Has science proven mathematically the universe and life could not have been formed by random chance alone

Science, so far, has indicated that with the proper ingredients and proper conditions, life can rise spontaneously. As to the Universe, the origin is still a mystery but everything after 10^-31 seconds is pretty much a result of physical law with no outside forces needed.

A scientific theory is based on evidence, not necessarily math. Biology is not heavily math based while theoretical physics is all about the math.

Exactly which theory are you talking about that needs tearing into?

No. The universe is not well enough understood to say what the physical constants are. For example, dark matter and dark energy are unexplained.

Life is a function of chemical interactions. Life-as-we-know-it is what we are made of. If other kinds of life are possible, we don't know it.

This is a philosophical question, not something one scientist can resolve in a journal article. We don't have a clue as to what there was before our universe began 13.7 billion years ago. There are interesting speculations, but no data

Note: edited a typo in the age of the universe.

The notion that life formed by random chance is a misnomer. There is nothing random about chemical bonding, the laws of conservation of mass and energy or any of the laws of nature.

According to the two slit experiment in quantum physics, if you observe something, there will be randomness. If you don't, then electrons will travel in a wavelike pattern and the system is deterministic.

If given infinite chances then the result of anything happening is 100%. However, on any given chance the chance of one particular outcome is infinitesimal.

It cannot be proved or disproved, as far as I know.