The Importance of Mathematics: From Equations to Everyday Insights

“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.” ― G.H. Hardy, A Mathematician's Apology

Mathematics is often seen as a complex and intriguing topic—frustrating with occasionally exhilarating, and the fun seems to be limited to experts in the field. If you have ever wondered why mathematicians seem to enjoy themselves amidst all those numbers and symbols, it might be because math offers a mix of challenge and satisfaction, like trying to solve a Rubik’s cube while blindfolded (except the stakes are occasionally higher).

So, why should we study mathematics? What are its benefits, and how does it impact our lives?? I will address these questions from two perspectives: direct and indirect benefits. And in the discussion, I will try to reinforce the profound connections mathematics has with our lives and the world around us.

The Direct Benefits of Studying Mathematics

Mathematics plays an important role in shaping careers that require significant analytical skills and problem-solving capabilities. From being a teacher, professor, or engineer to becoming a computer scientist, economist, or AI professional, mathematical knowledge serves as the foundation for a variety of high-demand professions. These fields not only offer financial stability but also provide opportunities for innovation and leadership in a rapidly evolving world.

For instance, an engineer relies on calculus and geometry to design structures, while an economist uses data and statistics to predict market trends. The skills developed through mathematical training—like logical reasoning and quantitative analysis—make you a valuable asset in nearly every industry.

The Indirect Benefits of Mathematics: Transferable Skills

Beyond careers, the study of mathematics fosters critical life skills. These include critical thinking, effective communication, creativity, and deductive and inductive reasoning - the skills which have been rated as essential for “jobs of the future”.??

In the environment we live in, we observe and experience various types of transformations and changes in which events (weather, etc.), objects (e.g., cars), entities (e.g., business), and people transition from the current phase to the next one. At a philosophical (and practical) level, understanding our life, its meaning and purpose, is mostly about learning and getting deep insights into these changes, transitions, and transformations happening all around us. And mathematical thinking and tools are our best friends, if we want to understand, measure, and estimate the impacts of these transitions on our lives.?

With mathematical thinking, you can

• Recognize that no investment scheme can make you rich overnight
• Balance trade offs and optimize risks in decisions and predictions rather than attempting to eliminate risks entirely
• Understand that outcomes are influenced by multiple factors, many of which may be beyond our control
• Learn that the probability of winning the lottery does not change based on who (e.g., you, friends, family) selects the numbers
• Transform seemingly complex problems into simpler frameworks for easier resolution
• Experiment with “what-if” scenarios by adjusting problem parameters

Mathematics as a subject of study

There are four key areas of study in mathematics — Arithmetic, Geometry, Algebra, and Calculus. And with a bit of stretch, you can also add a fifth (and an important one) under the umbrella of mathematics— Statistics and Probability.

In simple terms, Arithmetic is the study and manipulation of numbers, Algebra is the manipulation of equations, Geometry is the study of the properties of geometric shapes and objects, and Calculus is the study of continuous functions. The other branches of mathematics could stem from combining the knowledge and concepts of two or more areas of study. For example, algebraic equations can be converted into geometric shapes and vice versa, and they become topics of study under Algebraic Geometry. The geometry of smooth shapes is studied under Differential Geometry. The study of probability and chances, data manipulations, data modeling and analysis fall under Statistics and Probability.??

This interconnectedness of mathematical branches fosters a deeper connection of how the world operates, revealing insights that are both practical and profound.

The Pursuit of Mathematical Truth

If an absolute truth exists, mathematics may be its closest approximation. Unlike other fields, where theories can gain acceptance through repeated affirmations, mathematics demands rigorous proof applicable to all cases.?

In mathematics, you could have thousands of affirmations or examples about a phenomena (e.g., prediction, event, etc.) and you could still be “wrong”. It is still not enough to find millions of examples in favour of a concept, theory, or knowledge to be acceptable as a “valid” theory. The concept must be proved rigorously using logic and rules, which can prove it for “ALL” situations and not just to a few or millions or billions.? This unyielding standard ensures that mathematical truths remain universally valid.

Embracing the Challenge

The study of mathematics is not without its frustrations, but these challenges make the journey worthwhile. Every setback is an opportunity to contribute to a larger body of knowledge. Even if you fail to find a solution, your efforts may pave the way for others to advance - you probably have discovered the first step of a solution to a complex problem, which can eventually lead to an important knowledge discovery or a different way of approaching a problem. It is like a trick or treat and the fun is in either of the outcomes. In the field of “absolute truth”, there is no “absolute” failure.

Mathematics opens doors to intellectual exploration and a deeper understanding of life’s complexities. So, take on the challenge, embrace the frustration, and enjoy the thrill of discovery. Whether you’re calculating probabilities for fun or solving equations for work, remember: every step forward adds value to your journey. Start today—even if it’s just calculating the tip at dinner—and see where it takes you!

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Disclaimer: The views, thoughts, and opinions expressed in the text belong solely to the author, and not necessarily to the author’s employer (current or past), or organization, group or individual the author is directly or indirectly affiliated with. A few minor edits were made with the assistance of artificial intelligence. The author assumes no responsibility or liability for any errors or omissions in the content of the views and opinions expressed here.?Image created by Microsoft Designer