Yes, negatives can be proven. In fact, ten of the fifteen valid forms of the classical syllogism have negative conclusions. For example, premises “All A are B” and “No B are C” prove the universal negative, “No A are C”; and premises “Some A are not B” and “All C are B” prove the particular negative, “Some A are not C.” Likewise, in propositional logic, the premises “If A then B” and “It is not the case the B” prove the negative proposition, “It is not the case that A.” What holds in each case it that you can’t prove a negative conclusion without having a negative premise. And the same is the case with the scissors example. That is, from “There are stamps [paper clips, etc., etc.] in the drawer in cannot be concluded that “There are no scissors in the drawer” without the negative understanding that “There is no other place in the drawer where the scissors could be.”

Great comments and I have nothing to add that has not already been said. TY for posting and providing an enjoyable morning with coffee read.

I will say it is more likely just an individual thing. My Dad was raised Catholic, stopped 'believing' at an early age and claim to be atheist. Then decided agnostic was a better way to define things.
Sadly I never really got to sit down and talk with him about all this before he passed as I moved away when I was 20 and well many know how it is when relationships with one or both parents is strained. I think that is my greatest regret, the missed time chatting with a very intelligent human.

A deity has no mass or energy. How would we know this? I think pixies are living in my shoes. In fact, they are in there even when my feet are in there.

Is there a fairy called Mehitabel living at the bottom of my garden?

Can I PROVE she's not there? No. Can I PROVE she is there? No. I therefore do not believe the case for, or against, the existence of Mehitabel the Fairy is provable - making me a 'Mehitabel Agnostic'.

That said, do I actually believe Mehitabel IS there? No - of course I don't. The whole concept of Mehitabel existing makes no sense. I therefore do not believe in the existence of Mehitabel - therefore making me a 'Mehitabel Atheist'.

Atheism and Agnosticism are descriptions of two DIFFERENT AND INDEPENDENT perceptions of reality. One about the existence of god himself, and the other about the possibility of proving the matter.

You can be an Atheist without being an Agnostic - "I do not believe in the existence of god, and I further believe the matter is provable".

You can be an Agnostic without being an Atheist - "I do not believe the existence of god can be proven, but I believe he exists".

You can be neither Atheist nor Agnostic - "I believe in the existence of god, and I believe that existence is provable".

Or you can be both Atheist and Agnostic - "I do not believe in the existence of god, but I believe the matter unprovable."

It's two entirely separate questions:-

DO YOU BELIEVE IN THE EXISTENCE OF AT LEAST ONE GOD? Answer 'Yes' and you're a THEIST, answer anything else (ie, you don't actively believe) and you're not a theist. The word for 'not a theist' is ATHEIST. There is no option 3 - you're either one or the other.

DO YOU BELIEVE THE EXISTENCE OR NON-EXISTENCE OF GOD IS PROVABLE? Answer 'Yes' and you're a GNOSTIC, answer anything else (ie, you don't actively believe the matter provable) and you're not a gnostic. The word for 'not a gnostic' is AGNOSTIC. Again, there is no option 3 - you're either one or the other.

Personally I'm an Agnostic Atheist.

To the general public - if I'm going to state my position at all - I identify as an atheist. It's just simpler, and I'm doing my part thereby to erode the demonization of atheists as baby-eating monsters. The general public doesn't understand the meaning of the word "agnostic" anyway, and it's very time-consuming to explain. So I stick with "I'm an atheist."

But I'm both. I'm an atheist - I don't believe in any gods - and I'm an agnostic - humans are not in a position to know for absolute certain about the existence or non-existence of gods. The latter position isn't about hedging my bets for the afterlife. As @UpsideDownAgain so aptly said, "since I worship no gods, I'm screwed either way." Rather, it's about intellectual honesty. I was once so sure that the Christian God existed; now I'm equally convinced that it doesn't - but I've wisened up to recognize that nobody can know anything about intangible god things to the degree that I once "knew" the opposite.

How useful is this? Not at all. I'm also agnostic about the existence of green flying unicorns on some other planet. I don't believe in them. It's just about intellectual honesty. I'd also love to be able to bring a few Christians to the recognition that they don't know what they imagine that they know.

The only thing up for debate is what started the universe. But it seems very likely to me one day or species will figure that out too. Thus, I'm atheist.

No, you can't prove a negative and no, you can't know with 100% certainty. The latter claim is easily shown by the possibility that everything might be an illusion, a matrix scenario, brain-in-a vat etc. You can't even know 100% that the draw exists, so how could you say that it is scissor-less. There is always a tiny possibility that something might be wrong.
Now the former claim. In your example with the draw you don't prove a negative when showing it to be empty. You make a positive claim about the inside of the draw. If we could observe the whole universe at once somehow we could prove that something doesn't exist but only observable things that are inside of the universe and prove only in relation to the observation that could be faulty.
The difference between agnostic and atheist is most often only a definitional difference. Agnostics don't hold the believe that a god exists, which in my book is an atheist. 'Agnostic' only means that you can't know it. But some people for whatever reason don't want to call themselves atheist.

"Why else would you give it any thought at all?"..... My only observation is that it seems to me that you just did that.

I am perfectly happy to be a staunch atheist who knows that there is no divine authority as alluded to by all sorts of religions.
Religious people are true agnostics because they just believe rather than know.

Define a god and its conditions of existence/non-existence and we'll go from there. Most claims of gods or godly beings are so objectively and patently ridiculous that they can be dismissed outright, as they are presented not only without evidence but without substance, i.e. entirely untestable/undectectable.

There is no knowing the unknowable non sequitur should make no difference here just enjoy the people and ideas I think that is truly this place and people