Most Math Problems Do Not Have a Unique Right Answer

The title is both right and wrong. You are actually comparing school or college math with math applied in real world. School or college math works with few variables, for instance, and we consider most others remaining constant. Rarely have I seen school or college level students working with, say, derivatives of more than three variables. School or college math is an exercise to establish the rule, the rigour and in most cases to create an appreciation of what math can achieve.

In real world, variables are plenty. If you take a handful to solve a problem considering other important ones to be constants, you will end up with one set of answers as against others if you had taken a different set of variables. Real world applied math is contextual. You remove context from the problem and real world math looks like school or college math. As demonstrated by the engine-armour-plate example, without the context of the airplanes returning after taking hits, the mathematicians would probably have gone with a statistical answer and would have been proven wrong!

However, I do agree that most math problems may not have unique right answer. Of course, we are not talking of,say, square-root-of-two having two different answers. However, take an instance where the problem is:"Find a number that is a sum of two infinitesomely large numbers one ocurring at an infinitely large interval of time from the other. Does it essentially fall on the numberline?" Well the first reaction to this question is: well, yes. Because if we are sure to find those two numbers then we are more likely to find their sum which has to fall on the numberline. Now, a more discerning reader might pause and ask: can you define infinitely large number and infinitely large interval. Hence, a question like this may not have a unique right answer. If you allow philosophers in, you will definitely not have a unique answer :)

Coming to a more basic argument: With math we are striving to arrive at a single agreeable solution. Whether it is statistics or calculus, we are interested in modelling the world to arrive at a set of recognizable pattern or a set of patterns. We apply the templates we learnt in school and college. For instance in arithmetic, numerals -- which are nothing but symbols -- help us reduce our problems into an expression which we can solve. The operations allow us to take these symbols through a set of processes that helps us model the problem.

But thanks to the author, what is clear is that applied math is contextual and answer may vary with the change in context. While school math is merely an exercise in familairising ourselves with a template.