3 ms·

I can't pretend to be anywhere near the frontiers of math but aren't some contributions about providing a unifying framework or simplifying re-expression of som

by abeppu 4y ago

I can't pretend to be anywhere near the frontiers of math but aren't some contributions about providing a unifying framework or simplifying re-expression of something that was already known in a way that makes it more comprehensible? Is there not always hope that the right new perspective or innovation in one generation will allow subsequent generations to get up to speed faster?

szundi 4y ago
Point is that the low hanging fruits are finite and are picker continuously, thus sooner or later they run out. Reinventing something I consider low hanging just not recognized for some time.
tsimionescu 4y ago
It's not really plausible that such a process could continue forever. It may be plausible that there are some better foundations to various fields of math that could reduce the size of the proof for Fermat's last theorem by, say, 100 fold - but it's not plausible that it could ever be fitted onto the side of a page with the right abstraction. It's not plausible that, even in the far future, you'll be able to learn the information needed to derive formulas you'd learn in post-graduate maths today after a 1 week course in 5th grade. On the other hand, it's extremely plausible that math as an abstract idea could build arbitrarily complex structures that would be of interest if we were able to learn to model them - so, almost necessarily, within the limitations of current human cognition and/or lifespan, there will be some structures that it is impossible for a human to learn. Of course, in some arbitrary future we may find that those limitation of human cognitition/life-span can themselves be overcome - if that's the case, then the argument changes significantly.
pa7x1 4y ago
This effect clearly exists. It suffices to check how physics and math were expressed in the papers that discovered them and how they are currently represented to notice that sometimes organizing knowledge in the right framework and simple notational changes can be sufficient to power up our ability to make new advances. Question is, are we dedicating enough effort to this endeavors? Is rewriting known math under a different guise sufficient to survive the publish or perish attrition? And will these efforts keep returning results? I suspect the answer is no to the first two questions, and I don't know the answer to the third.

by abeppu 4y ago

szundi 4y ago

Point is that the low hanging fruits are finite and are picker continuously, thus sooner or later they run out. Reinventing something I consider low hanging just not recognized for some time.

tsimionescu 4y ago

It's not really plausible that such a process could continue forever. It may be plausible that there are some better foundations to various fields of math that could reduce the size of the proof for Fermat's last theorem by, say, 100 fold - but it's not plausible that it could ever be fitted onto the side of a page with the right abstraction. It's not plausible that, even in the far future, you'll be able to learn the information needed to derive formulas you'd learn in post-graduate maths today after a 1 week course in 5th grade. On the other hand, it's extremely plausible that math as an abstract idea could build arbitrarily complex structures that would be of interest if we were able to learn to model them - so, almost necessarily, within the limitations of current human cognition and/or lifespan, there will be some structures that it is impossible for a human to learn. Of course, in some arbitrary future we may find that those limitation of human cognitition/life-span can themselves be overcome - if that's the case, then the argument changes significantly.

pa7x1 4y ago

This effect clearly exists. It suffices to check how physics and math were expressed in the papers that discovered them and how they are currently represented to notice that sometimes organizing knowledge in the right framework and simple notational changes can be sufficient to power up our ability to make new advances. Question is, are we dedicating enough effort to this endeavors? Is rewriting known math under a different guise sufficient to survive the publish or perish attrition? And will these efforts keep returning results? I suspect the answer is no to the first two questions, and I don't know the answer to the third.