The ever-winning lottery ticket: Mathematicians solve a dusty mystery

question 2: how does science communication about math works?

the article is clearly a press release from the university were the result was found. it has a very catchy title, while the linked research is more dry. you can find many articles around "popularizing" this press release, yet the understanding of it seems limited, in particular:

* no explanation on how the infinite lottery works is found * if one reads the research article, the result is stated with respect to a specific set theoretic assumption and so it is not really (as it happens for some mathematical facts) an "absolute" result. one should say, assuming ramsey hypothesis, one can prove that no infinite lottery ticket exist (while the axiom of choice would imply that they do exits...)

question 1: how does this infinite lottery works?

not clear from this piece nor from the original article, which I was able to find on arxiv, and where the infinite lottery is never mentioned (the results is stated in terms of moern set theory):

https://arxiv.org/pdf/1904.05824.pdf