Timeline for How difficult will it be to start doing research in pure mathematics in the near future? [closed]
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 29, 2022 at 11:55 | comment | added | Hollis Williams | You have to bear in mind that although in the time of Newton there was less mathematical knowledge to learn, Newton also had to learn and practice a bunch of stuff that we do not use any more. There are also new emerging subjects in mathematics which have lots of ''low hanging fruit'' which isn't that hard to pick, the intersection of mirror symmetry/toric geometry might be an area with this type of fruit. | |
| Jan 30, 2021 at 4:29 | history | closed |
skupers Will Jagy Sam Hopkins user21349 Alexandre Eremenko |
Opinion-based | |
| Jan 29, 2021 at 23:06 | comment | added | JP McCarthy | In newer fields there are going to be interesting problems in the foothills that experts will bypass as they go for the higher peaks. | |
| Jan 29, 2021 at 21:47 | comment | added | Timothy Chow | Possibly helpful is an answer I gave to a related question, When is one 'ready' to make original contributions to mathematics? | |
| Jan 29, 2021 at 19:56 | review | Close votes | |||
| Jan 30, 2021 at 4:33 | |||||
| Jan 29, 2021 at 19:15 | comment | added | Lubin | I think there will always be relatively elementary doors opening up into worlds of advanced mathematics now undreamt of. | |
| Jan 29, 2021 at 19:01 | comment | added | Gerald Edgar | @FrancescoPolizzi ... in 2050 will AI write the proofs? Will AI write the novels (assuming people still read novels)? Will AI write the music? (Something like Facebook's algorithm will accurately suggest music you will like, or even write custom music you will like.) But this is not the place to discuss this. | |
| Jan 29, 2021 at 18:58 | comment | added | Andreas Blass | The increase of mathematical knowledge over time can be partly compensated (from the student's point of view) by better systematization and careful foundations for existing knowledge. 18th-century analysis and early 20th-century algebraic geometry relied heavily on intuition to avoid falling into the fallacies that imprecise methods facilitate; nowadays, the corresponding (correct) results can be proved without that hand-waving. | |
| Jan 29, 2021 at 18:53 | comment | added | Andreas Blass | @CarloBeenakker On the scale of centuries, one aspect of mathematical research has gotten easier: We no longer need to write our paper in Latin. | |
| Jan 29, 2021 at 18:51 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Jan 29, 2021 at 18:32 | comment | added | Francesco Polizzi | Well, unless there is some very big revolution (such as a pervasive use of AI in the proof verification) I guess that a PhD student will work in 20 or 30 years just as today: one starts by learning some subject, and then improves their understanding by "stretching tentacles" in nearby areas. In a first step, a complete understanding of all proofs is not always required, and gaps will be filled later. Of course, the role of supervisor will be an essential one during all the process. I also think that MO or is successors will be important. | |
| Jan 29, 2021 at 18:13 | comment | added | Alec Rhea | Your reasoning applies well to old subjects like number theory, where all the low-hanging fruit is picked and remaining morsels require either climbing extremely far out on a branch (specializing) or climbing extremely high up the tree (determined/brilliant). But there are always new, younger subjects emerging with plenty of ripe jewels hanging low — the one that comes immediately to mind for me is graph theory, but I’m sure there are even younger ones. | |
| Jan 29, 2021 at 18:12 | comment | added | Piyush Grover | Things will get hyper specialized. | |
| Jan 29, 2021 at 18:10 | comment | added | Sam Hopkins | Imo the biggest factor determining how easy/hard it will be to start doing math research in 2050 will not be the state of our collective math knowledge but the broader state of the world. | |
| Jan 29, 2021 at 18:09 | comment | added | Carlo Beenakker | the notion of writing a dissertation for a doctor's degree goes back more than two centuries; surely the changes over that time have been more substantial than those we can expect in the next decades; so why would you expect a disruptive change? | |
| Jan 29, 2021 at 18:05 | review | First posts | |||
| Jan 29, 2021 at 18:13 | |||||
| Jan 29, 2021 at 18:02 | history | asked | John117 | CC BY-SA 4.0 |