Will we discover extraterrestrial intelligent life in our universe? Or, might we create extraterrestrial intelligent life in our minds by the use of mathematics? While this may sound like a preposterous idea and an outright impossibility, there are many who have studied what mathematics is who have posited this notion, if not directly then at least indirectly and inferentially.

In math and science and philosophy a debate is raging quietly over whether math is discovered or created. And while this query seems almost insignificant and marginal, it is of the upmost significance for mathematicians and philosophers and scientists. In fact, it may be the most important question in the natural sciences and in mathematics. Some sciences, like physics and chemistry, will cease to be taken seriously if math simply turns out to be only an act of creation by the mind, although we will still continue to use these sciences for utilitarian reasons.

The branch of philosophy that deals with the foundations, assumptions, and ultimate meaning of mathematics is called the philosophy of mathematics. It is here where the deepest questions relating to math are asked. What is math? Is math created or discovered? Does math actually exist in our universe? Or, is it possible that math may be something that resides as an abstract entity in an immaterial world that somehow connects with our physical world? And while there are many more questions that one could investigate that relate to the mysteries of math, this paper will be focusing on the query is math created or discovered, paying special attention to the thought of what it might mean to those who believe that math is created in the human mind and what might they believe if humans made contact with an extraterrestrial intelligent civilization that used mathematics.

And while there are several ways of looking at the question is math discovered or created, the two main rivals that deal with this query are mathematical realists and mathematical anti-realists. There are several versions of each of these schools, and even more subtle versions within each of these schools, yet I will be clumping them together for brevity and comprehension sake, with some mentioning of the different ideas among the several schools of thought. Also, it will not be necessary to outline all the schools of thought in the philosophy of mathematics for the reader to see how some mathematical anti-realists schools of thought would have us believe extraterrestrial intelligent civilizations could be a creation of the human mind by way of our usage of mathematics.

Some philosophical thinkers believe math is real and does exist outside the human mind. Those who believe this way and say math is real are called mathematical realists. They state math is a universal truth in our universe and mathematical concepts and statements do describe the physical reality that we exist in. Numbers and equations and measurements and subtraction do exist and are part of our universe and aren’t just artificial constructs created by the human mind. And that is why those who believe this way tend to say the laws of physics are real. They accept and promote the idea that math has an existence even if humans weren’t here, believing we don’t have to be observing math for it to exist. And to them two plus two always equals four no matter what part of the cosmos you are in. The extreme belief that reality can be reduced to mathematics has been around ever since Pythagoras said numbers are the essence of all things, and there are mathematical realists who still believe in this idea, the best example being the Swedish-American cosmologist Max Tegmark, who promotes the idea that reality is a mathematical structure. And among mathematical realists the biggest debate is over the idea that math exists only in our universe (like Aristotle thought), or that math somehow exists as an abstract thing somehow outside our universe (as Plato thought).

The people that oppose this view are called mathematical anti-realists. They can range from the German mathematician David Hilbert to the American cognitive linguist George Lakoff. They say math doesn’t have an external, independent existence but is dependent on the human species. They propose that math is a language humans have created to deal with the problems of existence. It helps us deal with the trouble of understanding our universe, yet it is still only an exercise with its own internal logic that we have invented and nothing more. Math is not part of our universe, but simply a very advanced form of language we have made up using a lot of symbolism. Some accept natural numbers as being true, but not much else. Most say all the axioms and postulates and theorems and equations just don’t exist in our universe. Some have said math is best understood as a game we play in our heads, a useful fiction we create to explain patterns in our brains. And we create rules so that within this game there is a consistency, and we add more rules to the game as it goes along. It is all a fictional story we have painted in our heads to make sense of reality, but in fact it may not have any connection to how our universe really is. Mathematical anti-realists won’t even concede that we ever discovered the Higgs particle. In their view, we created it and simply attached this thing to fit inside our game.

Now knowing how these two belief systems see what mathematics is, how might these two views interpret humans coming into contact with extraterrestrial intelligent life that had math? Actually, let’s be more specific and make this event about what would happen if humans came into contact with a probe that had mathematical messages inside of it that came from an extraterrestrial intelligent civilization. And as many scientists and mathematicians predicted and expected, some of these mathematical messages would be understandable to us, while much of these messages in math would be incomprehensible to us because they simply would be too advanced for our comprehension.

If this event were to happen, mathematical realists would rejoice, believing this proves (or at least proves more likely) that math exists and is not just a fictional human invention. “Yes, Virginia, numbers do exist!” And while most mathematicians will see this as a good thing, there will be Stephen Hawkings out there who will interpret this as the beginning of our end, believing there is a high probability that these advanced creatures will most likely not be friendly to us.

But what might mathematical anti-realists do? Some would concede they were wrong to believe math was only a human-created language and convert to the light of mathematical realism. Yet, knowing human biases and penchants for believing what one wants to believe, and having seen what happens when a theory is disproven and believers still believe, I am pretty confident many mathematical anti-realists would continue to believe math is still a fictional human tool and nothing more. Many mathematical anti-realists wouldn’t accept this advanced-math probe proves math exists in our universe. They would postulate that this thing’s math is simply something we have created in our minds to describe some new phenomenon we are experiencing and see all of this as a continuation of the game we are playing. And I am sure several philosophers of math will even say if math exists for us and these aliens it only proves both of our intelligent civilizations are being duped by the same phenomenon. “If we found an extraterrestrial civilization and they also had God believers would this prove that God exists?”

Yet, what if we eventually came into contact with these aliens and they were so far ahead of us that they almost only existed in mathematical states of being and could only communicate to us by math? Would many of the mathematical anti-realists continue to deny that math still doesn’t exist except in our minds? Yes. And I have no doubt many would argue that this is all only further proof of how the mind can create extremely complex languages to explain what it is experiencing.

And if you think I am being far-fetched and silly and ludicrous, you obviously don’t know what mathematical anti-realists believe. Like mathematical realists they also believe math is beautiful and orderly and makes sense, but unlike mathematical realists they say math doesn’t exist as something in our universe (or something outside our universe). And yes, they know about the incredible effectiveness of math in dealing with the natural sciences; and yes, they know about the almost unbelievable complexity of what mathematicians do; and yes, they also know about the predictive nature of mathematics as it relates to science, but they still believe our mind is capable of creating these fictional truths of math. And they also hold true to the idea that quantum mechanics, a black hole, a singularity, gravity, an atom, the periodic table, and all the other descriptions of our physical universe where we use math to help us describe what these things are is all wrong. They assert our universe is completely different from what math is saying it is. The mathematical anti-realists say our universe is not math, and many also believe right now we can’t even say what it is.

So, what if you believe how they believe? Should SETI actually now be under the department of neuroscience? Should we give a Nobel Prize to the person who first mathematically creates extraterrestrial intelligent life? And should Stephen Hawking and Alexander Vilenkin and Alan Guth now make a gentleman’s bet over which profession will first create extraterrestrial intelligent life? Mathematics? Physics? Linguistics? Chemistry? Neuroscience?

And so maybe the next time you hear someone talking about the Fermi Paradox (If there are so many extraterrestrial intelligent civilizations out there, where are they and why can’t we find them?), simply say: “Oh, they’re not really out in the universe but in our heads and we haven’t yet mathematically created them…but don’t worry, we will.”