Note: Running commentary regarding whether some math terms are too rigorous for practical users of math elicited this response:
The reason that India might overtake the US in technology is that they teach strict adherence to the language of math, as they also do with the languages of philosophy and technology.
There are two fields where one might hear the following, "Next we instantiate an new instance of the entity." The fields, philosophy and technology. Search for the definitions of the supposed esoteric words of philosophy and you will likely find the companion definition from an online technical dictionary. The terms in their contexts have exact meanings, there is no room for interpretations from the "practical user" of philosophy, nor the "practical user" of technology. Fail to correctly understand those terms and watch your job get shipped offshore while holding your pink slip.
Also, try discovery-learning your own set of arithmetic order of operations and see how MS Excel processes them. The rules and esoteric language of math have exact meanings, they are beyond debate. Tom Loveless of the Brookings Institute edited an enlightening book, The Great Curriculum Debate, where a contributor lamented the lack of exactness in US math books. The contributor, Richard Askey, noted the incorrect use of the term exponential in a discussion of population growth, the correct term being polynomial. A researcher who casually substitutes one word for another will have results that are unpredictable at best. Certainly the "practical math user" is happy with the use of exponential, but it is absolutely wrong in the context of the discussion. The author of the math book in question was fine with his lazy use of the term exponential and refused to make a change.
A quick note on logic: The strict rules of logic are embedded in computer software. The computer does not care what one's intent was when substituting an and for an or in a logic gate. "Practical users" of internet search engines will find very odd results if they use these terms interchangeably. Sure we can create a gentlemen's agreement that such rigor is too demanding, but we will fall on our faces as we present our results for review.
Of course, law and legal documents rely on exact definitions. Maybe this is the next area of offshoring to the rising giants in the East.
The division of math knowledge into that which is used by "mathematicians" and that which is used by "practical users of math" is a error arising from the Progressive Movement. No wonder education in the US has falling into such a malaise.