My simple question is why are they interesting papers then if students are turned away from them? Some concepts require more understanding of the systems they are built upon. This is also where a big part of the mentor-student relationship come into play. A teacher/mentor can make content normally not accessible to a student available by translating the work of experts into something for the students. Some notations and symbolizations just lend themselves to how experts and researchers use them because:

1) Most researchers adopt that type of notation because somebody introduced it at some point and it seemed to make things a lot easier to write with it (which is pretty democratic...). Mathematical fields evolve all the time, especially how they are written. This can also relate to how the mathematics may be used.

2) There are plenty of resources out there on the WWW that can do things like this. Wolfram Alpha is a pretty good example. Not perfectly though (which is what most should expect).

3) Some notations do not simplify into "simpler ones". Some require further understanding to comprehend based on their definitions.

Overall I do not see how the question title you gave matches with the description you posed. Many notations used by mathematicians are pretty democratic. It is an interesting question, but not something I'd think is pragmatic as good researchers and students will "do the work" to understand what is going on.

Thank you for your considered and experienced views on my question.. and I do appreciate it. I hope the following would make the intent of my question clearer..

and I welcome any practical suggestions on the same.,

I have used Democratization in the sense I quote.. "It may be the transition from an authoritarian regime to a full democracy, a transition from an authoritarian political system to a semi-democracy or transition from a semi-authoritarian political system to a democratic political system..".unquote from wikipedia. So here the question implies making the power of Mathematics more accessible to the audience and the description enlarges on this idea.

1. Most researchers adopt that type of notation because somebody introduced it at some point and it seemed to make things a lot easier to write with it.. Precisely to whom the author or the reader..?

2. I think your answer amply conveys my intention eg ..."(which is what most should expect)". but as scientists we perhaps should not be satisfied with any given situation because there is always scope for improvement.. It is from this dissatisfaction that we may expect progress and improvments.

3. "Some notations do not simplify into "simpler ones".. It is not so much about

notation as it is about easy comprehension by many including novices so that

the circle of knowledge grows.

For example consider AI and Expert Systems and the explosion of knowledge including the trending Big Data Analytics ( where I am sure Mathematics would play a vital role)..there is always the danger that future generations

will not be able to get under the hood for possibly many rectifications

that may be necessary..

"good researchers and students will "do the work" ' I agree with you

but consider how much further they could go if they are helped with technology.

If we trace the development of computer programming ... we have travelled a long way from assembly language to easier higher human like languages I believe

precisely because there was someone who found there is no need to toil

on mundane skill type tasks , but human thought could be more productive

when applied in easy human language like programs.

I noticed that I have not answered a pertinent point which is important

"My simple question is why are they interesting papers then if students are turned away from them?"

I am not talking here of pure Mathematics but situations where they are used.

more as in Applied Mathematics. For example in Power systems it may be of interest to

find the location of a fault ..( even an incipient fault before it occurs). I am sure this would involve a good amount of probability concepts .. and tools developed by many brilliant mathematicians.

The point is from Power System engineer's perspective predictive fault analysis

is of definite interest. but maybe the mathematics needs some elaboration ..

. Here is some history which shows that there is space for divergent opinions..

from http://www-gap.dcs.st-and.ac.uk/history/ .

Lagrange published two volumes of his calculus lectures. In 1797 he published the first theory of functions of a real variable with Théorie des fonctions analytiques although he failed to give enough attention to matters of convergence. He states that the aim of the work is to give:-

... the principles of the differential calculus, freed from all consideration of the infinitely small or vanishing quantities, of limits or fluxions, and reduced to the algebraic analysis of finite quantities.

Also he states:-

The ordinary operations of algebra suffice to resolve problems in the theory of curves.

Not everyone found Lagrange's approach to the calculus the best however, for example de Prony wrote in 1835:-

Lagrange's foundations of the calculus is assuredly a very interesting part of what one might call purely philosophical study: but when it is a case of making transcendental analysis an instrument of exploration for questions presented by astronomy, marine engineering, geodesy, and the different branches of science of the engineer, the consideration of the infinitely small leads to the aim in a manner which is more felicitous, more prompt, and more immediately adapted to the nature of the questions, and that is why the Leibnizian method has, in general, prevailed in French schools.

and the pdf from staff.ustc.edu.cn/~zwp/.../A%20short%20history%20of%20probability.p..

is also of interest ,

Thank you for you response.

An excellent and very inspiring example of what the question means and implies is contained in the following link

http://crpit.com/abstracts/CRPITV20McAndrew.html

titled Teaching image processing using minimal mathematics

McAndrew, A.

It also contains results of students response over 5 years to such an approach .