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This was a collection of shorts by a single author. Every story had math as a key component of the plotline. In one story the world is saved by an alien's love of moonshine.
Throughout every story math was not only incorporated but the author gave explanations and background to why he wrote the stories. He was both hilarious and clever.
I cannot identify the math themed collection, but the story you describe certainly sounds like Joe Haldeman's All The Universe in a Mason Jar.
For one thing, it is about an alien who can only consume alcohol.
It ends
After a rather grim period of transition, the denizens of Earth settled down to concentrating on being good, trying to reach Class 3, the magic level.
It would take surprisingly few generations. Because humankind had a constant reminder of the heaven on Earth that awaited them, as ship after ship drifted down from the sky to settle by a still outside a little farm near New Homestead, Florida: for several races, the gourmet center of Sirius Sector.
There is some mathematical content in the story, when the retired-math-professor hero is trying to communicate with the alien.
This has been asked before (Looking for a collection of short stories that involved math as underlying theme in every story) but has no accepted answer. (The asker never returned to the site.)
If you are not the person who asked about this before, it means that this anthology almost certainly must exist, and just not be listed in isfdb. That database lists only "Infinite Dreams ", "Flying Saucers", "UFOs: The Greatest Stories", and "Subtropical Speculations". None of these are math-themed.
I think this has to be Infinite Dreams by Joe Haldeman.
The cover is from the era you read the book. It's been reprinted with several different covers since.
It isn't a maths themed anthology, but many of the stories do deal with maths and it is the only anthology of Haldeman's stories that includes All The Universe in a Mason Jar.
In the story All The Universe in a Mason Jar the human protagonist is a retired maths professor and it does involve mathematical jargon when communicating with the alien. From a quick skim.
In the first story Counterpoint one of the characters, Roger Wellings, is a maths genius.
In A Mind of His Own Leonard Shays is a maths PhD.
In 26 Days On Earth Jonathon Wu studies maths.
In Armaja Das John Zold is brilliant at maths.
I think that it could be Asimov's Mysteries. Published in 1968, this is a collection of 14 short stories that happen to be resolved with math, physic and others. Asimov put some explanations in later publications.
