Students, nowadays, can easily seek help and guidance in mathematics - be it in high school or in college. With options galore in Maths classes near me, the process to learn Maths online has become simple.

Moreover, there are many guidebooks and online maths resources for students to refer to such as the NCERT Maths solutions or other high school Maths companions. But, before you start your learning journey in Maths, why not take a journey back in time to uncover the fascinating history of the development and evolution of Maths as a discipline of scientific study.

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History of Mathematics

Mathematics, with all its branches (algebra, arithmetic, geometry, trigonometry, and others) has evolved from simple concepts of counting, measurement, and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination, and logic, to the broad, complex, and often abstract discipline we know today.

The history of modern mathematics can be traced back to ancient Mesopotamia and Egypt, ancient Greece and India, and Islamic civilization from the 9th to the 15th century. There was considerable interaction and influence between these civilizations. Islamic mathematics borrowed heavily from ancient Indian mathematics.

Archaeological evidence of the Egyptians' use of Maths
The ancient Egyptian civilization is known to have used mathematics (Source: commons.wikimedia.org)

Greek Mathematics

Thales and Pythagoras could be jointly hailed as the Father of Ancient Greek Mathematics. Thales contributed to geometry and both Thales and Pythagoras were inspired by the Babylonians and Ancient Egyptians.

Pythagoras coined the term 'Mathematics', which meant 'learning', and founded a religious movement called Pythagoreanism. The movement was based on the belief that the whole universe is composed of Mathematics and that numbers are real entities that do not exist in space and time.

The discovery of irrational numbers shocked the Pythagoreans. Irrational numbers cannot be expressed as a fraction or written down in full because they contain an infinite amount of numbers with no known repeating pattern. The Pythagoreans believed that irrational numbers were nature's flaw.

In about 387 BCE, the Greek scholar, Plato set up an academy in Athens, which became the Mathematical center of the world. Its students included the ancient Greek philosopher Aristotle, ancient Greek astronomer Eudoxus of Cnidus, and possibly the ancient Greek mathematician Euclid. The latter made a number of discoveries in geometry shortly after 300 BCE.

Ancient Indian Mathematics

Indian Mathematics and Indian Mathematicians made path-breaking discoveries that led to the study of trigonometry, algebra, arithmetic, and negative numbers. The decimal system is, perhaps, the most significant of India's contributions to the world of mathematics.

  • Zero: The first recorded zeros, in what is known as the Bakhshali manuscript, were simple placeholders – a tool to distinguish 100 from 10.
  • Calculus: The Kerala school of astronomy and mathematics, founded by Madhava of Sangamagrama in the 1300s, was responsible for many firsts in mathematics, including the use of mathematical induction and some early calculus-related results.
  • Solutions of Quadratic Equations: In his seminal text, the astronomer Brahmagupta introduced rules for solving quadratic equations and for computing square roots.

Basic Maths Symbols and Vocabulary

Mathematical symbols are often taken for granted because symbols are so common in maths. It is because of symbols that mathematical operations become easier to perform. Mathematical signs and symbols are considered representative of the value.

The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves.

Besides symbols, it is equally important to learn mathematics vocabulary for the development of mathematical proficiency. Mathematical vocabulary learning is a critical part of a student's language development and, eventually, mathematical proficiency.

Ways to Improve Maths Vocabulary

  • Systematic Approach: Students should practice mathematics in short spurts every day to avoid an overload of information.
  • Reading for Meaning: This research-based strategy for learning mathematics allows learners to make sense of challenging mathematical texts.
  • Context-specific Vocabulary: Students should learn mathematical terms, concepts, or vocabulary that have explicit meaning critical to understanding particular content.

Evolution of Maths Teaching

There have been significant alterations and modifications to the ways in which mathematics is taught. The first known systematic teaching of Mathematics started in the Third Millennium in states of Mesopotamia. Mathematics became a subject of general education for the first time in the city-states of Greece when a new class of free citizens governing their state emerged.

History of Teaching Maths in India

The most famous Indian Mathematicians belong to the classical era, including the likes of Aryabhata I (500 CE) Brahmagupta (700 CE), Bhaskara I (900 CE), Mahavira (900 CE), Aryabhatta II (1000 CE), and Bhaskarachrya or Bhaskara II (1200 CE). During this period, two centers of Mathematical research emerged, one at Kusumapura near Pataliputra and the other at Ujjain. Ramanujan (1887- 1920) is perhaps the most famous modern Indian Mathematician. The arithmetic theory of modular forms is his most lasting discovery.

During the 1960s and 1970s, there was a paradigm shift in mathematics education. It was during this period that educators realized the value of studying the teaching and learning of mathematics more specifically. Thus arose an interest in developing a psychological basis for understanding why some students learned but others did not, and what kind of teaching methods and curricula could affect student learning.

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Arabic Mathematics heavily influenced Western thinkers
Al-Biruni's explanation of the phases of the moon (Source: wikipedia.org - Al-Biruni)
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Relation Between Maths and Computer Science

Mathematics can be considered the foundation of Computer Science. People with a good understanding of Mathematical concepts easily understand how logic controllers workhow to write better algorithms, and how encryption works. Here are a few fundamental uses of mathematics in computing.

Discrete Mathematics

Really, discrete mathematics is the core foundation of programming and computer sciences. Logic Notation, Set Theory, Combinatorics, Graph Theory, Probability, Number Theory, Algebra, are all a part of Discrete Mathematics.

Mathematics and the Use of Algorithms

Anyone studying or even remotely familiar with computer sciences will have heard of algorithms. Essentially, algorithms are a set of instructions that demonstrate the implementation of a program or an application.

