essay about mathematics in modern world

Essay on Mathematics In Modern World

Students are often asked to write an essay on Mathematics In Modern World in their schools and colleges. And if you’re also looking for the same, we have created 100-word, 250-word, and 500-word essays on the topic.

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100 Words Essay on Mathematics In Modern World

Math in everyday life.

Math is everywhere in our daily lives. When we buy things, we use math to count money. We also use math when we cook, measuring ingredients to make our favorite dishes. Even our smartphones rely on math to work properly.

Technology and Math

Modern technology, like computers and video games, is built on math. Programmers use math to write the codes that run our apps and games. Without math, we wouldn’t have the internet or be able to send messages to our friends online.

Science and Math

Scientists use math to understand the world. Whether it’s a doctor giving the right amount of medicine or an engineer building a bridge, math is key. It helps us solve problems and make discoveries that improve our lives.

Math in Nature

Nature is full of math too. The patterns on a pineapple or the way a spider spins its web are based on math. By studying these patterns, we learn more about the world and how it works.

Education and Math

250 words essay on mathematics in modern world, math and everyday life.

Math is like a secret code that explains how things work in our world. It is not just about numbers and equations; it is everywhere around us. When we go shopping, we use math to count money and to figure out if we have enough to buy the things we want. When we cook, we measure ingredients using math. Even when we play sports, we use math to keep score and to improve our skills by looking at how far, how fast, or how high we go.

In today’s world, we use a lot of gadgets and machines. All of these are built using math. For example, our phones, computers, and video games all run on programs that are made using math. When we watch a movie with amazing special effects or use an app to talk to our friends, math is what makes it all possible.

Math is not just in the things we make; it is also in nature. The way a flower grows, the pattern on a snail’s shell, and the way the stars are arranged in the sky all follow math rules. By understanding these patterns, we can learn more about the world and how it works.

Jobs and Math

Many jobs need math. Doctors use it to understand medicine and to keep people healthy. Builders use math to make houses and buildings strong and safe. Even artists use math when they create beautiful pictures or music.

In short, math is a powerful tool that helps us understand and shape the world. It is not just for school; it is a part of life that helps us solve problems and create new things.

500 Words Essay on Mathematics In Modern World

The importance of mathematics.

In today’s world, technology is a big part of our lives. It’s in our computers, phones, and even our kitchen appliances. All these gadgets use math to work properly. Programmers use math to write the codes that tell our devices what to do. When you play a video game, math is what makes the characters move and the story progress. Without math, none of these amazing technologies would be possible.

Nature is full of math too. Have you ever looked at a snowflake or a seashell? They have patterns that can be explained by math. The way trees branch out or how flowers grow follows a mathematical rule. This shows that math is not just something humans created, but it is a language that describes how our world is put together.

Math in Health

Math in money matters.

Money is a big part of everyone’s life, and math is key to understanding it. Whether you’re saving up for a new toy or managing a weekly allowance, you’re using math. Businesses use math to make products, set prices, and figure out profits. Even governments need math to plan budgets and make sure there’s enough money for schools, roads, and other services.

Math in Education

In school, math might seem like it’s just about learning to add or multiply. But really, it’s about teaching you to think logically and solve problems. These skills are important for any job you might want to do in the future. Math helps you develop a way of thinking that is helpful in almost any situation.

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Table Of Contents

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mathematics , the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter. Since the 17th century, mathematics has been an indispensable adjunct to the physical sciences and technology, and in more recent times it has assumed a similar role in the quantitative aspects of the life sciences.

In many cultures—under the stimulus of the needs of practical pursuits, such as commerce and agriculture—mathematics has developed far beyond basic counting. This growth has been greatest in societies complex enough to sustain these activities and to provide leisure for contemplation and the opportunity to build on the achievements of earlier mathematicians.

All mathematical systems (for example, Euclidean geometry ) are combinations of sets of axioms and of theorems that can be logically deduced from the axioms. Inquiries into the logical and philosophical basis of mathematics reduce to questions of whether the axioms of a given system ensure its completeness and its consistency. For full treatment of this aspect, see mathematics, foundations of .

This article offers a history of mathematics from ancient times to the present. As a consequence of the exponential growth of science, most mathematics has developed since the 15th century ce , and it is a historical fact that, from the 15th century to the late 20th century, new developments in mathematics were largely concentrated in Europe and North America . For these reasons, the bulk of this article is devoted to European developments since 1500.

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

This does not mean, however, that developments elsewhere have been unimportant. Indeed, to understand the history of mathematics in Europe, it is necessary to know its history at least in ancient Mesopotamia and Egypt, in ancient Greece, and in Islamic civilization from the 9th to the 15th century. The way in which these civilizations influenced one another and the important direct contributions Greece and Islam made to later developments are discussed in the first parts of this article.

India’s contributions to the development of contemporary mathematics were made through the considerable influence of Indian achievements on Islamic mathematics during its formative years. A separate article, South Asian mathematics , focuses on the early history of mathematics in the Indian subcontinent and the development there of the modern decimal place-value numeral system . The article East Asian mathematics covers the mostly independent development of mathematics in China, Japan, Korea, and Vietnam.

The substantive branches of mathematics are treated in several articles. See algebra ; analysis ; arithmetic ; combinatorics ; game theory ; geometry ; number theory ; numerical analysis ; optimization ; probability theory ; set theory ; statistics ; trigonometry .

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My Reflection in Mathematics in the Modern World

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Cheryl Praeger

as the wonderings about the status of school mathematics are becoming louder and louder, the need for a revision of our reasons can no longer be ignored. In what follows, I respond to this need by taking a critical look at some of the most popular arguments for the currently popular slogan, “Mathematics for all.” This analysis is preceded by a proposal of how to think about mathematics so as to loosen the grip of clichés and to shed off hidden prejudice. It is followed by my own take on the question of what mathematics to teach, to whom, and how.

