The History of Mathematics

Introduction 

Mathematics refers to the study regarding the interactions between quantities and magnitudes among others. Mathematics is composed of various themes which define different aspects of mathematics such as arithmetic which involves the use of numbers or geometry which comprise of numbers of magnitudes. Over time, mathematics has expanded its scope to incorporate symbols, and it has diversified to cover more fields such as algebra, calculus and applied mathematics such as probability among others (Mastin, 2010). Mathematics has developed over time from defining simple associations to more complex relationships of higher capacities. Therefore, a look at the history and development of Mathematics helps one understand its origins and advancements and how mathematics has affected or been affected by cultures and civilization.

History of Mathematics 

Mathematics is believed to be as old as human life having begun with simple counting. The earliest evidence of mathematics is traced to the Lebombo bone and the Ishango bone. The 29 carvings on Lebombo bone are believed to represent a record of numbers. The series of carvings recorded on the Ishangoo bone, which appears in patterns are said to demonstrate knowledge of mathematical basics such as addition and subtraction among others. The bones represent tally sticks for over 20,000 years ago. With time, a written language of mathematics began to develop in Southern Mesopotamia. One of the early numbers was π (pi) which was well known by Babylonians and Egyptians. Afterward, Babylonians became aware of the Pythagoras theorem relating the sided of a right-angled triangle.

Pythagoras theory A 2 + B 2 = C 2

The Babylonians and Egyptians' knowledge became the inspiration for Pythagoras and Thales who advanced Greek mathematics. Pythagoras connected mathematics to nature and founded a belief; Pythagoreanism which was based on the faith that numbers were nonexistent real entities in time and space. Followers of the Pythagoras belief discovered irrational numbers. Centuries later Socrates and Plato retaliated against Pythagoras beliefs that numbers were real entities in a dominion of forms. Decades later, Euclid developed geometric and suggested the infiniteness of prime numbers. The concept of infinity, therefore, gained ground based on Zeno's infinity concept mentions centuries before Euclid. An Indian mathematician first used zero as a number in 628 CE

In the later years, developments took place in mathematics with the development of numbers such as i and the idea of positive and negative i by Rafael. Descartes and Pierre de Fermat advanced the Cartesian coordinate individually which enabled plotting on graphs. Isaac Newton and Gottfried Leibniz later used the Cartesian coordinate concept to develop calculus. The concepts developed in mathematics were later used by scientists to describe the movement of planets. Developments continued and later there was the introduction of number e which represents logarithms such as:

If 10 = e~2.3 then loge (10) = ~2.3 and the derivation of the logarithm scale based on Gause’s observation that the numbers between prime numbers increases by 2.3.

By the 19 th century, Plato's ideology of Mathematics has true knowledge began to gain criticism. Philosophers, therefore, sought ways to prove the reality of mathematics resulting in the emergence of logicism and formalism. Peano developed axioms that show that mathematics can be derived for rational laws such as Zero is a number. Thereafter followed developments of mathematical structuralism that defines numbers by place within mathematical structures or formalism which dictates that number does not exist. Ultimately, Philosophers deduced that mathematics is a creation of the human mind (Klus, 2011). Eventually, mathematics has continued to develop in the modern day to applied mathematics which explores mathematical applications beyond being about just numbers.

Development of Mathematics Across and Within Civilizations around the World 

Mathematics has established a good ground and advanced notably across all civilizations in the world. Mathematics is at the frontline in every society whether civilized or primitive. Mathematics has developed across every community to cater to the society’s needs. Mathematics is an invention that man stamped across in a bid to satisfy human wants. Therefore, every society develops and continues to advance mathematics in the course of living to satisfy its society wants. The complexities of societies define the complexity of mathematics. Primitive societies relied on mathematics to determine the position of the sun and the science of hunting.

Civilizations such as China, Egypt and Central America have been instrumental in the development of mathematics. Mathematics advanced with the growth and adaptation of civilization from the basic mathematics of counting to the development of algebra and geometry. With geometry, people in civilizations would compute volumes and areas and construct homes and design them. Algebra enables the division and allocation of resources in the civilization era.

Early civilizations studies and developments became building blocks of the mathematics of the Greeks. Greek became the epitome of mathematical advancements by developing abstract Maths through geometry and establishing systems of mathematical schools. Later on, with the fall of Rome Arabs advanced mathematics and passed it on to Europeans. Europeans developed mathematics with theories such as fractions, logarithms, probability, and analytics (Hom, 2013). In the modern civilizations, Mathematics is relevant and critical due to the development of applied mathematics which requires mathematical knowledge in all fields biological, social and physical.

