Short answer: Yes they exist
Long answer: No they don’t exist
On one hand of course they exist, they are what we use to measure time, distance and nearly everything else we know of. We are taught numbers from a very young age and we use them on a daily basis.If humans had never existed, there would still be a number, an amount of animals on the planet, of oxygen in the air. But it is the fact that humans are so called ‘intelligent’ life, that we can understand those amounts and then communicate them to others. We created the names of the numbers but we are even capable of expressing a number without talking, we can write it down, we can hold up fingers on our hands. Surely something so consistent and versatile in all of our forms of communication must exist right?
But on the other hand…
They say that humans use only a small percentage of their potential brain power, and that our subconscious influences us and our way of thinking without us being aware of it. What if our subconscious understands the universe perfectly, but it would simply be too much for us to comprehend and would leave us as dribbling wrecks in a corner. Therefore our subconscious creates concepts to help us.
One of those concepts being numbers, we don’t see the gravitational effects on an object falling with our eyes, so we create sums and equations to help us to understand the mechanics of why that brick is falling.
Our mind is programmed to recognise patterns, to learn and progress, which is another function of numbers. For example, Yellowstone park is a super-massive volcano that has erupted roughly every 600,000 years, our minds have processed this information and converted it into a chance, a likelihood that it’s going to erupt today tomorrow, next year. We could only do this because of the pattern that is evident throughout history, the concept of time does not need numbers so despite the fact that I wrote 600,000 years it could have been explained without the need of numbers, they’re just a human construct used to help our comprehension.
We use numbers as a means of measuring where we compare with everything and everyone. Without numbers we wouldn’t care about material things like money, being the top seller, or having the biggest house. It is because of numbers that we have a competitive and selfish streak, which is seen throughout the whole of humanity, always needing and wanting more and it’s because of this concept of numbers.
All in all, it doesn’t really matter whether numbers actually exist or if it’s just a figment of the human race’s imagination and culture, it is the only way we can come close to understanding where we have come from, where we are going and the universe that surrounds us. And who’s to say there isn’t a super intelligent race in the universe who has exceeded mere concepts such as numbers, they may have a much truer understanding of the universe than we do or ever will.