Peter Sarnak is a well known mathematician who is also a permanent member of the Institute for Advanced Study. In the ‘Final Perspectives’ of The Princeton Companion to Mathematics, Sarnak makes some useful comments on the nature of good scholarship. One of the points he discusses is the difference between elementary versus easy. Whereas easy results are obviously not valued because of their lack of novelty, using elementary tools or arguments to present interesting ideas should not take away anything from the ideas. It is desirable to present ideas or proofs (in the case of mathematics) in an efficient, elegant and simple manner as possible. In fact in mathematics, ‘proofs from the book’ are exactly those proofs which appear the most natural and elegant for the particular theorem. Sarnak particularly stresses the point that using fancy notation does not imply deep work:
There is a tendency among some young mathematicians to think that using fancy and sophisticated language means that what they are doing is deep. Nevertheless, modern tools are powerful when they are understood properly and when they are combined with new ideas. Those working in certain fields (number theory, for example) who do not put in the time and substantial effort needed to learn these tools are putting themselves at a great disadvantage. Not to learn the tools is like trying to demolish a building with just a chisel. Even if you are very adept at using the chisel, somebody with a bulldozer will have a huge advantage and will not need to be nearly as skilful as you.
This point is further highlighted by great papers. Authors of great papers worked extra hard to simplify the arguments and make the paper more readable and presentable.
