"Gott wuerfelt nur."
God only plays dice.
An answer to the famous quote from Einstein - "Gott wuerfelt nicht". In my opinion, the universe is only made of stochastic functions and any deterministic ones are only an approximation to it.
Or even, the universe might be made of deterministic equations, but we are cursed with a limited precision in our sensors (biological or not) that we will never see it the way it is.
That can be extended to problems, that is, if you happen to solve a problem in all situations, it might only be that your samples are limited.
It is very human to try and adopt systems where the certainty is 100%, or in other words, it is easier to develop and understand systems where the functionality is not under some noise conditions, where mistakes could not occur internally or externally and when the results expected are clear and not under a great number of trade offs and unclear multi-modal complex functions.
However, the real world seems to prefer the systems that are more adaptive rather than the ones that solves everything 100% correctly, under some precise conditions.
It might only be that our understanding of the world, as of today, is a bit ankward and much attention is paid into developing the certain than discovering the uncertain, leading to very few progress. It is no wonder, even Einstein that could figure relativity could not accept a probabilistic model of our world. It is that hard and it might be our big unability.
I would even say that stochastic systems are the evolution of mathematics, but given its high complexity, it is underused.
Though, things are changing, mathematics is not the same as it was before, it was reinvented by the advance of technology and nowadays it might even be easier to understand and tame stochastic systems as it once was with the deterministic field.
I will go further and give an example, if you would like to calculate the pi, there is a very easy to understand way of doing it using a simple stochastic system. Imagine that you have a square and a circle inside of it. If you get a random variable x,y and put it inside the square, there is a chance it falls inside of the circle. This chance is directly proportional to the area of the circle that is pi*R^2.
Now if you divide the number of samples from x,y that falls inside the circle by the total number of samples, you will get an approximation to the following: pi*R^2/((2*R)^2). That is, the result is proportional to pi/4.
The more you collect samples the near the result and it is very easy to program and understand. No complex at all, but try this without a computer and you will see how difficult it is to imagine the result.
I dare say, if mathematics is the deepest science of the world from which every other science depends, computer science is the tool to understand mathematics and therefore the base of science in a technological world.
But changes are not easily accepted in the cultural world, it is even harder to occur in a educational system. Though some guys are luckily experimenting programming before mathematics and things are getting much easier and clear. No wonder they are called sometimes as geniuses, hackers, and so on. But truth be said, the wheel is invented, it is here and there, they are just the unique humans that use the wheel appropriately.
I am sure you know Mathematics was once a forbidden and secret society, that people were once afraid of using a vehicle that travels more than 100km/h, and etc. Therefore, it was the same with mathematics, other sciences and discoveries, no reason to be different now.
