Timeline for Is the number of "breakthroughs" in mathematics decreasing, as it is claimed to be in other sciences?
Current License: CC BY-SA 4.0
37 events
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| Jan 25, 2023 at 14:11 | comment | added | Alexandre Eremenko | @Federico Poloni: I looked at the paper: on my point of view, this is a complete nonsense what they do. And certainly the question has nothing to do with "research level mathematics". | |
| Jan 25, 2023 at 13:47 | comment | added | Federico Poloni | @AlexandreEremenko The CD index is defined in the paper linked in the OP. The paper contains a quantitative methodology to 'define' breakthroughs; please do not jump to conclusions and vote to close before having at least skimmed that paper, because it answers some of your questions. | |
| Jan 24, 2023 at 10:52 | answer | added | Alessandro Della Corte | timeline score: 9 | |
| Jan 24, 2023 at 10:18 | answer | added | user43263 | timeline score: 3 | |
| Jan 23, 2023 at 19:55 | vote | accept | xeng | ||
| Jan 23, 2023 at 14:44 | comment | added | Alexandre Eremenko | @Timothy Chow: I don't know what CD index is, and I doubt that there exists any formal criterion which permits you to detect breakthroughs. | |
| Jan 23, 2023 at 13:35 | comment | added | Timothy Chow | @AlexandreEremenko But in principle it should be a simple matter to compute the CD index for the mathematical literature, to see if its behavior is the same as for other fields. I'd expect it to be similar, but the only way to be sure is to do the actual computation. | |
| Jan 23, 2023 at 10:45 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Jan 23, 2023 at 10:43 | history | edited | YCor | CC BY-SA 4.0 |
copied question to body
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| Jan 23, 2023 at 10:34 | history | edited | xeng | CC BY-SA 4.0 |
fixed title (the question does not concern the proportion but the absolute number)
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| Jan 23, 2023 at 2:03 | comment | added | Alexandre Eremenko | @Matt F.: I already expressed my attitude to this by voting to close. This activity is meaningless on my point of view. Modern mathematics is truly enormous; there is no single person who is able to understand and compare various areas of it. | |
| Jan 23, 2023 at 1:27 | comment | added | user44143 | @AlexandreEremenko, I’d enjoy seeing some examples on your list; we might end up agreeing that they’re radical breakthroughs but differing on whether to call them disruptive. | |
| Jan 23, 2023 at 0:44 | comment | added | Alexandre Eremenko | @Matt F. On my opinion, the list of radical breakthroughs in mathematics since 1945 is VERY much longer than you suggest. | |
| Jan 22, 2023 at 21:18 | comment | added | polfosol | Also worth mentioning Peter Higgs' interview which said he would have been considered an unproductive academic by today's standards and never could have dreamed of finding an academic job in today's universities. | |
| Jan 22, 2023 at 18:34 | comment | added | Timothy Chow | @AlexandreEremenko I don't think it's opinion-based, if we interpret the question as, "What happens if we apply the methodology of Park et al. to mathematics?" Whether their methodology is a good one might be opinion-based, but that's not the question being asked. | |
| Jan 22, 2023 at 17:56 | comment | added | user44143 | What would be good examples of the “most disruptive” mathematics since 1945? I’d suggest John Milnor’s exotic spheres (1956) and Paul Cohen’s forcing in set theory (1963) as clear examples; I’d suggest homotopy type theory (2012-13), Clausen and Scholze’s condensed mathematics (2019), and AlphaZero’s faster matrix multiplications (2022) as recent potential examples. But mathematics is mostly accretive: by comparison with other fields, the number of candidates for disruptive developments is small. | |
| Jan 22, 2023 at 17:28 | review | Close votes | |||
| Jan 29, 2023 at 3:07 | |||||
| Jan 22, 2023 at 17:14 | comment | added | Alexandre Eremenko | I vote to close as "opinion based": who and how determines what is a breakthrough and what is not? My personal knowledge supports the opinion that the number of breakthroughs per time in mathematics increases. | |
| Jan 22, 2023 at 16:32 | history | became hot network question | |||
