- mathbabe is pretty well summarized by its byline "exploring and venting about quantitative issues." Cathy O'Neil has written a lot about how math and big data can be used to perpetuate social inequality.
- The Liberated Mathematician also has a great byline: "power^people." In addition to blogging about social issues in math academia, Piper Harron wrote an amazing dissertation which explains abstract mathematics in a way that's accessible to laypeople.
- The Mathematical Yawp is the blog of Francis Su, who is a wonderful lecturer and has written inspiring posts about how to be a good math teacher (see e.g. this).
- Living Proof made me cry. It's actually an ebook (though there is an associated blog) full of stories of professional mathematicians sharing their experiences with setbacks, failures, imposter syndrome, and so on.
Other people I think are cool:
- Eugenia Chang writes on her website that she wants to rid the world of "math phobia." She makes math YouTube videos and has written several layperson-accessible books about math.
- Vi Hart makes fun math YouTube videos, which I absolutely loved when I first discovered them in early high school.
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