How did someone receive an arts degree and then become a scientist? Take de Broglie 


  De Broglie had intended a career in humanities, and received his first degree in history. Afterwards, though, he turned his attention toward mathematics and physics and received a degree in physics


And Edward Witten,a very famous theoretical physicist


  Witten attended the Park School of Baltimore (class of '68), and received his Bachelor of Arts with a major in history and minor in linguistics from Brandeis University in 1971. He published articles in The New Republic and The Nation. In 1968 Witten published an article in The Nation arguing that the New Left had no strategy.[citation needed] He worked briefly for George McGovern's presidential campaign. McGovern lost the 1972 election in a landslide to Richard Nixon.
  Witten attended the University of Wisconsin–Madison for one semester as an economics graduate student before dropping out.[citation needed] He returned to academia, enrolling in applied mathematics at Princeton University[citation needed] then shifting departments and receiving a Ph.D. in physics in 1976 under David Gross, the 2004 Nobel laureate in Physics. 


In china,student major in history or literature won't study mathematics at all,and almost everyone think it's impossible for someone receive BA then turn to science,so how did someone receive BA and then become a scientist?
The thing to remember is that an individual is more than their degree classification.

Every person has their own interests, hobbies, skills, and personal projects.  While a BA in one field may be an indicator of a person's interests, it does not mean that the person in question knows nothing outside of what was required for that degree.

For example, it is very possible that a person receiving a BA in philosophy may:


enjoy a STEM discipline, leading them to take classes in it for their own enjoyment
enjoy a STEM discipline or topic and choose to learn about it on their own
end up in a job that requires that they learn skills that are applicable to a different discipline
apply to graduate school for a STEM discipline and be willing and able to invest the time to catching up on the material
be naturally gifted at whatever the STEM discipline is


Most likely, in cases where people change disciplines, it's a combination of several of the above.

Anecdotally, I got a BFA, but continued taking calculus as a free elective in my undergraduate degree.  I had to learn programming for work after graduating and ended up in graduate school for Computer Science.  I entered graduate school with the knowledge that I would need to work at least twice as hard to catch up on the material and just went ahead and worked at it.

It may be completely different in other countries, but even in those countries, I can't imagine that anyone is completely limited to only knowing things that are required for their degree.  There are a lot of situations that can force you to learn new skills, and that's without taking into account that some people have hobbies that are cross-discipline.

Another way of looking at it is: would you be surprised if a famous physicist played the violin well enough to perform?  There's no logical reason why someone who plays the violin shouldn't be able to do the same the other way around.  Both require a progressive learning of skills and a large time investment, unless you're naturally gifted.