepted as a science and as a separate discipline outside of political science and other social sciences. There are a variety of modern definitions of economics. Scottish philosopher Adam Smith defined what was called political economy as "an inquiry into the nature and causes of the wealth of nations", in particular as: a branch of the science of a statesman or legislator a plentiful revenue or subsistence for the people... to supply the state or commonwealth with a revenue for the publick services. Jean-Baptiste Say, distinguishing the subject from its public-policy uses, defines it as the science of production and consumption of wealth. On the satirical side, Thomas Carlyle coined "the dismal science" as an epithet for classical economics, in this context linked to the pessimistic analysis of Malthus. John Stuart Mill defines the subject in a social context as: The science which traces the laws of such of the phenomena of society as arise from the combined operations of mankind for the production of wealth, in so far as those phenomena are not modified by the pursuit of any other object.
Alfred Marshall provides a still cited definition in his textbook Principles of Economics that extends analysis beyond wealth and from the societal to the microeconomic level: Economics is a study of man in the ordinary business of life. It enquires how he uses it. Thus, it is on the one side, the study of wealth and on the other and more important side, a part of the study of man. Lionel Robbins developed implications of what has been termed "erhaps the most accepted current definition of the subject": Economics is a science which studies human behaviour as a relationship between ends and scarce means which have alternative uses. Robbins describes the definition as not classificatory in "pick out certain kinds of behaviour" but rather analytical in "focus attention on a particular aspect of behaviour, the form imposed by the influence of scarcity." He affirmed that previous economists have centred their studies on the analysis of wealth: how wealth is created and consumed. But he said that economics can be used to study other things, such as war, that are outside its usual focus.
This is because war has as the goal winning it, generates both cost and benefits. If the war is not winnable or if the expected costs outweigh the benefits, the deciding actors may never go to war but rather explore other alternatives. We cannot define economics as the science that studies wealth, crime and any other field economic analysis can be applied to; some subsequent comments criticized the definition as overly broad in failing to limit its subject matter to analysis of markets. From the 1960s, such comments abated as the economic theory of maximizing behaviour and rational-choice modelling expanded the domain of the subject to areas treated in other fields. There are other criticisms as well, such as in scarcity not accounting for the macroeconomics of high unemployment. Gary Becker, a contributor to the expansion of economics into new areas, describes the approach he favours as "combin assumptions of maximizing behaviour, stable preferences, market equilibrium, used relentlessly and unflinchingly."
One commentary characterizes the remark as making economics an approach rather than a subject matter but with great specificity as to the "choice process and the type of social interaction that analysis involves." The same source reviews a range of definitions included in principles of economics textbooks and concludes that the lack of agreement need not affect the subject-matter that the texts treat. A
Staatsarchiv Zürich, or by its native name Staatsarchiv des Kantons Zürich and shortened to Staatsarchiv, is the name of the state archives of the Swiss Canton of Zürich of the former city republic of Zürich and its preceding statutories. The state archives host the administrative records of the Canton of Zürich, as it was established in 1803 in its current form, it preserves the administrative records of the predecessor of the Canton of Zürich, so the records of the Helvetic Kanton Zürich, in particular of the old city-state Zürich until 1798. In addition to being the "official memory of the administration", it is a versatile documentation and facility for scientific research and for the public; the 4 February 1837 marked the beginning of a new era in Zürich's archives, when Hans Jakob Ammann was elected by the cantonal authorities as the director of the Staatsarchiv. He succeeded the previous "registrar" historian Gerold Meyer von Knonau, given the title Staatsarchivar, as he first started to merge various special archives to a central archive, among them of Fraumünster, Grossmünster and the former city council, further non-official archives, but of the Grand Council, the Government and cantonal Supreme Court, as well as the documents of the former Kappel and Rüti monasteries and the cantonal Reformed churches.
Since 1837, therefore all cantonal, including all municipalities of the canton of Zürich oriented activities have to be recorded and stored by the Staatsarchiv. Staatsarchiv is the archive of the public institutions of the Canton of Zurich, so the cantonal parliament, the government, the cantonal central and district administration and the courts and institutions, it stores and permanently preserves the lore worthy documents. As a historical archive, it keeps the administrative records of the ancient city-state of Zurich since the European Middle Ages; the archives are supplemented by documents stocks of private origin, among them companies, guilds and individuals. The retention of these documents allows to make the state action understandable, enables historical research and the use of cultural interests in the broadest sense, accessible for all interested parties in accordance with legal provisions. In addition, it operates as a public reference library with the focus on "History of the Canton of Zurich" and "archival science".
It supervises and advises the municipalities of the canton in matters of archiving. Staatsarchiv preserves unique and large parts of medieval handwritten documents, but some documents related to the city of Zürich are still housed at the Haus zum Rechberg at Neumarkt, Zürich; the archival holdings date back to 853 AD, as Zürich was the imperial Pfalz Turicum, thenafter an imperial city, a federal center of the Reformation in Zürich. This history has been reflected in the holdings of the archive. Noteworthy is the continuity of the Zürich archives, that owes to the absence of large disasters and wars. For example, the government protocols, which can be described as the backbone of history, are nearly preserved since the late 15th century; the newer stocks of the Canton of Zurich started quantitatively to be the main focus of the tradition in the archives. Every year, the archives records 800 metres linear meters of new content in paper; the increased volume origins by the cantonal authorities, as cantonal council, councillor including central and district administration, cantonal institutions, courts.
