Mathematics is often seen as a subject full of complex formulas and abstract concepts. However, the key to solving difficult problems isn’t necessarily learning more advanced techniques—it’s about thinking simply. Many of the best problem-solvers, from engineers to physicists, rely on breaking down complicated ideas into their most basic parts.
When faced with a complex mathematical problem, it’s easy to become overwhelmed by the details. Trying to tackle everything at once can lead to confusion and mistakes. Instead, simplifying the problem—whether by breaking it into smaller steps, using a basic example, or stripping it down to fundamental principles—makes it easier to find a solution.
Strategies for Thinking Simply in Mathematics
1. Break the Problem Into Smaller Parts
Instead of solving everything at once, identify smaller sub-problems. For example, in calculus, breaking a complex function into basic derivatives or integrals can make it much easier to solve.
2. Look for Patterns
Many mathematical problems follow recognisable patterns. If you can identify these, you can apply known strategies rather than reinventing the wheel each time.
3. Use Simple Numbers or Visual Aids
Substituting simple numbers can help you understand relationships between variables before dealing with more complicated values. Similarly, drawing a diagram or graph often makes abstract concepts more tangible.
4. Go Back to First Principles
Often, the most advanced topics in mathematics still rely on fundamental concepts like addition, subtraction, multiplication, and division. If a problem seems too complex, revisiting the basics can reveal a clearer approach.
Some of the greatest mathematical discoveries were made by thinkers who focused on first principles. Albert Einstein once said, “If you can’t explain it simply, you don’t understand it well enough.” The same applies to problem-solving in mathematics—by thinking simply, you gain deeper understanding and improve your ability to tackle even the most complex challenges.
Emily Mackay
