This blog post goes to answering the following question on Quora:
That question actually seems like two questions.
Question 1. “…proof for the existence of the universe?” which Jeff Suzuki has provided an answer for.
Question 2. “…reason for the existence of the universe?”
Maybe you meant one or the other (or both) in asking your question but as I understand them, the words “proof” and “reason” can have quite significantly different meanings.
According to the Oxford Dictionary online here are their main/first definitions:
Proof – Evidence or argument establishing a fact or the truth of a statement.
Reason – A cause, explanation, or justification for an action or event.
Based on how/the language you used to ask the question, I could presume you are actually asking the question the 2nd way, as in “Do physicists and mathematicians believe that we will find a purely mathematical reason for the existence of the universe?”
Or simplifying the question, and taking the opinions of the physicists and mathematicians out of it, we can ask “Can there be a purely mathematical reason for the existence of the universe?”
To answer that question we need to understand properly (beyond a simple definition) what a “reason” is. When we use the word “reason”, we are referring to something that has an effect on something else. For example, the reason for my hat blowing off was the wind. So we think of the wind as having “caused” the hat to blow off.
Now it was the wind that blew the hat off, not a universal law or mathematical equation “representing” the wind. So if we ask the question, “Can mathematical equations, scientific theories and universal laws actually “cause” anything?” we can confidently answer, “No, they can’t cause anything.” They are only the symbolic representation of the regularity of the going-ons of the universe that we can observe (or theorise and then observe to confirm).
Now, because scientific laws/universal laws/laws of physics cannot “cause” anything, they cannot be the “reason” for anything. And as stated, for something to have a “reason”, it would seem to mean that the “reason” is what is “causing” the event to occur. In this case the event being the universe’s existence.
So, given a mathematical solution (universal law) can’t be the “cause” of anything, there can be NO purely mathematical solution that is the “reason” for the universe’s existence. And, if I haven’t equivocated in my reasoning, the opinions of mathematicians or physicists can’t change that, unless they equivocate themselves of course.
If you understand my argument to right or wrong, please feel free to comment, both here on my blog and/or on Quora, pointing out where my answer/argument breaks down, and ideally, your argument in relation to answering the question. No ad hominem arguments please. I’m always happy to be proven wrong if it helps us all get closer to the truth of things.