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As the time enters the 21st century, sciences such as those of theoretical physics, complex system and network, cytology, biology and economy developments change rapidly, and meanwhile, a few global questions constantly emerge, such as those of local war, food safety, epidemic spreading network, environmental protection, multilateral trade dispute, more and more questions accompanied with the overdevelopment and applying the internet, · · · , etc. In this case, how to keep up mathematics with the developments of other sciences? Clearly, today's mathematics is no longer adequate for the needs of other sciences. New mathematical theory or techniques should be established by mathematicians. Certainly, solving problem is the main objective of mathematics, proof or calculation is the basic skill of a mathematician. When it develops in problem-oriented, a mathematician should makes more attentions on the reality of things in mathematics because it is the main topic of human beings.

Amarnath Murthy

There is nothing in our lives, in our world, in our universe, that cannot be expressed with mathematical theories, numbers, and formulae. Mathematics is the queen of science and the king of arts; to me it is the backbone of all systems of knowledge. Mathematics is a tool that has been used by man for ages. It is a key that can unlock many doors and show the way to different logical answers to seemingly impossible problems. Not only can it solve equations and problems in everyday life, but it can also express quantities and values precisely with no question or room for other interpretation. There is no room for subjectivity. Though there is a lot of mathematics in politics, there is no room for politics in mathematics. Coming from a powerful leader two + two can not become five it will remain four. Mathematics is not fundamentally empirical —it does not rely on sensory observation or instrumental measurement to determine what is true. Indeed, mathematical objects themselves cannot be observed at all! Mathematics is a logical science, cleanly structured, and well-founded. Mathematics is obviously the most interesting, entertaining, fascinating, exciting, challenging, amazing, enthralling, thrilling, absorbing, involving, fascinating, mesmerizing, satisfying, fulfilling, inspiring, mindboggling, refreshing, systematic, energizing, satisfying, enriching, engaging, absorbing, soothing, impressive, pleasing, stimulating, engrossing, magical, musical, rhythmic, artistic, beautiful, enjoyable, scintillating, gripping, charming, recreational, elegant, unambiguous, analytical, hierarchical, powerful, rewarding, pure, impeccable, useful, optimizing, precise, objective, consistent, logical, perfect, trustworthy, eternal, universal subject in existence full of eye catching patterns.

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Mathematics plays a dominant role in today's world. Although not everyone will become a mathematical expert, from an educational point of view, it is key for everyone to acquire a certain level of mathematical literacy, which allows reflecting and assessing mathematical processes important in every day live. Therefore the goal has to be to open perspectives and experiences beyond a mechanical and tight appearance of the subject. In this article a framework for the integration of reflection and assessment in the teaching practice is developed. An illustration through concrete examples is given.

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Michele Emmer

It is no great surprise that mathematical structures and ideas, conceived by human beings, can be applied extremely effectively to what we call the "real" world. We need only to think of physics, astronomy, meteorology, telecommunications, biology, cryptography, and medicine. But that's not all mathematics has always had strong links with music, literature, architecture, arts, philosophy, and more recently with theatre and cinema

Liliya Samigullina

The article considers mathematics as a way of teaching reasoning in symbolic non-verbal communication. Particular attention is paid to mathematical ways of thinking when studying the nature and its worldview. The nature is studied through the theory of experimental approval of scientific concepts of algorithmic and nonalgorithmic "computing". Various discoveries are analyzed and the role of mathematics in the worldview is substantiated. The greatest value of mathematics is development of knowledge in order to express it in abstract language of mathematics and natural science, i.e., to move to the meta-pedagogical level of understanding of problems

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The Power of Mathematics: Unveiling its Influence on Nature and Phenomena

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How mathematics built the modern world

Mathematics was the cornerstone of the Industrial Revolution. A new paradigm of measurement and calculation, more than scientific discovery, built industry, modernity, and the world we inhabit today.

In school, you might have heard that the Industrial Revolution was preceded by the Scientific Revolution, when Newton uncovered the mechanical laws underlying motion and Galileo learned the true shape of the cosmos. Armed with this newfound knowledge and the scientific method, the inventors of the Industrial Revolution created machines – from watches to steam engines – that would change everything.

But was science really the key? Most of the significant inventions of the Industrial Revolution were not undergirded by a deep scientific understanding, and their inventors were not scientists.

The standard chronology ignores many of the important events of the previous 500 years. Widespread trade expanded throughout Europe. Artists began using linear perspective and mathematicians learned to use derivatives. Financiers started joint stock corporations and ships navigated the open seas. Fiscally powerful states were conducting warfare on a global scale.

There is an intellectual thread that runs through all of these advances: measurement and calculation. Geometric calculations led to breakthroughs in painting, astronomy, cartography, surveying, and physics. The introduction of mathematics in human affairs led to advancements in accounting, finance, fiscal affairs, demography, and economics – a kind of social mathematics. All reflect an underlying ‘calculating paradigm’ – the idea that measurement, calculation, and mathematics can be successfully applied to virtually every domain. This paradigm spread across Europe through education, which we can observe by the proliferation of mathematics textbooks and schools. It was this paradigm, more than science itself, that drove progress. It was this mathematical revolution that created modernity.

The geometric innovations

Advances in geometry began with the rediscovery of Euclid. The earliest known Medieval Latin translation of Euclid’s Elements was completed in manuscript by Adelard of Bath around 1120 using an Arabic source from Muslim Spain. A Latin printed version was published in 1482. After the mathematician Tartaglia translated Euclid’s work into Italian in 1543, translations into other vernacular languages quickly followed: German in 1558, French in 1564, English in 1570, Spanish in 1576, and Dutch in 1606.

Beyond Euclid, the German mathematician Regiomontanus penned the first European trigonometry textbook, De Triangulis Omnimodis ( On Triangles of All Kinds ), in 1464. In the sixteenth century, François Viète helped replace the verbal method of doing algebra with the modern symbolism in which unknown variables are denoted by symbols like x, y, and z. René Descartes and Pierre de Fermat built on Viète’s innovations to develop analytic geometry , where curves and surfaces are described by algebraic equations. In the late seventeenth century, Isaac Newton and Gottfried Leibniz extended the methods of analytic geometry to the study of motion and change through the development of calculus.

