I try to learn and understand as much facts as I can. Of course many people would like to benefit from opposite, that is digging into certain branch as deep as they can. I try to do opposite, which I see as my main advantage, as opposite to professional mathematicians. This is because they have its own careers, and has his professional criteria to fulfill ( writing articles in journals, gaining citation points etc). As amateur I am not obliged to do so, and this is great freedom. If You want to be creative, You may try to dig here and there, and probably You will be lucky to find certain problems which are not penetrated, or You may find just something interesting enough ( for example Your own point of view on well known area, maybe You find surprising connection even if it is well known it is funny to discover it once more etc) to wrote it somewhere, maybe on blog.

Reassuming: I read as much as I can, I learn as much as I can, I ask as much as I can.

As regards to low level entry (You need of course to be genius to discover it, but nothing more;-) example is Feigenbaum famous discovery about chaos etc. http://mathworld.wolfram.com/FeigenbaumConstant.html . As far as I know, he uses only programmable calculator to discover it, He was just inquisitive, nothing more, nothing less.

I try to learn and understand as much facts as I can. Of course many people would like to benefit from opposite, that is digging into certain branch as deep as they can. I try to do opposite, which I see as my main advantage, as opposite to professional mathematicians. This is because they have its own careers, and has his professional criteria to fulfill ( writing articles in journals, gaining citation points etc). As amateur I am not obliged to do so, and this is great freedom. If You want to be creative, You may try to dig here and there, and probably You will be lucky to find certain problems which are not penetrated, or You may find just something interesting enough ( for example Your own point of view on well known area, maybe You find surprising connection even if it is well known it is funny to discover it once more etc) to wrote it somewhere, maybe on blog.

Reassuming: I read as much as I can, I learn as much as I can, I ask as much as I can.

As regards to low level entry (You need of course to be genius to discover it, but nothing more;-) is Feigenbaum famous discovery about chaos etc. http://mathworld.wolfram.com/FeigenbaumConstant.html . As far as I know, he uses only programmable calculator to discover it, He was just inquisitive, nothing more, nothing less.