Is math real? The answer has major practical and philosophical implications (2024)

You are surrounded by abstract mathematics even if you do not know it. In fact, math may be the main reason why you, me, and a lot of other folks in the modern world are alive and functioning. The device you are reading these words on could only be fabricated because of sophisticated equations associated with quantum mechanics. Most of the food and the other products you buy made it to your store thanks to the subtle mathematics spinning around supply chain dynamics. So yes, you are surrounded by the real-world consequences of mathematics, however abstract they are. But beneath that important fact lies a deeper and more important question.

Is that mathematics real?

Are the truths embodied in all that math real, in and of themselves? Is mathematics somehow inscribed into the fabric of reality, the very thoughts of God? (This can be a metaphor or not, depending on your inclination.) On the other hand, maybe math is just something we invent. Maybe it is a language like any other — one that happens to be super useful for building computers and running supply chains.

There is a lot hanging on the answer to this question, including our ability to talk to aliens, should we ever meet any.

Math as the bones of the world

The idea that mathematics is the only true reality dates all the way back to the philosopher Plato more than 2,000 years ago. For Plato, mathematics, which for him was geometry, revealed a hidden reality underpinning this one. Math to Plato was like an invisible skeleton upon which the flesh of the world is hung. The geometrical relationships for a triangle constitute the perfect and true triangle. All the triangles you encounter in your life, however, are flawed, lesser examples of the ones math describes. In this way, everything you experience is a poor facsimile — a shoddy copy of the ideal forms of mathematics.

You might think this is just some ancient Greek version of nerdiness. But as the centuries spun on and modern science made its spectacular appearance in the 16th century, Platonism’s high appraisal of mathematics gained new followers. In the wake of Isaac Newton, the application of sophisticated mathematics to real-world problems became impossible to ignore. Newton’s invention of calculus ushered in a new era wherein dynamical equations could predict everything from the motion of planets to the trajectory of a cannon ball.

After Newton, these dynamical equations took on ever more abstract forms. In the hands of scientists like Joseph-Louis Lagrange or William Hamilton, the mathematics for something like a planet orbiting the Sun was projected onto a geometry that resembled multi-dimensional donuts. Know the properties of hyper-donut, and you could predict the motion of the planet.

If that level of abstraction wasn’t already strange enough, Einstein’s relativity would soon appear with its four-dimensional geometry for spacetime. The hyper-weird, abstract math of quantum mechanics followed. So rarified had the math become that it took years for even the most brilliant minds to master.

What really mattered, though, was that it worked.

A universal or colloquial language?

The abstractions yielded answers that allowed you to build computers, fly space probes to Mars, or describe the structure of matter. The uncanny ability of abstract mathematics to describe the world prompted the great theorist Eugene Wigner to write “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” In this famous essay, Wigner says, “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” That is why so many physicists have been Platonists in one form or another about the mathematics in their mathematical physics. It just seems like that mathematics is tapping into something that exists below this world — something that gives it a foundation.

Or maybe not.

For many mathematicians, physicists, and philosophers, this view of equations as “the thoughts in God’s mind” is a big mistake. For them, math works because we invented it. Its usefulness is a reflection of the fact that we, and our brains, evolved in the world. Our mathematical inventions work because our embodiment in the world means that we already are tuned to how it behaves. (This is the famous view of cognitive scientist George Lakoff.) Further complicating the argument, not all of our mathematics does work in the world. Much of it finds no expression in physics at all. There is a wide variety of non-Platonist views that deny the idea that math is the most real thing there is.

So, which is it? The answer clearly has some heavy philosophical implications, but there are practical consequences too. If we were ever to make contact with an alien species, how might we communicate with them? If Platonism is right, then all mathematical truth would have to be universal. Alien mathematics would have to be the same as our mathematics. In that case, we could use math as a kind of interstellar Rosetta Stone. It would give us a way to begin to understand each other. But if mathematics really is something invented and not discovered, there would be no reason to think alien math has anything to do with our own. In that case we might never be able to communicate.

So what do you think? Are you really just a shadow of a deeper set of mathematical truths? Or are you and your experience the precondition for there to be any mathematics at all?

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Is math real? The answer has major practical and philosophical implications (2024)

FAQs

What is the practical use of mathematics in real life? ›

For example, balancing a checkbook, household budgeting, comparing prices, making change for a customer, and calculating square footage all involve basic math skills. More advanced math is sometimes used in everyday life and is frequently used in academic disciplines such as physics and engineering.

