DEFINITION OF MATHEMATICS
The term “mathematics” has been defined in various ways throughout history. The Oxford English Dictionary from 1933 describes it as an abstract science that explores the logical outcomes of fundamental spatial and numerical concepts, encompassing branches like geometry, arithmetic, and algebra. Another definition from the American Heritage Dictionary in 2000 characterizes mathematics as the study of measurements, properties, and relationships using numbers and symbols. The Encyclopaedia Britannica defines it as the science of structure, order, and relation that has evolved from basic practices of counting, measuring, and describing shapes.
Earlier interpretations, such as Aristotle’s, viewed mathematics as the science of quantity, with arithmetic dealing with discrete quantities and geometry with continuous ones. Augusta Comte’s definition focused on mathematics’ role in indirectly measuring quantities that cannot be directly measured, like distances to planets or atomic sizes.
Philosophers like Kant emphasized mathematics as an indispensable tool for physical research, while figures like Gauss and Bacon regarded it as the foundation for all sciences, with arithmetic being particularly important. Lindsay highlighted mathematics as the language of the physical sciences, noting its ability to express ideas with unparalleled precision and conciseness through signs, symbols, terms, and operations. These definitions collectively underscore mathematics’ unique role as a powerful tool for understanding and exploring scientific concepts.
MEANING OF MATHEMATICS
The term “mathematics” originates from the Greek word ‘máthēma’, which translates to “that which is learnt” or “what one gets to know”. This word is derived from ‘manthano’, with the modern Greek equivalent being ‘mathaino’, both meaning “to learn”. In ancient Greece, “mathematics” referred more narrowly to “mathematical study”. Its adjective, ‘mathēmatikós’, meant “related to learning” or “studious”, eventually evolving to mean “mathematical”.
In Latin and early English, up to around 1700, “mathematics” typically denoted “astrology” or sometimes “astronomy”, before gradually shifting to its current meaning from the 1500s to the 1800s.
Mathematics is commonly understood as the exploration of patterns in structure, chance, and space. In simpler terms, it is the study of shapes and numbers. Formally, it involves investigating axiomatically defined abstract structures using logic and mathematical notation, although other philosophical perspectives on mathematics exist as well.
BRIEF HISTORY OF MATHEMATICS
A Concise Overview of Mathematics Through the Ages
The journey of mathematics begins with the simple act of counting. However, it’s only when people started recording their counts and representing numbers that mathematics truly took its first steps.
Around 2000 BC, in Babylonia, mathematics began to flourish. A sophisticated place-value notation system, based on the number 60, emerged, allowing for the representation of large numbers and fractions, laying the groundwork for future mathematical developments.
Early mathematical inquiries included problems like Pythagorean triples (sets of numbers that satisfy a^2 + b^2 = c^2), as well as the study of linear and quadratic equations, leading to the birth of numerical algebra. Geometric problems concerning area, volume, and the estimation of π were also explored during this time.
Greek mathematicians inherited and expanded upon Babylonian mathematical knowledge around 450 BC. Notable achievements include Zeno of Elea’s paradoxes, which spurred the development of atomic theory by Democritus, and the geometric formulation of irrational numbers to measure lengths accurately. Greeks made significant strides in mathematics until about 200 AD.
Following this, mathematical progress shifted to Islamic countries, particularly in Iran, Syria, and India. While not reaching the heights of Greek mathematics, this era preserved and expanded upon earlier knowledge. From the 11th century onwards, figures like Adelard of Bath and Fibonacci reintroduced Islamic mathematical concepts to Europe, sparking a resurgence of mathematical interest.
The 16th and 17th centuries witnessed significant advancements in European mathematics. Innovations such as logarithms by Napier and Briggs, infinitesimal methods by Cavalieri, and algebraic geometry by Descartes propelled the field forward. The discovery of calculus, notably by Newton and Leibniz, revolutionized mathematical thinking and its applications in physics and astronomy.
The 18th century saw the rise of Euler, whose contributions spanned various mathematical domains and included the invention of new branches like the calculus of variations and differential geometry. Towards the century’s end, Lagrange and Laplace made notable strides in mechanics and celestial mechanics, respectively.
The 19th century ushered in a period of rapid progress. Noteworthy developments include Fourier’s work on heat, Lobachevsky and Bolyai’s non-Euclidean geometry, Gauss’s contributions to differential geometry, and Galois’s insights into group theory. Additionally, significant advancements in algebra, analysis, and mathematical physics occurred during this time.
In conclusion, mathematics has evolved significantly over the centuries, driven by the curiosity and ingenuity of mathematicians across different cultures and eras. Each epoch has left its mark, building upon the foundations laid by those who came before, and paving the way for further exploration and discovery.