On top of theoretical improvements to mathematics, the instruments used to apply these theories to the world also advanced dramatically. One striking example comes from angular measurement, which saw large increases in precision as astronomers began to use new instruments, like the mural quadrant in the picture above. Angular measurement works by pointing instruments toward objects and reading off their angles on a measurement scale. The precision of pointing was improved by telescopic sights and finely tunable mechanisms, while better-designed measurement scales allowed astronomers to discriminate between similar angles. The graph below shows the trend of precision, going from seven arcminutes, or 0.11 degrees, in 1550, to 0.06 arc seconds , or 0.000017 degrees, in 1850 – an astounding improvement of almost 7,000 times over three centuries.

Computation was aided by the adoption of Hindu-Arabic numerals and the popularization of decimal notation . In 1614, John Napier’s introduction of the logarithm transformed multiplication into addition, and it was followed a decade later by the invention of the slide rule that could efficiently perform multiplication and division (see image below). The era also saw the introduction of printed mathematical tables. These tables document the values of standard mathematical functions and were crucial for computation before the advent of electronic calculators. Constructing them involved using known relationships such as trigonometric identities to compute new function values from old ones. While straightforward in theory, table construction was computationally demanding. The famous 1596 trigonometric table Opus Palatinum de Triangulis was an expensive endeavor financed by the Habsburg emperor Maximilian II: its 100,000 trigonometric ratios – accurate to up to ten decimal pIaces – took the mathematician Rheticus and his team of human computers 12 years to calculate , at a cost of more than 50 times Rheticus’s annual salary as a mathematics professor.

Applied geometry

The developments in mathematical knowledge, instrument making, and computation supported a wave of mathematically based innovations.

In the fifteenth century, linear perspective revolutionized painting by making it possible to represent three-dimensional space on a two-dimensional surface. The mathematical underpinnings are evident in Leon Battista Alberti’s seminal 1415 work, De Pictura ( On Painting ). The opening paragraph announces that the treatise will ‘borrow from mathematicians those aspects relevant to the subject’. After laying out the Euclidean concepts of points, lines, planes, and surfaces, Alberti employs this geometric language to explain the principles of perspective painting.

Surveying and cartography also advanced. In 1450, Alberti wrote Descriptio Urbis Romae ( Description of the City of Rome ), which featured a table of coordinates for important places in Rome together with instructions for land surveying , the measurement of geographic positions, distances, and areas.

The ensuing centuries saw further improvements. A key advance was the growth of triangulation. The diagram below illustrates the basic idea: if you have the points A and B and measure the angles ɑ and β to C, this uniquely pins down the position of C. Further, if the length between A and B is known, the method also delivers the distances from A and B to C. Triangulation was attractive because it replaced expensive measurement of distances with cheap measurement of angles. After the mathematician Gemma Frisius explained how triangulation could be used for mapmaking in 1533, the method spread rapidly across Europe. In 1578, the astronomer Tycho Brahe used triangulation to map the island of Hven where his observatory was located, and the method is described in many textbooks published before the end of the century.

The power of the concept can be further amplified by the use of triangulation networks, where triangulated points are used for further triangulation (see diagram below). With sufficiently exact angular measurements, there is no limit to the precision and range of such networks. In 1615, the Dutch mathematician Willebrod Snellius used a triangulation network based on church spires to determine the distances between 14 Dutch cities, and by the mid-eighteenth century, the French geodesic missions (attempts to measure the shape of the Earth) used triangulation networks and precise instruments to establish that the Earth bulges at the equator by showing that one degree of latitude is 111.9 kilometers at the Arctic circle, but only 110.5 kilometers at the equator. Triangulation networks formed the basis of mapmaking until the advent of GPS.

Mathematics also shaped Renaissance warfare. To counter the power of new artillery, the geometry of fortification grew more complex through the introduction of the star fort, the so-called trace italienne . Star forts were intricately shaped low-lying fortresses surrounded by a protective belt of glacis (sloping banks) and ravelins (outward-poking triangles of wall) that prevented direct cannon fire onto the walls. Their triangular bastions deflected cannon shots while allowing defenders to enfilade (fire along a line end to end) attackers seeking to scale the walls. To construct them, fortress building emerged as an area of applied mathematics , since getting the geometry right was crucial to combine protection from enemy cannon fire with a good line of sight for defenders.

At the same time, ballistics emerged as the mathematical study of artillery. The first treatise, Nova Scientia ( A New Science ), was published in 1537 by the Euclid translator Tartaglia. The book presents a rudimentary theory of projectile motion, provides an argument for why the 45-degree angle maximizes a cannon’s range, and offers guidance on instruments that gunners could use to measure distances and calibrate cannon elevations. The title page depicts Tartaglia demonstrating the new science of trajectories to the seven muses in a walled garden, with Euclid guarding the entrance.

Modern astronomy was also grounded in geometry. The competing celestial models of Ptolemy, Copernicus, Brahe, and Kepler had different implications for angular measurements, so geometric arguments became key to astronomical debates.

The mathematician Regiomontanus showed how basic geometry could be used to determine the distance to celestial bodies. The key idea was that whether you believe the Earth spins around its axis or the heavens around the Earth, the spinning is around the Earth’s center , not its surface , where observers are located. Given this, it turns out that proximate objects appear to move faster across the heavens than distant objects. The diagram below shows how an observer on the edge of a spinning body perceives proximate and distant objects: as the observer spins, the proximate red point appears to move past the distant black point. Tycho Brahe famously used this reasoning to argue that the 1572 supernova and the 1577 comet must be located far beyond the moon because they appeared to move much less than the moon relative to distant stars. This was important for astronomical debates,challenging the Aristotelian view that only the sublunary sphere saw change while the heavens were unchanging.

Later, the Ptolemaic geocentric model of the heavens was dealt a final blow by Galileo Galilei. Drawing on his mathematical knowledge and engineering experience , Galileo improved the magnification of the recently invented telescope and used it to discover that Venus had phases just like the moon. According to the Ptolemaic model, Venus is always located between the Earth and the Sun, and there could never be a ‘full Venus’, since this could only occur if Venus was located beyond the Sun from the perspective of the Earth. Galileo was able to demonstrate that the shadows of Venus were consistent with the planet orbiting the Sun rather than the Earth.

