What is science proof
The absolute proof
The story of Fermat's last theorem is essentially the search for a missing proof. The mathematical proof is much more demanding than our casual everyday term, but also more demanding as understood by physicists or chemists. The difference between scientific and mathematical proof is fine, but crucial, and if you want to understand the work of mathematicians since Pythagoras, you have to understand this difference.
According to the concept of classical mathematical proof, one begins with a series of axioms, that is, statements whose truth can be taken as certain or which are obviously true. By developing, step by step, a logical train of thought from these axioms, one arrives at a conclusion that is indisputable. The conclusion is the theorem or the proposition.
Mathematical proofs are based on this logical procedure and, once successful, are true until the end of time. In order to assess the value of such evidence, it should be compared to its poor relative, the less sophisticated scientific evidence. In science, a hypothesis is put forward to explain a particular phenomenon. If the observations agree well with the hypothesis, this is taken as evidence in their favor. The hypothesis should not only describe an unknown phenomenon, but also be able to predict the results of other phenomena. The predictive power of the hypothesis can be tested on the basis of experiments. If they are successful, this counts as renewed evidence in favor of the hypothesis. After all, the sheer volume of evidence can become so impressive that the hypothesis is accepted as a scientific theory.
Scientific theory can never claim absolute validity to the same extent as the mathematical theorem: it is only considered highly probable on the basis of the evidence available. So-called scientific evidence is based on observation and perception, both of which are fallible and only allow approximations to the truth. Bertrand Russel once stated: "It may sound paradoxical, but all exact science is dominated by the idea of approximation." Even in the widely accepted scientific "evidence" there is some doubt. Sometimes it wanes, if never entirely, and other times the evidence turns out to be false. This weakness in scientific evidence leads to the scientific revolutions in which a previously valid theory is replaced by another theory that may be just a more elaborate variant of the original one, or in complete contradiction to it.
In the search for the elementary components of matter, for example, each new generation of physicists overturns or at least refines the theory of their predecessors. The modern search for the building blocks of the universe was heralded at the beginning of the nineteenth century when John Dalton, through a series of experiments, came to the assumption that everything is composed of individual, indivisible atoms. Towards the end of the century, J. J. Thomson discovered the electron, the first subatomic particle, which is why the atom could no longer be considered the last building block.
Science works in a similar way to law. A theory is believed to be true when there is enough evidence to prove it "beyond reasonable doubt". Mathematics, on the other hand, is not based on faulty experiments, but on infallible logic.
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