Peter,
I'm pretty much with you all the way. Although, when arguing with atheists (which I've never had the pleasure of doing until I found these fora :-) ), I actually had a bit of a gestalt/epiphany/etc... I was basically in the realm that those particular atheists were almost professing a "belief in science... big bangs and whatnot" and it finally occurred to me that the true question that us poor carbon based ignorant life forms should be concerned with as far as math and science is concerned (since you can't very well reproduce the "creation" and none of us were here to witness it) is something like this...

"What is/are the probabilty/odds that life on earth in all it's forms evolved from random chaos"?

Before a knee jerk response, really think about it. Pretty damned miniscule odds/probability is my hypothesis... I don't pretend to have any of the "answers"... never have, but at least, this agnostic has the questions...

One more thing to consider as you venture in this realm, "since it's improbable for any human being to determine the existence/nonexistence of a creator/supreme being... what if the Jews or Muslims or the Christians (representing belief systems that are at least 8,000/2000/1400 years old) are actually right... Improbable maybe, but what if?

The short answer to your question about the burden of "proof"... it's individual and who the f*(k cares what you or I think? AND the burden of proof only applies to the person/thing/entity that desires it... :-)