Astronomical models contributed to navigation by supporting the creation of almanacs that predicted the positions of celestial objects at specific future dates and times. If sailors knew how high different celestial objects were above the horizon at different latitudes and different dates of the year, they could find the latitude by measuring their angles and consulting the relevant date in the almanac. This facilitated open sea navigation , as sailors with knowledge of the latitude of their destination could sail north or south until the position in the sky of the Sun or some other celestial object indicated that they had reached the desired latitude, and then sail along it. This released them from having to follow the coast. The importance of having the right latitude was amply demonstrated in 1707 when more than 1,400 British sailors drowned after four British warships crashed into the Isles of Scilly off the coast of Cornwall, due to a 24–36-nautical-mile misestimation of their latitude (not just a mistake in longitude, as common belief would have it).

Mathematical innovations were central to the period’s crowning achievement: modern science. In his Invention of Science , the historian David Wootton shows how innovations in painting, cartography, surveying, ballistics, astronomy, and navigation paved the way for the Scientific Revolution of the seventeenth century. A community of individuals gained experience in developing mathematical models of the world and confronting them with increasingly precise measurements from the new instruments. In astronomy, this process ultimately overturned the geocentric model. A similar process unfolded in mechanics, as Galileo combined instrument making, measurement, and mathematics to lay the foundation for our modern understanding of motion. When Galileo claimed that the universe is a book ‘ written in the language of mathematics ’, he expressed a central assumption underlying modern physical science. In the words of Wootton, ‘the Scientific Revolution was, first and foremost, a revolution by the mathematicians’.

The mathematization of social life

The beginnings of social mathematics came with the introduction of Arabic algebra into Europe. A significant milestone was the publication in 1202 of Liber Abaci by Leonardo of Pisa, better known as Fibonacci. Drawing on examples from business and everyday life, Liber Abaci introduced Hindu-Arabic numerals and basic algebra, showcasing how these tools could be used to perform standard arithmetic calculations and solve business problems such as the splitting of profits. Fibonacci was not the first to use Arabic numerals in Europe, but he was influential . He also introduced net present values , which turn flows of payments over time into a single value by discounting future incomes based on the interest rate.

These theoretical underpinnings led to innovations in social mathematics. An early example was double-entry bookkeeping, in which financial transactions are recorded in separate debit and credit accounts. The earliest known example dates to 1299 , but widespread dissemination across Europe followed the publication of the mathematician Luca Pacioli’s printed book Summa de Arithmetica, Geometria, Proportioni et Proportionalita (1494). By recording all transactions twice, double-entry bookkeeping reduced the likelihood of error and allowed firms to trace their changing financial positions to the underlying flows.

Double-entry bookkeeping spread among private merchants in Italy and, together with improvements in interest rate mathematics, supported the rise of private financial institutions. Banking empires like the Fuggers and Medicis relied on it to manage their sprawling activities and capital structures, and good accounting supported lending institutions by making it easier to supervise borrowers .

The era also saw improvements in the financial practices of states. The overarching motivation was the evolving needs of warfare. During the early modern era, the fealty-bound vassals of the Middle Ages were replaced by armies of predominantly professional mercenaries. Hard cash became the language of the battlefield, and good financial management became a survival imperative for the state.

In the late fifteenth century, the Habsburg monarchy developed the Hofkammer , or court chamber, model of state finances in which a centralized unit kept track of revenue, expenses, and credit flows. The Hofkammer approach spread across Germany during the sixteenth century, and has been linked to increases in fiscal capacity – that is, how much money a state can raise through taxes or borrowing. The accounting ideals of the Hofkammer can be seen in a 1568 instruction manual which states that the court bookkeeper should ‘set up orderly books with different rubrics and paragraphs and essentially maintain them’.

The lives of individual reformers suggest that innovations in public accounting diffused from the private sector. Thomas Cromwell worked in an Italian banking firm before returning to England to restructure the royal financial administration from a personalized feudal system toward a modern state bureaucracy, the so-called Tudor Revolution in Government . In the Netherlands, the polymath Simon Stevin worked at a merchant firm and published the first table of interest rate calculations before becoming the principal advisor to the stadtholder of the Netherlands, Maurice of Orange. (Stevin was also an accounting theorist who published the first analysis of government accounting in 1607.) In France, Jean-Baptiste Colbert was born into a family of prominent merchants, but entered government and was responsible for reforming the financial administration of France in the late seventeenth century.

Besides innovations in interest rate calculations and private and public accounting, the early modern era also saw developments in financial markets, especially in markets for government debt. Here, Italian city states were important innovators. In times of emergency, funds were raised by the imposition of forced loans on wealthy citizens. Although obligatory, these loans paid an interest and thus became assets for the creditors. A secondary market for these debts developed, making it possible for the creditors to turn their assets into cash even when the principal was not redeemed by the state.

It has been estimated that five percent of Italian debt was traded in a given year during the fifteenth century . The increased sophistication of private financiers and their public counterparts supported financial innovation: Sweden financed its rise to great power status by mortgaging its copper income, and in order to make its debt more attractive, England created the Bank of England as a separate entity with privileges such as note issuance.

Finally, the early modern era witnessed the birth of quantitative social science. After surveying Ireland for Cromwell’s army in the 1650s, the Englishman William Petty championed a new science called ‘ political arithmetic ’, which sought quantitative precision in matters relating to taxes, expenditure, trade, and monetary issues. Another Englishman, John Graunt, is often regarded as the founder of demography due to his analysis of mortality rates in his work, Natural and Political Observations Made upon the Bills of Mortality . Subsequently, life tables and the new theory of probability were combined to support pricing in the emerging life insurance industry, with the Dutchman Johan de Witt’s The Worth of Life Annuities Compared to Redemption Bonds (1671) considered one of the earliest applications of probability theory to finance. Building on these advances, the eighteenth and nineteenth centuries saw the evolution of modern disciplines such as economics, epidemiology, demography, and actuarial science.

