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I think one thing that humans have not come to terms with is the possibility that some fundamental fields are essentially dead in terms of possible new discover

I think one thing that humans have not come to terms with is the possibility that some fundamental fields are essentially dead in terms of possible new discoveries that most people will care about. That doesn't mean that there's nothing left to do. There are minor details in some fields but they are more like engineering problems. Physics may be one of those fields and I certainly think math is as well. However, it's sometimes hard to recognize because there is a core group of people that keep it going because it's their nest egg.

johndunne 4y ago
I believe this sentiment is what a large cross section of the physics community was thinking prior to Einstein’s breakthroughs.
jb1991 4y ago
I quite disagree with this. Visionaries come along to unseat centuries of limitations, raising the ceiling forever. Those visionaries are rare, but there will be more.
- vouaobrasil 4y ago
  Maybe, but if you look at the list of famous unsolved problems in math, it has been dwindling for a long time. The list used to contain problems that undergrads could understand. Biology is still like this -- you can take quite a few interesting unsolved problems in biology and explain it to most people. Math has a few left like the Riemann hypothesis, but the vast majority of new work that has been coming out is more like refinements (I say this as a PhD in math who as actually read them). We look at history and expect it to repeat itself, but if you closely examine math history you can actually see a decline. Take the time to truly examine "visionary" things that have happened in math and those events are actually getting fewer and fewer. I seriously doubt there is much left to do that is of interest to more than 5-10 people in each subfield.
  - galleywest200 4y ago
    Are you suggesting there are no more unknown problems in mathematics, that "the list" will not be added to?
    - vouaobrasil 4y ago
      Well, due to the nature of math there are technically hundreds of questions you can ask (specific behaviour of the infinite number of diophantine equations, improving constants in estimation, whether there exists a prime number that satisfies XYZ, etc), but those problems are becoming so hyperspecialized that very few people if any will care about them. There may be one more paradigm shift that is related to stuff that Sholze is doing and there is certainly some work to do in proof theory ala Voevodky's univalent foundations so we could see a couple more things but the vast majority of basic foundational work in math is done. So while we have a few more fundamental problems that most people have heard of like the Riemann hypothesis and the twin primes conjecture, don't expect to have any more of those. (Certainly the more recent ones are already so specialized that few people outside the immediate area would ever understand or even care about them). I'm also not sure why there's such a negative view towards the end of progress on this site---a lot of people seem to take it as an axiom that currently "useless" things will eventually become useful but I simply do not believe that is the case (and this is coming from someone who has published quite a few papers in pure math).
tsimionescu 4y ago
Physics still has major gaps right in the middle - our two main theories of how the world works are mathematically incompatible. This leaves room for some significant new discoveries that could upend everyone's understanding of the world. Not to mention that both QM and GR in themselves have inconsistencies or infinities. GR famously has a singularity in the center of a black hole, which means the math doesn't actually apply there. QM has the measurement problem, and the (probably related) problem of making the laws of motion linear, when we can clearly see highly non-linear behavior in reality.
barrysteve 4y ago
Depends what you mean by care about, because the majority of praised discoveries are an extra foot on the millipede. Precisely because we designed our universities and technologies that way. You can nurture in systems and cultures that break open the fundamentals again if you so wish. Most people don't wish it, they are happy living out incremental improvement in the city and surrounds.

johndunne 4y ago

I believe this sentiment is what a large cross section of the physics community was thinking prior to Einstein’s breakthroughs.

jb1991 4y ago

I quite disagree with this. Visionaries come along to unseat centuries of limitations, raising the ceiling forever. Those visionaries are rare, but there will be more.

vouaobrasil 4y ago
Maybe, but if you look at the list of famous unsolved problems in math, it has been dwindling for a long time. The list used to contain problems that undergrads could understand. Biology is still like this -- you can take quite a few interesting unsolved problems in biology and explain it to most people. Math has a few left like the Riemann hypothesis, but the vast majority of new work that has been coming out is more like refinements (I say this as a PhD in math who as actually read them). We look at history and expect it to repeat itself, but if you closely examine math history you can actually see a decline. Take the time to truly examine "visionary" things that have happened in math and those events are actually getting fewer and fewer. I seriously doubt there is much left to do that is of interest to more than 5-10 people in each subfield.
- galleywest200 4y ago
  Are you suggesting there are no more unknown problems in mathematics, that "the list" will not be added to?
  - vouaobrasil 4y ago
    Well, due to the nature of math there are technically hundreds of questions you can ask (specific behaviour of the infinite number of diophantine equations, improving constants in estimation, whether there exists a prime number that satisfies XYZ, etc), but those problems are becoming so hyperspecialized that very few people if any will care about them. There may be one more paradigm shift that is related to stuff that Sholze is doing and there is certainly some work to do in proof theory ala Voevodky's univalent foundations so we could see a couple more things but the vast majority of basic foundational work in math is done. So while we have a few more fundamental problems that most people have heard of like the Riemann hypothesis and the twin primes conjecture, don't expect to have any more of those. (Certainly the more recent ones are already so specialized that few people outside the immediate area would ever understand or even care about them). I'm also not sure why there's such a negative view towards the end of progress on this site---a lot of people seem to take it as an axiom that currently "useless" things will eventually become useful but I simply do not believe that is the case (and this is coming from someone who has published quite a few papers in pure math).

tsimionescu 4y ago

Physics still has major gaps right in the middle - our two main theories of how the world works are mathematically incompatible. This leaves room for some significant new discoveries that could upend everyone's understanding of the world. Not to mention that both QM and GR in themselves have inconsistencies or infinities. GR famously has a singularity in the center of a black hole, which means the math doesn't actually apply there. QM has the measurement problem, and the (probably related) problem of making the laws of motion linear, when we can clearly see highly non-linear behavior in reality.

barrysteve 4y ago

Depends what you mean by care about, because the majority of praised discoveries are an extra foot on the millipede. Precisely because we designed our universities and technologies that way. You can nurture in systems and cultures that break open the fundamentals again if you so wish. Most people don't wish it, they are happy living out incremental improvement in the city and surrounds.