Is Mathematics the Queen of Science? Insights from a Physicist’s Perspective

Social media can get pretty snarky, especially when people debate which science is the most fundamental. Often, some enthusiasts claim that sociology is just applied psychology, psychology relates to biology, and so on, down to chemistry being a form of physics. As a physicist, I find a lot of truth in this perspective. For many, physics is the queen of sciences.

However, one idea goes even further, suggesting that all science is just a practical use of applied math. If physics reigns as queen, then mathematics is the empress. A humorous xkcd comic pokes fun at this debate. Notable physicists have echoed similar sentiments.

Take Eugene Wigner. In 1960, he published a paper titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” He discusses the curious ways that math mirrors the physical world, marveling at how well it works. Max Tegmark took this idea further, proposing that reality isn’t just similar to math; it actually is math. He believes each mathematical structure represents different universes within a much larger multiverse. Though this idea is debated, it certainly prompts discussions about whether math holds more importance than physics.

There’s no doubt that mathematics is vital for physicists. Much of my college years focused on mastering math to tackle specific research questions. For instance, one key equation in particle physics takes up an entire page just to be expressed. This heavy reliance on math can lead some people to think it holds the top spot among sciences. While they respect other fields, to them, mathematics is the most important.

But I see things differently. Arguing over which is more important, science or math, misses the mark. Science studies the natural world, while physics dives into its deepest rules. We explore how matter and energy behave. Particle physicists and cosmologists seek links between different phenomena to uncover their true nature. A good example is James Clerk Maxwell, who showed that electricity and magnetism are different forms of the same force: electromagnetism.

In contrast, mathematics is more about logic than physical reality. It’s essentially the logic of numbers and quantities. When I say “mathematics,” I mean a broader concept, not just subjects like arithmetic or calculus. It involves selecting a set of objects, often numbers, and creating rules that describe how they relate. For instance, basic arithmetic establishes rules for integers, demonstrating what happens when you add or subtract.

If you want to discuss fractions, you need to add multiplication and division. This leads you to the realm of real numbers, expanding your mathematical framework to include everything from negative infinity to positive infinity. You can even explore different types of math, like “clock math,” where 11 + 4 equals 3, which shows how different reasoning patterns can create unique systems.

How do math and science fit together? The natural world is independent of us, governed by rules we are continuously trying to understand. Science aims to unravel these rules through models based on assumptions. We select the mathematical logic that best matches our model and use it for calculations. Importantly, calculations are not the same as the real world; they manipulate models using mathematical principles.

Not every type of math works for every scientific model. For example, when studying water at a larger scale, we might use continuous math. But at the molecular level, we need discrete math because water molecules cannot be divided. Choosing the right mathematical framework is crucial; otherwise, our predictions might miss the mark.

To summarize, math is pure logic, not a human invention. The universe is shaped by its own rules, which are also outside human influence. Modern science builds models based on assumptions and uses suitable mathematical logic to reflect nature’s rules. When a model’s predictions align with measurements, it may offer insights into untested phenomena.

Consider Einstein’s general theory of relativity. Released in 1915, it accurately predicted Mercury’s orbit and how stars appear to shift during a solar eclipse. It also forecasted concepts like black holes and gravitational waves, which took decades to confirm. Math empowered researchers to explore the implications of this theoretical framework.

Despite their close relationship, math and science remain distinct. Math can stand alone, serving as an effective tool for scientists to form theories that model reality. If it were easier to uncover truths through interpretive dance, scientists would gladly embrace that method instead!

While I appreciate the ingenious work of mathematicians who delve into the intricacies of numbers, after studying mathematics in college, I recognized that my passion lies in understanding the laws of nature. I’ll leave the complexities of math to those who thrive on it, grateful for how it eases the scientific quest to comprehend the universe.

So, for those who love to argue about the hierarchy of sciences online, remember that all are interesting in their own right. While I may believe physics forms the foundation, math exists outside of science and remains a vital ally in our shared journey to fathom the universe.

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