A case from this year is that of Aubrey de Grey.
Aubrey de Grey, a biologist known for his claims that people alive today will live to the age of 1,000, posted a paper to the scientific preprint site arxiv.org with the title “The Chromatic Number of the Plane Is at Least 5.” In it, he describes the construction of a unit-distance graph that can’t be colored with only four colors. The finding represents the first major advance in solving the problem since shortly after it was introduced. “I got extraordinarily lucky,” de Grey said. “It’s not every day that somebody comes up with the solution to a 60-year-old problem.”
De Grey appears to be an unlikely mathematical trailblazer. He is the co-founder and chief science officer of an organization that aims to develop technologies for “reversing the negative effects of aging.”
https://www.quantamagazine.org/decades-old-graph-problem-yields-to-amateur-mathematician-20180417/
The excellent Quanta Magazine likes to report about such exciting happenings in the world of science. They have covered those mentioned so far except Kurt Heegner:
Then there other cases of professionals who, like Yitang Zhang, count as outsiders:
As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of geometry, probability theory and statistics that had eluded top experts for decades.
Known as the Gaussian correlation inequality (GCI), the conjecture originated in the 1950s, was posed in its most elegant form in 1972 and has held mathematicians in its thrall ever since.
https://www.quantamagazine.org/statistician-proves-gaussian-correlation-inequality-20170328/
