shmoe said:What I would call "experimental number theory' happens all the time, and is in fact a large driving force behind many conjectures. Packages like pari/gp weren't developed by number theorists to take up disk space. What does the phrase "experimental number theory" mean to you?
Just got back, from finishing up my MS and moving. I pm Kurk to see if this thread was dleted. He sent me what I interpreted to be a turse PM for criticizing the establishment. So that sort of feeds in to your question about experimental number theory.
I will probably have to open a separate thread in the general discussion area about the culture in mathematics. There is much ot be discussed there. Having been around the community for some amount of time I too have had my share of dealing with folks who think that .999... >< 1. What can you do. But not everyone who has a unique approach is of that vein. Of course it is rare to meet the exception and I do not claim to be the one who can reinvent number theory or that it even needs to be reinvented. But I do chaff, and begin gnawing at the bit when I see a mathematician that is effectively a social retard making others feel bad because they don't get it. Those types of things lead to Bastille Day. Being smart is not enough, the mindless masses pay your salary through taxes. Either get your attitude in check with reality or take your chalk and go home! That is a rebuke I am willing to accept myself. I spent many years after my BS puffed up by the 'mentoring' of various elements in the math community.
So yes experimentation. I mean free and creative thinking, which De Morgan felt was essential to all mathematical progress. That does not remove the precedent of established mathematical truths. However techniques are still growing. We all should aspire to do something where we can be original, in my opinion. If math isn't that for someone, then maybe they would be happier somewhere else. At any rate, we need library books. Some folks function as wetware, library collections of facts about math and science. I have no problem with that but a jerk is a jerk is a jerk. A saying I really like is by Plutarch , "Be kind, everyone you meet is fighting a hard battle."
I came back because I am working out a partial proof of the Goldbach Conjecture, at least I have a solid idea. I will post the key question in the number theory thread.