Binary Math

Binary math is one of the most essential types of maths used in computer science. Binary is used to symbolize every number within the computer. The binary number system is an alternative to the decimal system.

Binary math helps to simplify computer design. Moreover, standard arithmetic is utilized in numerous functions of computer programming. Knowledge of binary math is also a necessary prerequisite for job seekers in the fields of mathematics and computing.

Relation Between Maths and Art

The link between mathematics and art can be traced back to the 5th century BCE when the Greek High Classical sculptor; Polykleitos implemented the 1:√2 ratio of human body proportions in his sculptures.

Applications of Geometry in Art

Geometry is the most fundamental link between art and mathematics as both subjects involve drawing and the use of shapes and forms, as well as an understanding of spatial concepts, two and three dimensions, measurement, estimation, and pattern.

Artists make use of various geometrical elements such as lines, angles, and shapes to create a theme throughout their artwork. These geometric elements are utilized by artists to create a sense of perspective. This art is known as Optical or Op Art.

Applications of Golden Ration in Art

Leonardo da Vinci

Da Vinci illustrated a book written by Luca Pacioli in the late 15th century all about the Divine Proportion. He used the measurement in many of his paintings, including Mona Lisa and The Last Supper.

Salvador Dali

Salvador Dali’s painting, The Sacrament of the Last Supper (1955), is widely cited as utilizing the Golden Ratio.

Piet Mondrian

Mondrian is said to have used the Golden Ratio in his abstract paintings. Apparently, some of his paintings line up better with the proportions than others, which means he wasn’t too picky about precise measurements.

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One of Leonardo's many sketches
Da Vinci's Study of a Horse (Source: commons.wikimedia.org)

Albert Einstein: The Maths Genius

One of the most influential figures of the 20th century, Albert Einstein had a significant impact on the field of mathematics with his crucial discoveries and theories.

Theory of Special Relativity

Developed in 1905 by Einstein, the theory of special relativity became the basis of modern physics. The theory explains how space and time are linked for objects that are moving at a consistent speed in a straight line. One of its most famous aspects concerns objects moving at the speed of light.

Theory of General Relativity

The theory was published in 1915 by Einstein who wanted to expand on his theory of special relativity. The theory holds that what we perceive as the force of gravity arises from the curvature of space and time. This theory with its mathematical equations is the best description of how gravity works and the most accurate way to predict gravitational interactions.

Einstein Field Equations

The Einstein Field Equations are ten equations that describe gravity as a result of spacetime being curved by mass and energy. G__{\mu\nu} is determined by the curvature of space and time at a particular point in space and time, and is equated with the energy and momentum at that point. The solutions to these equations are the components of the metric tensor g_{\mu\nu}, which specifies the spacetime geometry. The inertial trajectories of particles can then be found using the geodesic equation.

Examples of Maths in Art

At first glance, there appears to be no connection between the two worlds of art and mathematics. But, on closer inspection, one discovers that the two are inextricably linked. Consider this: a creative mind is necessary to make mathematical discoveries, while, artists require mathematical tools to achieve perfection in their artwork.

Fractals

Fractal, a mathematical term used to denote complex geometric shapes that are different from simple figures, are repetitive in design but vary in scale. Fractals appear in abundance in nature. Artists often incorporate fractal patterns in their works. Archaeological evidence suggests the use of fractals as early as the great civilizations of the Egyptians, Romans, Mayans, Incans, and Mayans.

The Illustrative Art of M.C. Escher

The mathematical influence was heavily reflected in Escher's works, illustrated best in his Relativity, a faultless image of a staircase that seemed impossible to construct physically. The precision in symmetry and form that he had achieved in his art was of particular mathematical interest to mathematician and cosmologist, Roger Penrose. Escher's work of art inspired Penrose's mathematical research paper, 'Impossible Objects: A Special Type of Visual Illusion', which explored the concept of physically impossible geometries

Mathematical art using fractals
Fractals in art (Source: pixabay.com - Successcoach)

Busting Maths Stereotypes

Mathematics is an enigma. You can love it or hate it. But, you cannot ignore it because mathematics is all around us! However, the cause for the unpopularity of the subject is based on often unsubstantiated claims. What are some of these myths surrounding maths?

Boys are Better at Maths than Girls

Despite progress in women's education, mathematics continues to be a male-dominated field. STEM educational programs (science, technology, engineering, and math) remain underrepresented by women, creating a math gender gap.

The “math is for boys” stereotype is culturally ingrained in the Indian psyche. This can have an adverse effect on the activities that girls can engage in and their career aspirations. There is a widespread cultural belief in India that women cannot succeed in mathematically demanding fields.

How to Break Gender Stereotypes

  • Planning and implementing interventions during early childhood before children can consolidate the concept of gender stereotypes
  • Preventing the development of unrealistic and negative perceptions of girls’ abilities in mathematics
  • Tackling the gender stereotype beliefs among teachers

There is no innate gender difference in mathematics ability. This is proved by inconsistent gender differences among countries and over time in terms of mathematical ability.

Only Born Geniuses Do Maths

It is a popular myth that some children are born with a natural ability to do maths better than others. The reality is that some students enjoy maths more than others. The perpetuation of this myth, in fact, can have disastrous consequences for the success of women in maths by reinforcing gender stereotypes.

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Shreyanjana

Shreyanjana is an archaeologist who ironically finds the written word to be the most powerful means of storytelling. A travel buff and a photography enthusiast, she has been writing and sharing stories of all sorts ever since she can remember.