Cultures and the History of Mathematics 

Through years mathematics has been accompanied by a stereotype based on cultures. Apparently, cultures influence perspective in mathematics and mathematics, in turn, has its role in cultures. There is a significant difference in the reception and performance of mathematics around the world regions, and it has been attributed to social, political and economic factors. Culture has a profound impact on mathematics, and the world acknowledges the role of culture in developing mathematics. The history and advancements of mathematics show that it developed from Middle East cultures. The cultures of Egypt, India, and Asia are seen to be critical to the development of Mathematics and are said to have a better glimpse of mathematical concepts. Different cultures approach mathematics differently leading to diversity in the influence culture has on mathematics. For instance, Middle East countries such as India are business societies which ideally develop a child's ability to count at an early stage. India teaches children to count using the division lines on each finger allowing them to count up to twenty on the one hand. Western cultures, on the other hand, taught children how to count using fingers which enabled them count up to five.

Secondly Language is also instrumental in comprehending mathematics and language is part of culture. For instance, Romans have a well-developed and acknowledged mathematical language system while western cultures used the common language to teach mathematics.For example the well know Roman numerals that are globally used:

1 is I, 50 is L and 100 is C

1944 = MDCCCXXXXIIII= MCMXLIV

Religion plays a central role in influencing mathematics. Systemized and abstract religions contribute to a society thinking in abstract ways, and abstract faiths have higher responsiveness and performance in mathematics (Puteh, 2016). Mathematics becomes the basic quantity measure of life aspects, and people derive their livelihood based on mathematical analysis. Determination of the weather, seasons, calculations on world demographics and economics of cultures are all mathematical deductions which show that mathematics affects cultures significantly.

Past Present and Future Mathematical Problems 

Mathematics has evolved through its history from the simple counting of quantities to more complex computations of modern-day applied mathematics. The evolution brings across a difference in the mathematical problems of the past and the present. Statistically, mathematics continues to develop and advance into the future and with advancement in technology which shows that present mathematical issues are bound to change in the future. Mathematical development has been a series of solving previous era problems and generating a new one in the present eras and the system continues. In the beginning, mathematics problems involved developing the basic mathematics structure and language. From the carvings tallying on the bones to the discovery of numbers over time mathematics solved the issue of establishing a mathematical language.

The problem of associating complex quantities and properties led to the development of theories such as prime numbers, irrational numbers, and logarithms among others. Through ages, the issues of complex associations have been solved through the development of concepts, theories, and formulas to reach the modern day discrete and applied mathematics. For instance the calculus concept is a complex computation from the past mathematical approach

Example 1: Find the derivative of .

diff(sin(x))= cos (x)

Example 2: Find the derivative of using the chain rule.

diff(x^2+sin(2*x^4)+1,x) =

Present day mathematical problems revolve around applying mathematics to provide solutions for modern day and future economic problems. Mathematics is overcoming barriers and changing its foundations of numbers and symbols to accommodate complex technologies.

Certainly, in the future, there lies the challenge of crossing the barriers of symbols and developing interdisciplinary relations between mathematical concepts (Shapiro, 2014). More mathematics problems will arise which will become the basis for the future mathematics developments, and that cycle continues as mathematics advances to meet human wants. It is important to remember that mathematics developed to cater to human needs and as long as human needs are changing problems will arise which mathematics will be required to solve. As a result;t, the development of mathematics is infinitely tied to the changing human needs.

Conclusion 

In conclusion, the story of mathematics is incomplete as it continues to advance and may continue to infinity. Mathematics is now an established human invention that is widely embraced and has formed a common language for all humanity throughout the world. Civilization continues to alter mathematics and influence its modifications, and it opens new pathways for advancing mathematics. Mathematics affects aspects of modern human life such as business and transactions diversifying its concepts and quantifying every essential element of human life. Mathematics has become a fundamental part of humanity and continues to be embraced as an essential in human life . 

References

Hom, E. J. (2013). What is mathematics? Live Science. Retrieved on 13 September 2018, from https://www.livescience.com/38936-mathematics.html

Klus, H. (I2011). A brief history of mathematics: From Plato's philosophy of mathematics to modern mysteries. The Star Garden. Retrieved on 13 September 2018, from http://www.thestargarden.co.uk/History-of-mathematics.html

Mastin, L. (2010). Welcome to the story of mathematics. Story of Mathematics . Retrieved on 13 September 2018, from https://www.storyofmathematics.com/

Puteh, M. (2016). Does cultural influences have a huge impact on the students' ability to learn mathematics in general? Does certain culture has an advantage? Research Gate. Retrieved on 13 September 2018, from https://www.researchgate.net/post/Does_cultural_influences_has_a_huge_impact_on_the_the_students_ability_to_learn_mathematics_in_general_Does_certain_culture_has_an_advantage

Shapiro, J. (2014). 5 things you need to know about the future of math. Forbes. Retrieved on 13 September 2018 from https://www.forbes.com/sites/jordanshapiro/2014/07/24/5-things-you-need-to-know-about-the-future-of-math/#461046c5590e