It is an irony that only those who do not understand science can pronounce on it with such certainty.

An admirably clear and succinct explication of the strengths and limits of science, Where's the Proof in Science? There Is None by Geraint Lewis. Well worth reading the entire brief essay.

What does it mean to prove something?

Mathematicians prove things, and this means something quite specific. Mathematicians lay out a particular set of ground rules, known as axioms, and determine which statements are true within the framework.

The important bit, the bit that defines science, is whether such mathematical laws are an accurate description of the universe we see around us.

To do this we must collect data, through observations and experiments of natural phenomena, and then compare them to the mathematical predictions and laws. The word central to this endeavour is “evidence”.

The mathematical side is pure and clean, whereas the observations and experiments are limited by technologies and uncertainties. Comparing the two is wrapped up in the mathematical fields of statistics and inference.

Many, but not all, rely on a particular approach to this known as Bayesian reasoning to incorporate observational and experimental evidence into what we know and to update our belief in a particular description of the universe.

Here, belief means how confident you are in a particular model being an accurate description of nature, based upon what you know. Think of it a little like the betting odds on a particular outcome.

In mathematics, the framework of assumed truths, the axioms, is a given.

In science, there are no assumed truths, there is no framework. Every assumed truth is waiting to be further tested to understand what are the natural but perhaps unknown axioms within which it is known to be true.

For example, water boils at 100 degrees celsius is a useful assumed truth. But it is precisely true only under given conditions such as the degree of purity of the water, the elevation at which the experiment is conducted, the barometric pressure, etc. All science is conditional upon discovering the limits of the truth.

All knowledge is contingent and those who seek to shut out debate or discussion ("The science is settled") are either a fool, a liar, or a politician (and sometimes all three).

It is an irony that only those who do not understand science can pronounce on it with such certainty.