The calculating paradigm

The innovations in our narrative encompass a broad range of domains, but they have one unifying characteristic: the use of measurement and mathematical calculations to tackle real-world problems. We call this ‘the calculating paradigm’. The diagram below illustrates the core of the paradigm. To solve a problem, one must first translate it into a numeric representation using quantitative measurement. The representation is then subjected to modeling and calculation to arrive at a solution that is applied to the real world.

The first step in the paradigm is measurement – the numerical encoding of the real-world situation. For example, when Galileo studied uniform acceleration, he first measured the time taken for a ball to roll down inclines of different lengths. Similarly, an accountant converts an inventory of physical goods, assets, and transactions into a set of quantities that are expressed in a common monetary unit and allocated to different cost, revenue, asset, and liability accounts. In both cases, the end product is a mathematical representation.

Next is manipulation, which involves the use of mathematical techniques and models to process the representation. Galileo needed to compute ratios to discover that the time for a ball to roll down an incline grows as the square root of the distance of the incline. Accountants calculate profits as the difference between total revenues and costs, and equity as the difference between total assets and total liabilities. In both cases, the end product is a mathematical result.

The final step is to apply the mathematical result to perform a real-world action. In physics, it could be the design of a clock that depends on laws of motion, or a scientific decision to reject a particular model of motion. In accounting, it could be an investment decision based on a profitability calculation, or a bankruptcy decision based on a solvency calculation.

Today, different types of mathematically guided decision-making are often viewed as fundamentally distinct activities. The use of mathematics to explain the natural world belongs to science; the use of geometric calculations to determine directions belongs to navigation; the use of accounting calculations for business decisions belongs to financial analysis. But these practices all share an underlying logic in how they combine quantitative measurement and mathematical manipulation to guide behavior.

The origin and spread of the calculating paradigm

What is the evidence for the spread of the calculating paradigm? As a cognitive strategy, the calculating paradigm is close to what anthropologists call a cultural trait , or a discrete unit of cultural transmission. Anthropologists generally infer the diffusion of cultural traits from the spread of attendant artifacts and behavioral patterns, similar to our procedure in the innovation narrative. However, in principle, the diffusion of cultural traits can also be observed directly through the process of learning and imitation. While often difficult in practice, this route is possible for the calculation paradigm, since mathematics is almost universally learned through schools and textbook materials.

Using this strategy, the origin of the calculating paradigm in Europe can be traced to the introduction of Arab mathematics during the late Middle Ages. The epicenter was northern Italy. This was where Leonardo of Pisa’s Liber Abaci was published in 1202 , and from the thirteenth century onward the region saw widespread adoption of Hindu-Arabic numerals and attendant methods for calculation and problem solving.

The diffusion of the calculating paradigm was supported by a new form of educational institution: the Abacus schools. These schools catered to the merchant class and differed from traditional Latin schools by teaching in the local language, and by eschewing classical studies in favor of practical skills in calculation, measurement, and bookkeeping. With a commercial focus, they taught mathematics to young children using problems related to currency exchange, labor contracts, and profit distribution.

Abacus schools became a powerful educational force. In Renaissance Florence, up to one in three of all boys attended Abacus schools – famous students included Luca Pacioli, ‘the father of accounting’, and a young Leonardo da Vinci. The schools also created a market for mathematicians to support themselves as teachers of practical mathematics, so-called maestri d’abaco . Nicolo Tartaglia – whom we encountered earlier as a Euclid translator and a writer on ballistics – was an Abacus teacher.

Over time, practical mathematics education spread northward from Italy. During the fifteenth century in Germany, so-called Rechenmeisters established Rechenschulen , which provided practical arithmetic education. By 1615, Nuremberg had no less than 48 such schools in a city of fewer than 50,000 people . The spread was supported by the printing press, which let mathematicians reach broad audiences through popular textbooks. Many became classics: Adam Ries’s 1522 Rechnung auff der Linihen und Federn went through 114 editions and Robert Recorde’s 1543 The Ground of Artes went through 46.

In a recent effort to study the diffusion of the new mathematics, the historian Raffaelle Danna compiled a database of 1,280 practical arithmetic texts with Hindu-Arabic numerals. The database contains all known arithmetic manuals in manuscript and printed format written from the publication of Liber Abaci in 1202 up to 1600. The map below displays their cumulative numbers over space and time, illustrating how the new mathematics was initially concentrated around northern Italy before spreading outward during the fifteenth and sixteenth century.

During the sixteenth century, Protestantism also contributed to the proliferation of mathematical skills. Protestant reformers placed a strong emphasis on education both for theological and practical purposes, and in the Protestant educational program designed by Philip Melanchthon –himself a student of the mathematician and astronomer Johannes Stöffler – mathematics was given a central role . The Frenchman Petrus Ramus created a program in the mid-sixteenth century aimed at expanding and enhancing education. Although Ramus was not a mathematician, he believed strongly in the value of the practical skills provided by mathematics and it was central to his educational ideas. His program, known as Ramism , gained short-term but substantial influence in schools in Germany, the Netherlands, England, Scotland, Sweden, and, to a certain extent, France. Although the impact of his ideas diminished in the seventeenth century, they remained relevant among the religious dissenters who won the English Civil War and colonized New England.

In Catholic Europe, education became dominated by the Jesuit order. Established in 1540, a key aim of the order was to educate children and youth. Their schools were financed by donations and payments from cities where they had established themselves, and they could expand rapidly by requiring that their graduates taught for three to five years after graduation. Initially, Jesuits used the teaching of mathematics as a competitive tool against existing Abacus schools and as a way to attract local patronage . But their main focus was on theology and classical learning, and the role of mathematics remained contentious.

