Is the number of "breakthroughs" in mathematics decreasing, as it is claimed to be in other sciences?


Background for the question:


1. Park, M., Leahey, E. & Funk, R.J. Papers and patents are becoming less disruptive over time. Nature 613, 138–144 (2023). <https://doi.org/10.1038/s41586-022-05543-x>
2. [What Happened to All of Science’s Big Breakthroughs?](https://www.nytimes.com/2023/01/17/science/science-breakthroughs-disruption.html)



> 
> A new study finds a steady drop since 1945 in disruptive feats as a share of the world’s booming enterprise in scientific and technological advancement.
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Has a similar analysis been conducted for the field of mathematics (or, say, pure mathematics)? If yes, how do the findings compare?



Is the number of "breakthroughs" in mathematics decreasing, as it is claimed to be in other sciences?
**Q:** *Is the number of "breakthroughs" in mathematics decreasing?*


To get some quantitative feel for the question I considered the [Timeline of mathematics](https://en.wikipedia.org/wiki/Timeline_of_mathematics) on Wikipedia. Not all entries are "breakthroughs", but most could be considered as such. Here is a plot of the cumulative number of entries since 1900. I do notice a kink in the slope around 1965, so based on this evidence on might conclude that, indeed, the rate of discovery has decreased somewhat. Or perhaps the 1960's was just an unusually productive decade.


![](https://i.stack.imgur.com/bCWq2.png)
Relative to the total output the discovery rate is obviously much smaller now than in the past.


