Mathematics: The Civilization It Has Created and the Future Ahead

Written by KOH SEUNGHAN from Grade11

Mathematics has played a decisive role throughout human history in understanding nature and the universe, advancing technology, and driving civilization. This great journey of mathematics has not been easy. What we know as mathematics today actually started from simple counting methods. People relied on arithmetic to govern their countries, collect taxes, and trade goods. This became the driving force behind economic and political success. Concepts such as geometry, algebra, calculus, and logarithms, which we learn in school, were developed independently by various mathematicians. They have since become integral to our daily lives, turning human ambitions into reality and reshaping history, continuing to do so even today.

I. Geometry

Geometry began with the quest to find the perfect form of numbers that build the universe and evolved through periods of human greed. In the 3rd century BC, the ancient Greek mathematician Eratosthenes used geometric principles to measure the Earths circumference. By comparing the sun’s angle at Aswan and Alexandria, he estimated the Earths size, proving scientifically that the Earth is round. In modern times, geometry has driven innovation in architecture. Renaissance architects used geometric proportions and principles to pursue balance and beauty in their buildings. For instance, Filippo Brunelleschi applied geometric structures in designing the dome of the Florence Cathedral, opening new horizons in architectural engineering. The application of geometry continues to play a crucial role in architectural design and urban planning today.

II. Algebra

Algebra involves using known knowledge to uncover hidden information, such as solving basic algebraic equations. In real life, we convert problems into equations, define unknowns, and solve for them. This was once an art form, like decrypting a code. People deciphered these equations to predict the future, and mathematicians’ sharp thinking further advanced this field. Algebra played a pivotal role in the Industrial Revolution and the development of the computer era. In the 17th century, Isaac Newton and Gottfried Leibniz independently developed calculus, providing tools to solve problems in physics and engineering. This allowed for the mathematical modeling and analysis of complex phenomena such as the movement of machines and the flow of fluids.

In the mid-20th century, with the advancement of computer science, algebra entered a new era. The binary system, which is the fundamental operating principle of computers, is based on algebraic concepts and enables computations and data processing. The binary system uses only the two numbers, 0 and 1, to represent information, making it ideal for expressing the two states of electrical signals (on and off), which is optimized for computer hardware design and operation. This allows computers to efficiently perform complex calculations and process large amounts of data. Additionally, algebra plays an essential role in key areas of computer science such as algorithm efficiency analysis and data structure optimization. Big-O notation, used to evaluate the time and space complexity of algorithms, is based on algebraic concepts, enabling predictions of how efficiently an algorithm operates based on the size of the data it processes. This helps developers select optimal algorithms and improve system performance.

III. Logarithms

Logarithms were introduced in the early 17th century by mathematician John Napier, bringing about significant changes by simplifying complex calculations. Before this, astronomers and merchants struggled with large-scale numbers, but by using logarithms, they could transform multiplication and division into addition and subtraction, greatly enhancing calculation efficiency. This contributed greatly to the development of navigation and trade, especially helping navigators calculate the positions of stars, increasing the accuracy and safety of voyages. In modern times, logarithms are used in a variety of fields in everyday life. For example, the Richter scale, used to measure the magnitude of earthquakes, employs a logarithmic scale to express the energy released during an earthquake. This helps provide a more intuitive understanding and comparison of earthquake intensities. Additionally, pH levels use the logarithmic value of hydrogen ion concentration to represent acidity or alkalinity. This is a crucial indicator in chemistry and biochemistry for assessing the acidity or alkalinity of substances. Thus, logarithms not only simplify mathematical calculations but also play an indispensable role in understanding natural phenomena and scientific measurements.

Conclusion

Each branch of mathematics has developed independently but is closely interconnected, contributing to human progress. Geometry helps us understand space and shape, algebra analyzes calculations and structures, calculus explains changes and motion, and logarithms simplify complex calculations. These mathematical principles provide the foundation for the development of modern technology and science, and their importance will continue to grow in fields such as artificial intelligence, big data, and biotechnology. Mathematics, beyond being a scholarly pursuit, will continue to shape our lives and future as a core element, maintaining its value in the years to come.