I was recently intrigued by the following comment made by Ricky Gervais in [this](https://youtu.be/P5ZOwNK6n9U) discussion with Stephen Colbert (Timestamp: 3:50).

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> If we took every science book, right, and every fact and destroyed them all, in a 1,000 years they'd all be back
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I was curious as to the extent of truth in the above statement. It is obviously highly likely that notation will differ in these *new* books. My question, however, is directed towards the similarities in the underlying meaning of the *old* and *new* books. Considering that math and science, in general, is based on certain fundamental definitions, what is the likelihood of variations in definitions? More importantly, however, will different definitions create different *versions* of science?

To elucidate, I shall cite an example that illustrates present definitions on infinity. We may consider the infinite sum 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + ... Fitting with our modern mathematical conception of infinity, the sum would be regarded as [divergent](https://en.wikipedia.org/wiki/Divergent_series). A new generation, however, may choose to allocate a value to the sum, using a technique such as [Cesàro summation](https://en.wikipedia.org/wiki/Ces%C3%A0ro_summation). The choice of attributing [convergence](https://en.wikipedia.org/wiki/Convergent_series) or divergence to a series is a purely aesthetic choice. In the case of differing definitions of infinite sums created by the distinct generations, would this alter mathematical ideas?

In the above example, it seems to me that there is no correct answer. I want to also highlight a situation where I believe there is a correct answer but the correct answer is unknown. The video by YouTuber Veritasium [Why No One Has Measured The Speed Of Light](https://youtu.be/pTn6Ewhb27k) talks about the physical limitations of measuring the unidirectional speed of light. This has lead scientists to make the assumption that light travels at the same speed in all directions. My question is what if it was scientifically impossible to ever know an answer to the question "Does light travel at the same speed in all directions?". Wouldn't this obfuscate the possibility of the same assumptions being made by different generations?

To present some similar examples, [analytic continuation](https://en.wikipedia.org/wiki/Analytic_continuation) may be an example of there being no correct answer. Further, [Kurt Gödel's incompleteness theorems](https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems) may have mathematical relevance with the second example.

I believe that the purpose of this post is to explore the inherent limitations of math and science. What do these limitations tell us about our reality if even the most sophisticated tool that is presently known to us (i.e. scientific reasoning) may be subjected to variations in definitions and may be characterised by an element of uncertainty?

My question may also have similarities with the following questions, which may help bring clarity to the question.

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> If we compared our scientific books with the books of an alien civilisation, to what extent would they be the same?
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> Is mathematics invented or discovered?
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The question may also have relevance to [this](https://math.stackexchange.com/q/4418589/954997) post (now deleted) on math.se.