Mandarin is the standard accent spoken on national news stations and being taught in schools. It's the official accent. The different "languages" people speak in different provinces are dialects. The dialect in Beijing is closest to Mandarin as Chinese government created Mandarin based on this dialect.
I don't know about other countries in Asia but India has a similar issue with its linguistic variations. But Indians think of their dialects as languages because some of them involve different writing (spelling) systems, if my memory serves me right. Both countries have a long history with wars, invasions & conquers of different ethnic groups and cultures, and hence different dialects (or languages). But Indian used to be the colony of the Queen so there are a lot of more Indians speaking English than Chinese. And I believe the same with SG. As for China, although people are catching up, once you are out of modern cities like Beijing, Shanghai, HK, etc., the majority of citizens don't speak English. So a really good interpreter is a necessity.
You run into that problem in Vietnam too. The South and the North don't understand each other.
To succeed in doing business with Chinese, not only do you have to learn the language, but also the culture, norms and etiquette (which is more important than the language). But I do think you are humorously correct when you said we just need to know math and science well. Everyone knows alpha, beta, what's a circle and what makes the Earth rotate.
Porche, ppl in SG speak Chinese and English, right?
Yes but when you go to China, the DIFFERENCE in Mandarin across China is Starling. There are just too many provinces. Their language style is not the type that you learn.
The worst part is what seems for example calling a girl "young lady" in madarin seems acceptable in Singapore and some provinces in China, but can be offensive in Shanghai when the term is taken as "prositute"
When doing business and you're not sure of the language either a) get some who can interpret the langauge or don't do the deal if the other party can't understand the language you're speaking in.
Certainly learning a language in 10 days is rubbish to me. I'll probably land up offending the other party and getting no deal done.