I do not know the song of Lou Reeds, but I can sure tell you that regular guys can sure make great mathematical discoveries. My students are just average guys. Some of them were even below average before doing their thesis. Since writing a thesis is a requirement before graduation, then they are forced to make one.

I am proud to say that my average students turn out excellent discoveries. Some of the papers are even presented internationally.

I am an average guy, but I would say that a lot of my papers have caught the interest of a lot of both excellent and average guys.

I do not know the song of Lou Reeds, but I can sure tell you that regular guys can sure make great mathematical discoveries. My students are just average guys. Some of them were even below average before doing their thesis. Since writing a thesis is a requirement before graduation, then they are forced to make one.

I am proud to say that my average students turn out excellent discoveries. Some of the papers are even presented internationally.

I am an average guy, but I would say that a lot of my papers have caught the interest of a lot of both excellent and average guys.

Fernando -

I don't think anyone can really be described as 'average.' People have different mixes of talents and occasional inspirations. I have noticed that it is always a good idea to listen to people, because you never know when someone will say something inspired, that may surprise you. I had also heard from an on-the-job course once, I think it was, that most innovations in a field (or at least the dramatic ones I suppose) are made by people who specialized in another subject matter. The idea being that breaking a paradigm is often hard. That is, it is difficult to "think outside of the box." Training and education can stifle creativity from the beginning. I once heard school described as "a conveyor belt to conformity." And I think there is a great deal of truth to that.

However, there is also the adage, made popular in Newton's letter to Hooke, that progress is made by "standing on the shoulders of giants." Yes, an occasional breakthrough is made by someone from 'outside' of a field, but I think that most progress still comes from building on past work.

At a statistical agency where I worked, providing Official Statistics, I saw very convoluted and unnecessarily complex methodologies in use, and it seemed invariably linked to one phenomenon: People who did not understand the basics cobbled a process together, trying to get what they wanted, when a basic understanding would have revealed a far more efficient, effective, and useful method. Then instead of trying to understand, they just kept adding on more modifications to the mess they already had, and then bragged about how complicated their work was.

So one ideally needs to combine knowledge with creativity. Knowledge can either be personal or a knowledge as to where information can be found or whom should be consulted.

At an annual statistics conference I attended on a number of occasions, I liked to hear papers from various areas of statistics that did not directly pertain to my areas. I found that sometimes people used different names to describe the same techniques, which had apparently been developed in parallel, like parallel evolution, whereas more 'cross fertilization' of ideas may have been helpful.

So ideas do occur from both systematic and haphazard sources, and I think many people can have their inspired moments - which naturally may then need a great deal of hard work to develop.

If some researchers just think of others as "average," and do not listen to others and discuss ideas with everyone seriously, I think a great deal could be missed. Cooperation can be much more useful and progressive than competition.

Cheers -

Jim

I don't believe that we can call some body "average". One's mathematical aptitudes and skills are average only because he get minimal or insignificant exposure to the world of mathematics. One can gain or regain the necessary  mathematical foundation and hence the knowledge in advanced mathematics through hard work.  So One who has intense desire and will to learn and practice mathematics can contribute to the researches in Mathematics.