| Jan 22, 2023 at 14:43 | comment | added | Vladimir Dotsenko | @Carl-FredrikNybergBrodda or perhaps one may simply argue that specialisation created a new kind of breakthroughs, the specialised ones. Also, I can easily give speculative examples of what kind of breakthroughs in enumerative combinatorics can seriously impact studying monoidal categories (think Drinfeld associators), so you should be careful about sweeping statements like that ;-) | |
| Jan 22, 2023 at 14:31 | comment | added | Wlod AA | @DavidRoberts, several of my friends have the principle of publishing only results that bring significant progress, they were above publishing just to publish. | |
| Jan 22, 2023 at 14:29 | comment | added | Gil Kalai | A related observation regarding "Angry bird" is presented here gilkalai.wordpress.com/2015/04/06/angry-birds-update | |
| Jan 22, 2023 at 13:53 | answer | added | Joseph O'Rourke | timeline score: 13 | |
| Jan 22, 2023 at 13:43 | history | edited | Steven Landsburg | CC BY-SA 4.0 |
edited title
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| Jan 22, 2023 at 13:16 | comment | added | Timothy Chow | Scott Alexander has pointed out that one needs to be careful not to draw incorrect conclusions from this type of data. In particular, depending on how you define "breakthrough," a decrease in the number of breakthroughs doesn't necessarily mean that "progress is slowing down" (again, depending on what you mean by that). | |
| Jan 22, 2023 at 12:42 | comment | added | Carl-Fredrik Nyberg Brodda | One major issue to keep in mind is the phrasing of "the field of mathematics". A breakthrough in enumerative combinatorics, no matter how impactful, will likely not impact the research on anyone working on monoidal categories (say). This degree specialisation is more of a modern phenomenon. "Breakthroughs in mathematics", at least when counting their impact on the subject as a whole, is about as meaningful as "breakthroughs in studying living things". | |
| Jan 22, 2023 at 12:38 | comment | added | user44143 | The number of breakthroughs is going up; it’s the ratio of breakthroughs to scientific work that’s going down. Will you edit the question to state the comparison case more accurately? This may require writing out the main question in the text of the post, and not just in the title. | |
| Jan 22, 2023 at 11:54 | answer | added | Carlo Beenakker | timeline score: 19 | |
| Jan 22, 2023 at 11:37 | comment | added | Brendan McKay | It is important to note that the decline in "disruptiveness" (their term for breakthrough-ness) in research found by Park et al refers to the average publication. When it comes to the absolute number of breakthrough papers they report consistency over time. So it isn't that there is less breakthrough research, but rather that there is more non-breakthrough research. | |
| Jan 22, 2023 at 11:34 | comment | added | Michael Greinecker | Similar patters show up in corporate innovations, for further background: https://web.stanford.edu/~chadj/IdeaPF.pdf | |
| Jan 22, 2023 at 10:42 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
bibliographic details, top-level tag
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| Jan 22, 2023 at 10:40 | comment | added | David Roberts♦ | I wonder if the pressure to publish means that people now will publish things that in time past wouldn't have been considered worth publishing. I know one older mathematician (but not retirement age) who only wanted to work on big, meaningful projects, and not publish incremental work. He saw this as a massive cultural failure in mathematics. Sadly, it ended his career—he was more-or-less pushed to retire early—but he was principled to the end on this matter. | |
| Jan 22, 2023 at 10:27 | answer | added | coudy | timeline score: 0 | |
| Jan 22, 2023 at 9:11 | comment | added | Federico Poloni | @WlodAA The methodology of that paper is based on citations among papers, so it seems difficult to adapt it to art. | |
| Jan 22, 2023 at 9:01 | comment | added | Wlod AA | xeng, an interesting question. I hope that you will get some reasonable answers. Here, in addition to science and inventions, one may also include art. | |
| S Jan 22, 2023 at 8:25 | review | First questions | |||
| Jan 22, 2023 at 9:16 | |||||
| S Jan 22, 2023 at 8:25 | history | asked | xeng | CC BY-SA 4.0 |