10 ms·
> but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results ar
by maegul 4y ago
> but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap.
The sad part is that as the trend continues we may reach a point where a mathematician's intellectually productive life is not sufficient to contribute anything novel, statistically speaking.
IMO, an under appreciated dynamic across the board of human endeavours.
With increasing complexity comes the need for more time to understand and master anything.
- trash3 4y agoThis sentiment is humorous, as I'm an optimist apparently. More children will learn more quickly. Applying AI to education should supercharge the smartest.
- deanCommie 4y ago> Applying AI to education should supercharge the smartest. What does that mean?
- wnkrshm 4y agoI don't know but it also fails to disregard that the smartest people (whatever that means) can have executive function issues that are orthogonal to their mental capacity. Additionally, the belief that intelligence alone will improve the world is misguided imo. You need empathetic, intelligent people.
- kwhitefoot 4y agoAs we do not yet have artificial intelligence making confident statements about what its effects might be is surely rather rash.
- ConceptJunkie 4y agoYou must be an optimist if you think what passes for AI right now could in any way help education. It's an incredibly useful tool, but not in the way you almost certainly are thinking.
- inamberclad 4y agoAgreed, it feels like the days of maverick engineers leading huge efforts is mostly over. Will there be any more Kelley Johnsons, or Gene Kranzs in our lifetimes?
- zip1234 4y agoTools can be used for this purpose. New tools can unlock new abilities for engineers. I’m not sure if it applies to math but I don’t have any reason why it shouldn’t.
- colordrops 4y agoEngineering is different from math. A large part of the reason why engineering innovation is lacking in a particular field is due to entrenched players, heavy bureaucracy, and government regulation, for instance with spaceflight and EVs.
- ciphol 4y agoThere is still plenty of amazing engineering going on, for example EUV development at ASML.
- kjellsbells 4y agoThat's a very big claim, perhaps true only if human endeavor only ever builds linearly. But I dont think that is true. Certainly not in the arts or music, e.g. the Beatles did not need to ingest the entire corpus of Mozart or even Scott Joplin to be highly productive. Although, it certainly helped that they were extremely open minded to all types of music. A second example is that of recent advances in virtualization, where the last decade of advances in things like cgroups, namespaces and containers were all done by people who I assert had no training in IBM MVS/zOS and therefore weren't building on what went before (imho, to their detriment).
- npunt 4y agoThe Beatles themselves didn't need to ingest the entire corpus of past musicians to be productive & inventive, but they did stand on the shoulders of giants musically (vs being born in some prior century), and they were in the right time & place to be part of a growing scene whose smarts exceeded that of any of it's individual participants. This is the nature of 'scenius' and of golden ages - a lot of ideas are already teed up in the collective consciousness.
- FabHK 4y ago> only if human endeavor only ever builds linearly. A lot of mathematics is cumulative, though. And even if you can go further by going thinner (specialising more), maybe breakthroughs require lateral thinking and connections that are predicated on not being too specialised, but having breadth also. If that is the case, sooner or later we might be in trouble.
- hoseja 4y agoIt's also a major failure in didactics. It feels like very little of the new knowledge since twentieth century has been truly digested for easy teaching. Why isn't general relativity taught in elementary school? It should be possible.
- maegul 4y agoInteresting! As other comments ts have pointed out, didactics as an important aspect of how humanity responds to such a dynamic. Otherwise, I’d say our two thoughts are connected. With increasing difficulty in understanding new progress, there could be an inertial tendency to over emphasise the importance of old knowledge because it’s comforting/easier/pragmatic for teachers and parents.
- germandiago 4y agoFWIW I notice how remarkably bad I was taught math at school. When I started to go to university I really noticed how bad it was. At university the jump forward was really noticeable. For example, at school they would show you a couple of simple explanations about derivative math or integrals, briefly and start with all the formulas. At university I used to have a teacher that started with: history of mathematics, why they were invented, made a point about its primarily practical origins. To explain things, he could most of the time come with real-life instances of application and there were much more often intuitive or geometric interpretations of the techniques used much more often even before starting the explanation itself to have an intuitive idea and visualization of what you were achieving. After that, I noticed that to learn math, the first thing is to develop an intuitive, non-mathy idea of what you are doing and later formalize it. At school and high school they just taught it as almost-memorize tables, apply formulas. Talking about Spain, btw.
- robertlagrant 4y agoWhen I came across the (obvious, in retrospect) visual explanation for why (a + b)(a + b) == a^2 + 2ab + b^2 I was blown away by how simple it was, and by why on earth I had to just memorise that formula in school.
- deleted 4y ago[deleted]