I came across this article in scientific american article with the title "Mathematicians Measure Infinities, and Find They're Equal". I am quite quite baffled by this. Can someone give me some implications that this new finding might have and how it affect might affect the mathematical community ??
Here's very rough summary of the context of that article:
It's been known for a long time that there are different infinities. Two particular infinities technically known to mathematicians in this research area as $\frak p$ and $\frak t$ were long thought to be (consistently) different, but no one could prove that.
It turns out that they are equal.
The article goes on to say
[Malliaris and Shelah]'s work has ramifications far beyond the specific question of how those two infinities are related. It opens an unexpected link between the sizes of infinite sets and a parallel effort to map the complexity of mathematical theories.
which begins to answer your question about
implications that this new finding might have and how it affect might affect the mathematical community.
I doubt that it will affect most of everyday advanced mathematics much, but may be very significant in particular areas of research.