Is Math invented or discovered?
Mathematics is the science of number, quantity, and space.
Math can be either studied in its own right (known to be pure mathematics), or
it can be applied in various disciplines such as physics and engineering. Math
is fundamental for our knowledge system. It is basically what we use to
describe everything that surrounds us: the length of the chair that you sit on,
the weight of your index finger, etc… This is crucial for our society. Many
people say that math itself is discovered. However, what we know is that we
invented our type of math to perfectly suit the human world. The language
itself was invented. For example, we use algebraic language to solve math
problems, which was invented by the Arabs. However, different cultures
established different forms of math based on their own needs. A famous Einstein
quotes resumes everything about our math: “How can it be mathematics, being
after all a product of human thought which is independence of experience, it so
admirably appropriate to objects of reality?” What Einstein means is, for
example, if the universe disappeared, our math would not serve for anything,
meaning another “form” of math would fit better in the “new world”. Let’s take
the different bases, for example. We use the common base, known as base 10. Other
societies use base 4, or even base 2. It all depends on the form of math used.
Just like any other language, math was invented itself. Just like the
cosmologist Max Tegmark said, math is indeed a human discovery and the
universe is essentially one gigantic mathematical object. In other words,
mathematics describes no more the universe than atoms describe the objects they
compose. Math is the universe. Another example is that an ancient civilization in the Andes
used strings to count, and, therefore, used a completely different math system.
For them, 1+1 would not necessarily equal to two. However, in our math system,
there is no way that this is wrong. This just shows how different cultures
establish math based on their own needs. This Andes population would never say
that 10 times 35 is 350, since they count based on strings, and they might not
even have 350 strings in their system. They might have 10, so they consider
everything past 10 as infinite. Our infinite is different, and so it goes on
and on and on. However, what can be told as well is that our math is invented,
but the relationship between the numbers is discovered, and, therefore, proven
to exist. A perfect example is Fermat’s theorem. Before, we only knew that it
was true, and it perfectly suited our world (we could apply any number in the
equation that the result would be right). However, Andrew Wiles, a famous
mathematician, proved the opposite. He proved that this theory is not true.
This just shows how the relationship of the numbers is discovered. Wiles took a
long time to prove it, but he “discovered” the relationship of the different
numbers that could be used in the Fermat theorem. There are some examples,
however, that are the opposite. For example, Godel’s first theorem (X=X) is
something that we assume it is true, and that this was actually discovered.
However, we can’t prove that it is true. This is the beauty of math. Sometimes
we encounter problems that are important to solve, and we only want to “discover”
the right answer, but when we look at it again, we can’t prove that what we
did. I know that this did not happen to Wiles, but he is an exception. To sum everything
up, the math system itself is invented, but the relationship between the
numbers is actually proven and, therefore, discovered.
Math can be either studied in its own right (known to be pure mathematics), or
it can be applied in various disciplines such as physics and engineering. Math
is fundamental for our knowledge system. It is basically what we use to
describe everything that surrounds us: the length of the chair that you sit on,
the weight of your index finger, etc… This is crucial for our society. Many
people say that math itself is discovered. However, what we know is that we
invented our type of math to perfectly suit the human world. The language
itself was invented. For example, we use algebraic language to solve math
problems, which was invented by the Arabs. However, different cultures
established different forms of math based on their own needs. A famous Einstein
quotes resumes everything about our math: “How can it be mathematics, being
after all a product of human thought which is independence of experience, it so
admirably appropriate to objects of reality?” What Einstein means is, for
example, if the universe disappeared, our math would not serve for anything,
meaning another “form” of math would fit better in the “new world”. Let’s take
the different bases, for example. We use the common base, known as base 10. Other
societies use base 4, or even base 2. It all depends on the form of math used.
Just like any other language, math was invented itself. Just like the
cosmologist Max Tegmark said, math is indeed a human discovery and the
universe is essentially one gigantic mathematical object. In other words,
mathematics describes no more the universe than atoms describe the objects they
compose. Math is the universe. Another example is that an ancient civilization in the Andes
used strings to count, and, therefore, used a completely different math system.
For them, 1+1 would not necessarily equal to two. However, in our math system,
there is no way that this is wrong. This just shows how different cultures
establish math based on their own needs. This Andes population would never say
that 10 times 35 is 350, since they count based on strings, and they might not
even have 350 strings in their system. They might have 10, so they consider
everything past 10 as infinite. Our infinite is different, and so it goes on
and on and on. However, what can be told as well is that our math is invented,
but the relationship between the numbers is discovered, and, therefore, proven
to exist. A perfect example is Fermat’s theorem. Before, we only knew that it
was true, and it perfectly suited our world (we could apply any number in the
equation that the result would be right). However, Andrew Wiles, a famous
mathematician, proved the opposite. He proved that this theory is not true.
This just shows how the relationship of the numbers is discovered. Wiles took a
long time to prove it, but he “discovered” the relationship of the different
numbers that could be used in the Fermat theorem. There are some examples,
however, that are the opposite. For example, Godel’s first theorem (X=X) is
something that we assume it is true, and that this was actually discovered.
However, we can’t prove that it is true. This is the beauty of math. Sometimes
we encounter problems that are important to solve, and we only want to “discover”
the right answer, but when we look at it again, we can’t prove that what we
did. I know that this did not happen to Wiles, but he is an exception. To sum everything
up, the math system itself is invented, but the relationship between the
numbers is actually proven and, therefore, discovered.
You did a good job with the examples that suggest that math is invented, and you brought in some interesting outside sources that confirm this. But some of what you said in the second half got a little muddled. The turning point should have been the Einstein quote. Einstein does indeed say there that math is an invention, but you missed the second half of the quote, where he wonders how it can be that an invention of our mind so perfectly matches the workings of the universe. What would have helped you sort this out is the distinction between truth of coherence (math is just an invented system) and truth of correspondence (math corresponds to the real world).
ReplyDelete