In addition, there are more and more private documents related to the modern history of the Canton of Zurich, so company archives, individual documents, heritage documents in the widest sense. More than 30 kilometres of paper files are stored, terabytes of electronic files, but just accessible to the public; as of 3 October 2017, all documents of the former city republic of Zürich back to 1803 have been digitalized and are accessible to the public. Between 1888 and 1978, more than 50,000 inventive and innovative Zürich citizens applied for more than 50,000 patents at the Swiss Federal Patent Office, united in the collection Patentschriften. Ammong them a bathing suit invented by Hermann Brupbacher in 1894, described as a "bathing suit for people who are unfamiliar with swimming...in which floating bodies made of rubber tubes filled with crushed cork pieces are sewn in". There are not only curiosities to be found, there are patents for a motor vehicle registered by F. Vogel in Küsnacht in 1905, or the patent for the nuclear reactor of the Sulzer Winterthur industries from 1957 The digitized patent specifications, which in most cases include a drawing, are available online.
The seal stamp of the city seal of 1347, which shows the three saints Felix and Exuperantius, is the oldest example of the collection Objekte. It includes younger state objects such as the Zürich standard weight, a dog measuring device from 1909, or the ballotage box of the cantonal council of 1831, used to vote on petitions for pardon; the Plansammlung collection of plans consists of around 25,000 documents back to the 17th century, this valuable collection of plans can be viewed online. As a public institution, the state archives are part of the cantonal administration and associated to the cantonal Department of Justice and Interior; the archives houses a scientific library, a library housing all magazines published in the canton of Zürich, reading rooms, an administrativ service to handle the public access by all interested people. In addition to the archive materials, a digital library is provided, as well a collectio
Times Higher Education World University Rankings
Times Higher Education World University Rankings is an annual publication of university rankings by Times Higher Education magazine. The publisher had collaborated with Quacquarelli Symonds to publish the joint THE–QS World University Rankings from 2004 to 2009 before it turned to Thomson Reuters for a new ranking system; the publication now comprises the world's overall and reputation rankings, alongside three regional league tables, Latin America, BRICS & Emerging Economies which are generated by different weightings. THE Rankings is considered as one of the most observed university rankings together with Academic Ranking of World Universities and QS World University Rankings, it is praised for having a new, improved ranking methodology since 2010. The creation of the original Times Higher Education–QS World University Rankings was credited in Ben Wildavsky's book, The Great Brain Race: How Global Universities are Reshaping the World, to then-editor of Times Higher Education, John O'Leary.
Times Higher Education chose to partner with educational and careers advice company QS to supply the data. After the 2009 rankings, Times Higher Education took the decision to break from QS and signed an agreement with Thomson Reuters to provide the data for its annual World University Rankings from 2010 onwards; the publication developed a new rankings methodology in consultation with its readers, its editorial board and Thomson Reuters. Thomson Reuters will collect and analyse the data used to produce the rankings on behalf of Times Higher Education; the first ranking was published in September 2010. Commenting on Times Higher Education's decision to split from QS, former editor Ann Mroz said: "universities deserve a rigorous and transparent set of rankings – a serious tool for the sector, not just an annual curiosity." She went on to explain the reason behind the decision to continue to produce rankings without QS' involvement, saying that: "The responsibility weighs heavy on our shoulders...we feel we have a duty to improve how we compile them."Phil Baty, editor of the new Times Higher Education World University Rankings, admitted in Inside Higher Ed: "The rankings of the world's top universities that my magazine has been publishing for the past six years, which have attracted enormous global attention, are not good enough.
In fact, the surveys of reputation, which made up 40 percent of scores and which Times Higher Education until defended, had serious weaknesses. And it's clear that our research measures favored the sciences over the humanities."He went on to describe previous attempts at peer review as "embarrassing" in The Australian: "The sample was too small, the weighting too high, to be taken seriously." THE published its first rankings using its new methodology on 16 September 2010, a month earlier than previous years. The Times Higher Education World University Rankings, along with the QS World University Rankings and the Academic Ranking of World Universities are described to be the three most influential international university rankings; the Globe and Mail in 2010 described the Times Higher Education World University Rankings to be "arguably the most influential."In 2014 Times Higher Education announced a series of important changes to its flagship THE World University Rankings and its suite of global university performance analyses, following a strategic review by THE parent company TES Global.
The inaugural 2010-2011 methodology contained 13 separate indicators grouped under five categories: Teaching, citations, international mix, industry income. The number of indicators is up from the Times-QS rankings published between 2004 and 2009, which used six indicators. A draft of the inaugural methodology was released on 3 June 2010; the draft stated that 13 indicators would first be used and that this could rise to 16 in future rankings, laid out the categories of indicators as "research indicators", "institutional indicators", "economic activity/innovation", "international diversity". The names of the categories and the weighting of each was modified in the final methodology, released on 16 September 2010; the final methodology included the weighting signed to each of the 13 indicators, shown below: The Times Higher Education billed the methodology as "robust and sophisticated," stating that the final methodology was selected after considering 10 months of "detailed consultation with leading experts in global higher education," 250 pages of feedback from "50 senior figures across every continent" and 300 postings on its website.
The overall ranking score was calculated by making Z-scores all datasets to standardize different data types on a common scale to better make comparisons among data. The reputational component of the rankings came from an Academic Reputation Survey conducted by Thomson Reuters in spring 2010; the survey gathered 13,388 responses among scholars "statistically representative of global higher education's geographical and subject mix." The magazine's category for "industry income – innovation" came from a sole indicator, institution's research income from industry scaled against the number of academic staff." The magazine stated that it used this data as "proxy for high-quality knowledge transfer" and planned to add more indicators for the category in future years. Data for citation impact, comprising 32
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes 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, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. 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 of sine and cosine, an early form of infinite series. During the Golden Age of Islam 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 notable achievements of the Islamic period are 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-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to