When the Jesuits debated their curriculum in the late sixteenth century, the prominent mathematician Clavius, himself a Jesuit, argued for a central role for mathematics, but he faced opposition from those who wanted to prioritize theology and philosophy . In the end, his program was scaled back, and in the 1599 Ratio Studiorum, which was to govern Jesuit education for the next two centuries, mathematics is only mentioned in a few paragraphs across a 100-page document, and its study was relegated to the last year of a seven-year program. Jesuit schools still produced elite mathematicians like René Descartes, but by placing mathematics at the end of a long classical curriculum, they discouraged the widespread dissemination of the practical arithmetic skills favored by the earlier Abacus schools and by the Ramist program found in Protestant countries.

Traditional universities had a mixed impact on the spread of mathematical knowledge. In the fourteenth and fifteenth centuries, the universities of Paris and Vienna contributed significantly to the introduction and development of Arabic mathematics, and universities remained important for pushing the frontier of mathematical knowledge. Melanchthon’s educational program for Protestant universities granted mathematics an important role, but mathematics still faced competition from the traditional scholastic curriculum, which focused more on grammar, logic, and rhetoric.

There were exceptions, particularly in areas where the Ramist program was influential, such as in the Netherlands and Sweden in the early seventeenth century, and in Scotland later in the seventeenth century. The expansion of mathematics in higher education became more widespread when it was recognized as a strategic interest of the state. An early example was the seventeenth century French engineering colleges, and this practice spread in the eighteenth century, which saw a proliferation of military schools of higher education with mathematics as an important part of the curriculum.

As universities vacillated in their attitude toward the calculating paradigm, the teaching of practical mathematics proved a fertile ground for private education, as occupational opportunities in business, navigation, and instrument making created a willingness to pay for mathematical skills. Private academies started to be formed in England during the seventeenth century to provide teaching in practical skills such as letter writing, double-entry bookkeeping, and arithmetic. At the end of the eighteenth century, there were 200 such academies. England also had a system of Dissenting Academies, which provided education for non-Anglicans who were excluded from regular higher education. The Dissenting Academies typically provided a more practically oriented education than the traditional institutions of higher learning.

The spread of mathematical skills can be gauged quantitatively in the spread of books in applied mathematics. The graph below, based on research by the economic historians Morgan Kelly and Cormac Ó Gráda, shows the number of books published in England with headings in the following subject groups: arithmetic, astronomical instruments, bookkeeping, compasses, geometry, gunnery, logarithms, mathematics, mathematical instruments, measuring, navigation, shipbuilding, surveying, and trigonometry. We see that these subjects virtually did not exist in England in the early sixteenth century, but by the 1700s each had hundreds of publications per decade.

Mathematics, the mechanical arts, and the Industrial Revolution

By 1750, the calculating paradigm had spread across Europe. It had supported innovations across a wide range of areas, and in doing so, it had paved the way for the modern world. But the classic Industrial Revolution had not yet started, and mathematics did not yet have widespread success in the area of mechanized production.

The failure was not for lack of interest. Since the Renaissance, mathematicians had dreamed of conquering the mechanical arts. Leonardo da Vinci studied mathematical treatises on mechanics and drew his famous flying machine. In 1588, the Italian engineer Ramelli introduced his collection of machine drawings with an eight-page preface celebrating mathematics as the basis for all mechanical arts .

Before the Industrial Revolution, however, aspiration often outran achievement. Many of Leonardo’s machines were famously unworkable, and while Ramelli’s machinery book was popular, practitioners remained unimpressed . Before the Industrial Revolution, men of practice often saw mathematicians as frivolous.

This would change after 1750. During the Industrial Revolution, engineers achieved remarkable success in treating production as the execution of a mathematical plan. Why did eighteenth-century engineers succeed where Renaissance mathematicians had failed?

One important reason was that eighteenth-century engineers could achieve a higher degree of precision in production. Precision is crucial for mechanization, since it decreases friction and ensures that parts behave in a uniform way – even small frictions and performance variations can endanger the fine-tuned workings of a machine.

More generally, precision makes it possible to produce real-world objects that conform to mathematical idealizations. Engineers can then move beyond envisioning machines in the abstract and start producing reliable prototypes. The pioneers of the Industrial Revolution valorized precision, and as the revolution gathered speed, requirements for precision grew ever more stringent. In the 1770s, James Watt proudly declared that the cylinders of his steam engine were bored to the precision of 1/20 of an inch. By the 1850s, the self-acting machines of Joseph Whitworth aimed for a precision of 1/10,000 of an inch.

Eighteenth-century England stood out in its ample supply of craftsmen able to do high-precision work. From 1700–1800, England saw a doubling in the number of clockmakers and instrument makers, according to evidence collected by Kelly and Ó Gráda. Besides clocks, these producers made instruments for mathematical disciplines such as surveying, navigation, bookkeeping, and astronomy. Craftsmen in these industries provided a bridge between mathematics and manual labor – understanding the products required mathematical understanding, while constructing them required manual dexterity. When the Industrial Revolution got underway, these instrument makers were recruited to construct the complex steam and weaving machines that drove the revolution.

Designing the machines of the Industrial Revolution required basic arithmetic and geometry: you cannot obsess over precision unless you follow a mathematical plan. However, the mathematics required was not advanced. Once you knew basic mathematics and were committed to using it in practice, the main challenge was implementation.

From this perspective, the Industrial Revolution required that basic mathematics and a quantitative outlook reached the class of people actually engaged in production. This is what happened in England.

While many of the pioneers of the Industrial Revolution only had a modest formal education, they found ways to acquire basic mathematical skills. Sometimes, the brief education at the village school gave a mathematical training. The spinning mule inventor Samuel Crompton lost his father and had to work as a yarn spinner from an early age, but he went to a school where the teacher ‘ had considerable reputation as a teacher, particularly of writing, arithmetic, book-keeping, geometry, mensuration and mathematics ’. Evening classes catered to people who had missed out on a formal education. This was how George Stephenson , ‘the father of railways’, learned writing and arithmetic by the age of 18. A burgeoning textbook market also made self-education possible – this was the route of the famous clockmaker John Harrison .

