Let us begin by defining our terms. We consider science to mean the accumulated knowledge based on observations and experiment--data. After analysis, workers in the field attempt to organize their data and make generalizations based on what they have found. The generalizations are then subjected to further observations and tests. If the tests are passed, if generalizations are born out by further observations, they may be called a hypothesis or a theory. If a hypothesis or theory continues to be confirmed over many tests and a long period of time it may be called a law.
The procedure we have described is the scientific method. Theories or laws obtained in this way may be accepted as "true," or as "scientific facts." However, at the heart of the scientific method is that any conclusion is always subject to revision. In this sense, there can never be a final proof or a truth in science--or if there were to be such certainty, we could never be sure of it.
The scientific method rests on generalizations that are consistent with specific observations or experiments. Conclusions drawn in this way are said to be made by induction. This technique may be contrasted with deduction, which is used in mathematics or logic. Deduction begins with generalizations, and reaches conclusions based on them. Those conclusions or proofs have a finality that is absent in science.
We may speak of the proof of certain conclusions based on observation, or of the extrapolation of ideas to a new situation. Consider the following story. Two people are in a room with the shades pulled. It is winter, and one person has heard a weather prediction that it will snow that day. He says to the other, "It is snowing outside." The other says he doesn't think so, and demands proof.
The first person pulls up the shade to reveal falling snowflakes, and a dusting of snow on the ground. He has collected data and offered scientific proof. His companion is convinced.
Both people then open the front door and walk outside. They discover snow blowing off the roof on a clear, sunlit day.
While a scientific proof may be reversed, the same is not true of a mathematical proof. Euclid's theorems remain as valid today as in his time. The existence of non-Euclidian geometries may be said to generalize them, but does not invalidate them.
There is, of course, a sense in which scientific conclusions should be considered at least provisionally, as facts. Much of the progress in technology and medicine rests on the acceptance of provisional "facts." It is folly to ignore the general consensus of experts in a given field.