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In practice, the distinction between the last two concepts is not so clear. For instance, the axioms in Euclid’s Elements would be considered horribly insufficient by modern standards, but still most mathematicians would probably accept that Euclid proved the theorems that appear in that work. This is because the arguments Euclid made still work as long as they are properly translated into the modern framework. Of course, Legends Were Born In January 1950 Perfectly Life Begins At 71 T-Shirt the distinction is crucial from a formalist point of view, but in reality, the formal systems usually turn out to correspond to existing mathematics and intuition. Perhaps it would be more meaningful to consider something to be “proved” if the proof is accepted as valid by the community of mathematicians at the time.

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Perhaps it would be more meaningful to consider something to be “proved” if the proof is accepted as valid by the community of mathematicians at the time. This does have issues, as there have been “proofs” that were later overturned. Nevertheless, this generally seems to fit with how most of mathematics is considered to have developed historically. Whenever there are changes in the formalisation or the rigour requirements, Legends Were Born In January 1950 Perfectly Life Begins At 71 T-Shirt it is usually the case that theorems proved in the past stay theorems because their proofs can be made rigorous within the new system. the way you write it there is little difference between a mathematical proof and a catholic dogma as it was understood in the middle ages

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Of course, it was only supposed to give a rough idea. One might add the condition that the proof remain accepted as valid (or “can-be-made-valid”) by future mathematicians, but that has the difficulty of us not being able to know the future, unless one claims that “modern” mathematics has reached the maximum rigour and formality requirement. Ideally, one would like to say that a proof is a sequence of valid logical deductions (although it is ultimately people who decide whether the logical steps are valid), and thus anyone from any time period could in principle check for oneself that the proof is correct. However,Legends Were Born In January 1950 Perfectly Life Begins At 71 T-Shirt why should we expect something like this to be the case? There are some possible explanations which I mention below.