The lives of the pioneers provide further evidence of a mathematical outlook. Joseph Bramah (1748–1814) was a locksmith who contributed to early precision manufacturing. He left school at the age of 12 to work on his father’s farm and was later apprenticed as a carpenter. But this mathematical outlook is clear from the Rudimentary Treatise on the Construction of Locks . The book explains how Bramah’s locks became essentially unbreakable through what mathematicians nowadays call combinatorial explosion : the fact that even a small number of objects can be ordered in an extraordinary number of ways. Bramah notes that even if a lock only has 12 moving parts with 12 distinct positions, ‘the ultimate number of changes that may be made in their place or situation is 479,001,600; and by adding one more to that number of slides, they would then be capable of receiving a number of changes equal to 6,227,020,800; and so on progressively, by the addition of others in like manner to infinity’.

Another example is Bramah’s most famous disciple Henry Maudslay , the founding father of machine tools production . Maudslay also started working at the age of 12, but had a mathematical outlook: he was famous for his relentless focus on precise measurement, invented a new type of slide rule, and in his personal life applied a system where he ranked individuals on a degree scale ranging from 0 to 100 . Evidently, a quantitative worldview did not require college-level calculus.

Calculating today

Our narrative shows how the rise of the modern world is linked to the spread of the calculating paradigm.

After the paradigm’s introduction to Europe from the Arab-speaking countries in the thirteenth century, it was initially limited to a few universities and Italian merchant towns. However, the paradigm found fertile ground and gradually diffused across space, supported by the printing press and by new forms of educational institutions. It also diffused across social classes, moving from its origin among merchants and university professors to encompass administrators, craftspeople, small business owners, and seafarers. By the late eighteenth century, the paradigm had even reached Samuel Crompton’s modest village school in Bolton, in the north of England.

In the wake of the paradigm’s diffusion, we see innovations in painting, cartography, astronomy, navigation, physics, statecraft, finance, and accounting throughout the early modern era. But there was one key holdout: the process of production, which long eluded mathematicians as they failed to bridge the gap between theory and practice. Here, the breakthrough came in eighteenth-century England as a new class of engineers and instrument makers combined basic mathematical skills with the craftsmanship needed to make mathematical ideas workable.

Our story concludes in 1800, when the paradigm finally reached the process of production. Over the next 200 years, that paradigm has continued to spread, reaching more people and touching more domains. Since the advent of universal schooling, we have come to expect that all children should know how to calculate with Hindu-Arabic numerals. Tellingly, we use the term ‘basic arithmetic’ for a skill that until relatively recently was confined to specialized experts, and was not widely taught outside of a few northern Italian towns.

The last 200 years have seen the influence of mathematics deepen across almost all domains of human activity, amply supported by torrents of data and dramatic increases in computing power. Now we use math to model nuclear wars, pick players for baseball teams, track changes in literature, and forecast presidential elections. Sometimes, it seems the paradigm has reached its limits; that every field that can benefit from math has been introduced to it. But we may now be nearing the computational paradigm’s greatest success of all: modeling intelligence through math using large language models. In that sense, the computational paradigm may be reaching its logical conclusion: turning us all into math.

Bo Malmberg is a Professor at the Department of Geography of Stockholm University. His main areas of focus are human geography, demography and segregation.

Hannes Malmberg is an Assistant Professor at the University of Minnesota. He is currently researching input intensification in agriculture, the role of human capital and market integration in economic development, and the macroeconomic effects of population aging.

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What Students Are Saying About the Value of Math

We asked teenagers: Do you see the point in learning math? The answer from many was “yes.”

By The Learning Network

“Mathematics, I now see, is important because it expands the world,” Alec Wilkinson writes in a recent guest essay . “It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention.”

In our writing prompt “ Do You See the Point in Learning Math? ” we wanted to know if students agreed. Basic arithmetic, sure, but is there value in learning higher-level math, such as algebra, geometry and calculus? Do we appreciate math enough?

The answer from many students — those who love and those who “detest” the subject alike — was yes. Of course math helps us balance checkbooks and work up budgets, they said, but it also helps us learn how to follow a formula, appreciate music, draw, shoot three-pointers and even skateboard. It gives us different perspectives, helps us organize our chaotic thoughts, makes us more creative, and shows us how to think rationally.

Not all were convinced that young people should have to take higher-level math classes all through high school, but, as one student said, “I can see myself understanding even more how important it is and appreciating it more as I get older.”

Thank you to all the teenagers who joined the conversation on our writing prompts this week, including students from Bentonville West High School in Centerton, Ark, ; Harvard-Westlake School in Los Angeles ; and North High School in North St. Paul, Minn.

Please note: Student comments have been lightly edited for length, but otherwise appear as they were originally submitted.

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Math Essay Ideas for Students: Exploring Mathematical Concepts

Are you a student who's been tasked with writing a math essay? Don't fret! While math may seem like an abstract and daunting subject, it's actually full of fascinating concepts waiting to be explored. In this article, we'll delve into some exciting math essay ideas that will not only pique your interest but also impress your teachers. So grab your pens and calculators, and let's dive into the world of mathematics!

The Beauty of Fibonacci Sequence

Have you ever wondered why sunflowers, pinecones, and even galaxies exhibit a mesmerizing spiral pattern? It's all thanks to the Fibonacci sequence! Explore the origin, properties, and real-world applications of this remarkable mathematical sequence. Discuss how it manifests in nature, art, and even financial markets. Unveil the hidden beauty behind these numbers and show how they shape the world around us.

The Mathematics of Music

Did you know that music and mathematics go hand in hand? Dive into the relationship between these two seemingly unrelated fields and develop your writing skills . Explore the connection between harmonics, frequencies, and mathematical ratios. Analyze how musical scales are constructed and why certain combinations of notes create pleasant melodies while others may sound dissonant. Explore the fascinating world where numbers and melodies intertwine.

The Geometry of Architecture

Architects have been using mathematical principles for centuries to create awe-inspiring structures. Explore the geometric concepts that underpin iconic architectural designs. From the symmetry of the Parthenon to the intricate tessellations in Islamic art, mathematics plays a crucial role in creating visually stunning buildings. Discuss the mathematical principles architects employ and how they enhance the functionality and aesthetics of their designs.

