Scientific and logical reasons for the existence or non-existence of the O(n^2) algorithm for multiplying matrices

[Dr. Sadeghi]

As someone who has been involved in solving the problem of multiplying matrices with O(n^2) for many years, I wanted to ask the opinion of other experts: do you think it is possible to multiply two vectors of order O(1)? I have no doubt that the methods used so far do not lead to correct and practical results because instead of focusing on vectors, they have focused on the matrices. My main point is that looking for order O(1) for multiplicative vectors requires a deep insight into the philosophy of numbers in nature, and the solution is a magical and eternal way that will take the world to the brink of a great revolution. what is your idea about this? Therefore, it should be solved with a big and creative mind. So my main question is, can we give definitive reasons to reject the multiplication of two vectors with O(1)? And if there is an algorithm that makes this possible, how should the information of vectors that are n-dimensional, be expressed by a finite number of variables? For example, in their decimal part or somewhere else?