Math

A highly entertaining book on cellular automata: http://williampoundstone.net/Recursive.html

A book I've enjoyed on Riemann surfaces: https://bookstore.ams.org/gsm-5/

Do the mathematical outputs of the human mind coincide with those of the ideal computer? An interesting Penrose venture: https://www.pdcnet.org/collection/authorizedshow?id=jphil_2018_0115_0007_0337_0360&pdfname=jphil_2018_0115_0007_0337_0360.pdf&file_type=pdf&googlescholar=true 

A singularity in the Euler equations: https://www.quantamagazine.org/famous-fluid-equations-spring-a-leak-20191218

A disproof of the strong cosmic censorship conjecture: https://www.quantamagazine.org/mathematicians-disprove-conjecture-made-to-save-black-holes-20180517/

Climate

See the current forecasts: https://www.tropicaltidbits.com/

Geostrophic adjustment via a variational problem: https://journals.ametsoc.org/view/journals/atsc/49/13/1520-0469_1992_049_1144_mapoga_2_0_co_2.xml?tab_body=pdf

Climate Change and the Integrity of Science: https://www.researchgate.net/publication/44578592_Climate_Change_and_the_Integrity_of_Science

What is coupled data assimilation? https://www.ecmwf.int/en/newsletter/160/meteorology/coupled-ocean-atmosphere-data-assimilation-ecmwf#:~:text=What%20is%20coupled%20data%20assimilation,is%20used%20to%20initialise%20forecasts.