Fractals: Nature's Infinite Complexity

Step into the mesmerizing world of fractals, where infinite complexity arises from simple patterns. Did you know that the famous Mandelbrot set , a classic example of a fractal, has been studied extensively and generated using computers? In fact, it is estimated that the Mandelbrot set requires billions of calculations to generate just a single image! This showcases the computational power and mathematical precision involved in exploring the beauty of fractal geometry.

Explore the beauty and intricacy of fractal geometry, from the famous Mandelbrot set to the Sierpinski triangle. Discuss the self-similarity and infinite iteration that define fractals and how they can be found in natural phenomena such as coastlines, clouds, and even in the structure of our lungs. Examine how fractal mathematics is applied in computer graphics, art, and the study of chaotic systems. Let the captivating world of fractals unfold before your eyes.

The Game Theory Revolution

Game theory isn't just about playing games; it's a powerful tool used in various fields, from economics to biology. Dive into the world of strategic decision-making and explore how game theory helps us understand human behavior and predict outcomes. Discuss in your essay classic games like The Prisoner's Dilemma and examine how mathematical models can shed light on complex social interactions. Explore the cutting-edge applications of game theory in diverse fields, such as cybersecurity and evolutionary biology. If you still have difficulties choosing an idea for a math essay, find a reliable expert online. Ask them to write me an essay or provide any other academic assistance with your math assignments.

Chaos Theory and the Butterfly Effect

While writing an essay, explore the fascinating world of chaos theory and how small changes can lead to big consequences. Discuss the famous Butterfly Effect and how it exemplifies the sensitive dependence on initial conditions. Delve into the mathematical principles behind chaotic systems and their applications in weather forecasting, population dynamics, and cryptography. Unravel the hidden order within apparent randomness and showcase the far-reaching implications of chaos theory.

The Mathematics Behind Cryptography

In an increasingly digital world, cryptography plays a vital role in ensuring secure communication and data protection. Did you know that the global cybersecurity market is projected to reach a staggering $248.26 billion by 2023? This statistic emphasizes the growing importance of cryptography in safeguarding sensitive information.

Explore the mathematical foundations of cryptography and how it allows for the creation of unbreakable codes and encryption algorithms. Discuss the concepts of prime numbers, modular arithmetic, and public-key cryptography. Delve into the fascinating history of cryptography, from ancient times to modern-day encryption methods. In your essay, highlight the importance of mathematics in safeguarding sensitive information and the ongoing challenges faced by cryptographers.

Writing a math essay doesn't have to be a daunting task. By choosing a captivating topic and exploring the various mathematical concepts, you can turn your essay into a fascinating journey of discovery. Whether you're uncovering the beauty of the Fibonacci sequence, exploring the mathematical underpinnings of music, or delving into the game theory revolution, there's a world of possibilities waiting to be explored. So embrace the power of mathematics and let your creativity shine through your words!

Remember, these are just a few math essay ideas to get you started. Feel free to explore other mathematical concepts that ignite your curiosity. The world of mathematics is vast, and each concept has its own unique story to tell. So go ahead, unleash your inner mathematician, and embark on an exciting journey through the captivating realm of mathematical ideas!

Tobi Columb, a math expert, is a dedicated educator and explorer. He is deeply fascinated by the infinite possibilities of mathematics. Tobi's mission is to equip his students with the tools needed to excel in the realm of numbers. He also advocates for the benefits of a gluten-free lifestyle for students and people of all ages. Join Tobi on his transformative journey of mathematical mastery and holistic well-being.

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Essay on Mathematics In Modern World - aspiringyouths.com
It helps us understand and shape the modern world. From technology and nature to health and money, math is the hidden force behind many things. It’s important to learn and understand math because it opens doors to many opportunities and helps us make sense of the world we live in.
Mathematics | Definition, History, & Importance | Britannica
Mathematics, the science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. Mathematics has been an indispensable adjunct to the physical sciences and technology and has assumed a similar role in the life sciences.
My Reflection in Mathematics in the Modern World - Academia.edu
Mathematics plays a dominant role in today's world. Although not everyone will become a mathematical expert, from an educational point of view, it is key for everyone to acquire a certain level of mathematical literacy, which allows reflecting and assessing mathematical processes important in every day live.
Mathematics in the Modern World Essay - Studocu
MATHEMATICS IN THE MODERN WORLD COLLEGE ESSAY. I learn something that I've won't ever anticipate. Educators of my Elementary and High School days have forever been saying that "Math is all over. Math is around us", without expounding its genuine importance.
The Power of Mathematics: Unveiling its Influence on Nature ...
This essay embarks on an exploration of mathematics' pervasive influence on our world, weaving together its applications in various scientific contexts. The introduction emphasizes mathematics' integral role in daily life, setting the stage for a comprehensive discussion.
MATHEMATICS IN THE MODERN WORLD - University of Toronto ...
Introduction. There is hardly any area of human endeavour that mathematics does not have any sort of role. Apart from commerce and engineering, and applications is sciences such as physics and chemistry, mathematics is also involved in political matters, biology, the making of decisions and fair division of assets.
Essay 'Importance of Mathematics in The Modern World ... - Scribd
Mathematics is essential in modern society. It has allowed for the development of a robust education system, advances in fields like medicine, science, technology, and agriculture. Nearly every profession requires some basic mathematical knowledge.
How mathematics built the modern world - Works in Progress
Mathematics was the cornerstone of the Industrial Revolution. A new paradigm of measurement and calculation, more than scientific discovery, built industry, modernity, and the world we inhabit today.
What Students Are Saying About the Value of Math
“Mathematics, I now see, is important because it expands the world,” Alec Wilkinson writes in a recent guest essay. “It is a point of entry into larger concerns. It teaches reverence. It...
Math Essay Ideas for Students: Exploring Mathematical ...
In this article, we'll delve into some exciting math essay ideas that will not only pique your interest but also impress your teachers. So grab your pens and calculators, and let's dive into the world of mathematics!