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The New Yorker. Probably the leading general interest magazine in the English-speaking world; runs occasional pieces on scientific developments and research, both by scientists and by its excellent staff writers
Science. Another leading science journal. Like Nature, it offers some articles for non-specialists.
Science News. Has mostly brief pieces, written mainly by staff writers, on breakthroughs and trends
Scientific American. Probably the premier science magazine in English; articles by both science journalists and leading researchers