How are math and philosophy connected? ›

Historically, there have been strong links between mathematics and philosophy. Logic, an important branch of both subjects, provides a natural bridge between the two, as does the Philosophy of mathematics module.

What are the philosophical views of math? ›

The “Big Four” philosophical views on the nature of mathematics that emerged during this period were logicism, intuitionism, formalism, and platonism. According to logicism, the truths of mathematics are ultimately truths of logic.

Is math real or abstract? ›

For example, the abstract concept of number springs from the experience of counting discrete objects (requiring the human senses such as sight for detecting the objects, touch; and signalling from the brain). It is held that mathematics is not universal and does not exist in any real sense, other than in human brains.

Why is math useful in real-life? ›

Mathematics is important in everyday life because it helps humans solve various problems and meet their needs 1. It is used in decision-making, such as choosing modes of transportation and planning vacations 2. Mathematics is also essential for understanding and relating mathematical concepts to real-world problems.

What are the uses of math functions in real-life? ›

Applications of functions include finding profit, populations, and distance traveled. Functions are used by plugging a number into the formula or finding that independent variable on the table or graph and then calculating the resulting dependent variable.

What is mathematics and philosophy major? ›

This major explores the philosophical foundations of mathematics, including questions about the nature of mathematical knowledge and the status of the axioms of mathematics and probability theory, while also applying key tools from mathematics to philosophical problems such as those that arise in evolutionary game ...

What is your philosophy of math? ›

The philosophy of mathematics studies the nature of mathematical truth, mathematical proof, mathematical evidence, mathematical practice, and mathematical explanation. Three philosophical views of mathematics are widely regarded as the 'classic' ones.

Do you need math in philosophy? ›

Yes, absolutely. Philosophy needs logic, which is also part of mathematics.

What is mathematical truth in philosophy? ›

Mathematical truths are the kinds of statements that are both certain to a high degree and also easily knowable by humans, through the practice of mathematical proof. Each of these aspects of mathematical truth is explained by one of the two views above but not the other.

What will happen if mathematics does not exist? ›

It would mean no time, no calendars, no buildings, no transportation, no recipes… the list goes on and on. Quite simply, all of the comforts which make our lives what they are today would be no more.

What is a mathematical explanation in philosophy? ›

The philosophical analysis of mathematical explanation concerns itself with two different, although connected, areas of investigation. The first area addresses the problem of whether mathematics can play an explanatory role in the natural and social sciences.

What is the relationship between philosophy and math? ›

Both maths and philosophy require problem solving, critical thinking and logic, in order to pursue their respective truths. Logic is possibly the most obvious link between maths and philosophy. Bertrand Russell went so far as to claim that all of pure mathematics is simply a prolongation of logic.

Is Maths real or made up? ›

Showing it is true, however, requires the invention of a proof. And over the centuries, mathematicians have devised hundreds of different techniques capable of proving the theorem. In short, maths is both invented and discovered.

Is reality made of math? ›

We've arrived at many ideas, some of which are physically relevant to our reality, through purely mathematical ideation. However, mathematics alone won't paint an accurate picture of reality; we must reconcile what we “think” with what we can observe and measure.

What is the use of mathematics in the modern world in real life? ›

Some of the most common applications of mathematical expertise in the modern world are in business, finance, and engineering. In business, mathematical expertise can be used to calculate financial ratios and statements, to analyse data, and to make predict future financial trends.

What are the five reasons why mathematics is important? ›

Here's why.
  • Math promotes healthy brain function. ...
  • Math improves problem-solving skills. ...
  • Math supports logical reasoning and analytical thinking. ...
  • Math develops flexible thinking and creativity. ...
  • Math opens up many different career paths. ...
  • Math may boost emotional health. ...
  • Math improves financial literacy. ...
  • Math sharpens your memory.
Sep 23, 2022

How important is numeracy in our daily life? ›

Good numeracy is essential to us as parents helping our children learn, as patients understanding health information, as citizens making sense of statistics and economic news. Decisions in life are so often based on numerical information; to make the best choices, we need to be numerate.

Why are numbers important in our daily life? ›

We use numbers in our day to day life. They are often called numerals. Without numbers, we cannot do counting of things, date, time, money, etc. Sometimes these numbers are used for measurement and sometimes they are used for labelling.

References

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