Numbers exist because everything has a number behind it. There is nothing, a number. There are three bananas, three is a number. Also in science you can't create or destroy matter, matter is always there, there is always a certain amout of particles, there can't be no particles in the universe. There always can't be no particles. There can't be no nothing. Without that there would be "nothing" in the world!!!
Numbers did exist, but they do not exist by themselves. Numbers are not just mental inventions. We can say numbers are abstract objects, they exist out of space and time.
For example, There exists prime number, which is the sum of squares of two integers. We use the word "exists" for numbers.
Numbers also used to descripe objects (1 book, 3 apples and etc.), but this ideas runs into trouble when you ask to describe object using 2+5i, or π (pi).
Mathematical fictionalism is just fiction, it is just idea, which has no basis.
When converting fractions to decimals, 1/3=0.3333... Forever and 2/3=0.6666... Forever, holding that pattern (math is all about patterns), 3/3 should equal 0.9999... Forever the reason that it isn't is because there must be a difference when you subtract 0.9999... From 1. Because people could not find any number to represent that difference, it was concluded that 0.9999... And 1 were the same numbers. However I have recently discovered that it is possible to find the difference between these two numbers and that difference is 1X10^(negative infinity). I feel that if 3/3 does not equal 1, then mathematics will fall apart at the hinges, and following math will come science, technology, medicine, communications, construction and government (the last one isn't so bad). Please feel free to dispute my hypothesis in any way that you can under the assumption that I will respond to the rebuttal
Do numbers exist? Well, not really. You see, a number has no tangible existence. If you have three apples, you have apples, and there are three of them. You cannot have three, as three is merely a descriptor.
Though it seems counter-intuitive, numbers are merely a concept, an artificial construct used to explain the world around us. The system works, it's very precise, and it's very useful. But it exists because we have made it that way.