If the humanity disappear

[fl]

Honestly you save, on clay tablets for example, the Elements of Euclid, the complete works of Archimedes, 

the Conics of Apolonius, the Algebra of Al Khwarizmi, the First Analytics of Aristotle and you need nothing 

more. In 500 years you reconstruct all mathematics.

-- 

FL

[vvs]

I suppose that you mean much more than keeping just mathematics of all culture. Otherwise I'd be sorry for such humanity.

[vvs]

 In 500 years you reconstruct all mathematics.

BTW, this is really interesting topic per se. Is it even possible to reconstruct every proof by any arbitrary person? In other words: do we really need geniuses or it's just a convenience? So, would a culturally very different civilization create the same definitions and theorems?

P.S. I suppose some civilizations will omit magmas and monoids :P

[fl]

BTW, this is really interesting topic per se. Is it even possible to reconstruct every proof by any arbitrary person? In other words: do we really need geniuses or it's just a convenience? So, would a culturally very different civilization create the same definitions and theorems?

A genius is no more than a person with an inner double core processor. No more. No magic.

I'm pretty sure we would reconstruct the same collection of definitions and theorem. Including magmas and semigroups.

 

Another question is; would class relations and domination have an influence?

-- 

FL

[vvs]

Another question is; would class relations and domination have an influence?

I guess that would depend on equality and real values. That in turn shows that definitions depend on semantics which is embedded in our culture.

[fl]

I think class relationships would have no effect except it can inhibit the development of the discourse . No effect on the content anyway.

There is an internal logic in mathematics that makes it quite insensitive to the social system state.

-- 

FL

[vvs]

There is an internal logic in mathematics that makes it quite insensitive to the social system state.

I'd argue that our logic reflects our way of reasoning. And I'm not at all sure that other cultures will have the same logic. That is if it's non-human, but even humanity itself has no clear definition of humans. Two legged bird without feathers and with flat nails, perhaps?

[fl]

A genius is no more than a person with an inner double core processor. No more. No magic.

I feel like I'm being unpleasant. I just want to say that there are men like art brut artists who are obviously not 

intelligent (in the academic sense) but who obviously have an interesting intellectual life.

-- 

FL

[Sauer, Andrew Jacob]

I think there is a lot of room for culture to determine, for example, which axiom systems are most interesting to study, and even within the same axiom system, which areas of study are most explored. But, as metamath and other similar computer systems demonstrates pretty well, the fact of entailment from some particular axioms to a particular theorem is rock solid, and can't be undone or changed by culture.

On Mon, Feb 24, 2020 at 2:33 PM vvs <vvs...@gmail.com> wrote:

There is an internal logic in mathematics that makes it quite insensitive to the social system state.

I'd argue that our logic reflects our way of reasoning. And I'm not at all sure that other cultures will have the same logic. That is if it's non-human, but even humanity itself has no clear definition of humans. Two legged bird without feathers and with flat nails, perhaps?

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[Sauer, Andrew Jacob]

> A genius is no more than a person with an inner double core processor. No more. No magic.

Obviously it's not magic but you seem to be saying it's a simple matter of genetics, and a simple matter of having more computational power, and I'm not sure either of those things fully explain why some people are smarter than others. For example intelligence can probably depend on things like upbringing and experience, and high intelligence is probably a matter of having better methods for learning/understanding/thinking about things rather than computational brute force.

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[vvs]

But, as metamath and other similar computer systems demonstrates pretty well, the fact of entailment from some particular axioms to a particular theorem is rock solid, and can't be undone or changed by culture.

That doesn't say anything in particular. Of course the fact that there exists some logical derivation can't be changed. But this doesn't mean that such logical derivation should be actually discovered by particular culture. Even if you restrict your logical foundations to intuitionistic or use only analytic functions as your definition that would preclude many theorems from being formulated and proved. And which definitions and logic is used depends on subjective choice based on culture.