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However, I'm certainly not a domain expert in most of these topics, which makes reading these papers difficult. Is there somewhere where I can read summaries about the newest developments in some topic (e.g. math, cosmology, etc.) in layman's terms?
The common advice is to read the abstract and then conclusion, and only the method if you want to dig deeper.
Try to find a well-cited “meta analysis” or “literature review” in the field you’re looking into. These will common on the current state of the research field, and reference influential papers. They’re a great starting point.
I find myself needing to do something analogous to “suspending disbelief” when reading about a new topic. There is usually a lot of terminology I don’t understand, but I put up with it for a while. Eventually it makes sense. Other times, I need to look up the actual definitions.
Following Twitter is good for discovering things you didn't know to search for.
I also think magazines are good to get for general reading, for example: IEEE Spectrum, Scientific American, Nature, Physics Today, etc.
Google Scholar is good for finding papers on topics you want to search for. Following Twitter is good for discovering things you didn't know to search for. I also think magazines are good to get for general reading, for example: IEEE Spectrum, Scientific American, Nature, Physics Today, etc.
https://www.quantamagazine.org/
Brilliant popular science writing about contemporary discoveries in math, computer science, and the physical sciences.
Also, see if you can find good blogs by researchers in the topics you're interested in. There are some good ones out there (as an ecologist, I like "Ecology for the Masses"). Their spectrum will be a lot narrower than a magazine - constrained by the authors' expertise and interests - but they can be more "bleeding edge".