I've read several writings on the problems that consciousness presents to science and the materialistic worldview. One thing that is confusing is that different writers bring up different problems but still talk about it as if it's one problem. Out of all that I've read, there are 3 articles that stand out as my favorites. I highlighted some good information that explains the problem and I'll share some of the details here so that others can hopefully gain a clearer understanding of this complex issue. At the end, we can debate on if consciousness is really a hard problem for science to solve.

Again, the problem is described in different ways by different authors, but I'll lay out what I think it is the strongest version...

Here are the articles:
1. Published on The Conversation; "Science as we know it can’t explain consciousness – but a revolution is coming" by Dr. Philip Goff.
2. Published in the Journal of Consciousness Studies; "Facing up to the Problem of Consciousness" by Dr. David Chalmers
3. Published in Psychology Today; "There are Two Hard Problems of Consciousness, Not one" by Gregg Henriques Ph.D.

Here is a General summary of the problem...

From Article 1 (Dr. Philip Goff):
Explaining how something as complex as consciousness can emerge from a grey, jelly-like lump of tissue in the head is arguably the greatest scientific challenge of our time.

We have made a great deal of progress in understanding brain activity, and how it contributes to human behaviour. But what no one has so far managed to explain is how all of this results in feelings, emotions and experiences. How does the passing around of electrical and chemical signals between neurons result in a feeling of pain or an experience of red?

From Article 2 (Dr. David Chalmers):
The really hard problem of consciousness is the problem of experience. When we think and perceive, there is a whir of information-processing, but there is also a subjective aspect.
This subjective aspect is experience.

From Article 3 Gregg Henriques Ph.D. :
Consider, for example, that we can surmise that if you are reading this post and thinking about it, the following is happening: (1) light patterns are coming off the screen, (2) flowing into your retina where they are (3) translated into the “language” of neurobiological information. The (4) incoming information is sorted and tracked back into the occipital lobe, where it is sorted further, integrated with higher-order processes, and connected (5) to your semantic-linguistic processing system. We can track all this via the activity of your nervous system. And as psychologists, we can assess your "functional awareness and response" by asking questions to obtain information about how well you processed the information. We can even monitor your affective system and see if you were positively or negatively inclined to what you are reading. All of this can be done via a “third person” perspective that adopts a cognitive-neuroscience functionalist view of human mental processes.

The hard problem of consciousness refers to the fact that we can learn all of this and still not know for certain that you are not a "philosophical zombie." A philosophical zombie is a thought experiment that refers to an individual who looks like us and talks like us but has no inner life.
"Inner life" refers to our subjective experience.

From Article 2 (Dr. David Chalmers):
Materialists hope that we will one day be able to explain consciousness in purely physical terms. But this project now has a long history of failure. The problem with materialist approaches to the hard problem is that they always end up avoiding the issue by redefining what we mean by ‘consciousness’. They start off by declaring that they are going to solve the hard problem, to explain experience; but somewhere along the way they start using the word ‘consciousness’ to refer not to experience but to some complex behavioural functioning associated with experience, such as the ability of a person to monitor their internal states or to process information about the environment. Explaining complex behaviours is an important scientific endeavour. But the hard problem of consciousness cannot be solved by changing the subject.
[emphasis added]

Let's get a little more specific with the problem of consciousness...
From Article 3 Gregg Henriques Ph.D. :
David Chalmers’ essay on the hard problem of consciousness has sparked many analyses, arguments, and counterclaims. Here I explain why we should think about the hard problem as two different problems, rather than one.

One problem is the "ontological problem" of how it might be possible to engineer the felt experience of being. The other is the "epistemological problem" of directly knowing another's primary experience.
While I agree that there's two different problems, however, I don't agree with Dr. Henriques's example of an ontological problem. I think the example he gave is really an epistemological problem, one that requires know how and explanation. I agree with his description epistemological problem, but the aspect he choose to focus on is not the strongest epistemological problem in my view. So in both cases, I'll reference other articles to explain the ontological and epistemological problems that consciousness brings to science and materialism.

From Article 1 (Dr. Philip Goff):
The problem of consciousness, however, is radically unlike any other scientific problem. One reason is that consciousness is unobservable. You can’t look inside someone’s head and see their feelings and experiences. If we were just going off what we can observe from a third-person perspective, we would have no grounds for postulating consciousness at all. Of course, scientists are used to dealing with unobservables. Electrons, for example, are too small to be seen. But scientists postulate unobservable entities in order to explain what we observe, such as lightning or vapour trails in cloud chambers. But in the unique case of consciousness, the thing to be explained cannot be observed. We know that consciousness exists not through experiments but through our immediate awareness of our feelings and experiences.

Now, the epistemological problem of consciousness... this gets into the 'explanatory gap'

From Article 1 (Dr. Philip Goff):
There is growing suspicion that conventional scientific methods will never be able answer these questions. ...
...the best we can do is to establish correlations between the quantitative brain processes we can see and the qualitative experiences that we can’t, with no way of explaining why they go together.

From Article 1 (Dr. Philip Goff):
So how can science ever explain it? When we are dealing with the data of observation, we can do experiments to test whether what we observe matches what the theory predicts. But when we are dealing with the unobservable data of consciousness, this methodology breaks down. The best scientists are able to do is to correlate unobservable experiences with observable processes, by scanning people’s brains and relying on their reports regarding their private conscious experiences.

By this method, we can establish, for example, that the invisible feeling of hunger is correlated with visible activity in the brain’s hypothalamus. But the accumulation of such correlations does not amount to a theory of consciousness. What we ultimately want is to explain why conscious experiences are correlated with brain activity. Why is it that such activity in the hypothalamus comes along with a feeling of hunger?

From Article 2 (Dr. David Chalmers):
How can we explain why there is something it is like to entertain a mental image, or to experience an emotion? It is widely agreed that experience arises from a physical basis, but we have no good explanation of why and how it so arises. Why should physical processing give rise to a rich inner life at all? It seems objectively unreasonable that it should, and yet it does.
It is tempting to note that all sorts of puzzling phenomena have eventually turned out to be explainable in physical terms. But each of these were problems about the observable behaviour of physical objects, coming down to problems in the explanation of structures and functions. Because of this, these phenomena have always been the kind of thing that a physical account might explain, even if at some points there have been good reasons to suspect that no such explanation would be forthcoming. The tempting induction from these cases fails in the case of consciousness, which is not a problem about physical structures and functions. The problem of consciousness is puzzling in an entirely different way. An analysis of the problem shows us that conscious experience is just not the kind of thing that a wholly reductive account could succeed in explaining.

At the end of the day, the same criticism applies to any purely physical account of consciousness. For any physical process we specify there will be an unanswered question: Why should this process give rise to experience? Given any such process, it is conceptually coherent that it could be instantiated in the absence of experience. It follows that no mere account of the physical process will tell us why experience arises. The emergence of experience goes beyond what can be derived from physical theory. Purely physical explanation is well-suited to the explanation of physical structures, explaining macroscopic structures in terms of detailed microstructural constituents; and it provides a satisfying explanation of the performance of functions, accounting for these functions in terms of the physical mechanisms that perform them. This is because a physical account can entail the facts about structures and functions: once the internal details of the physical account are given, the structural and functional properties fall out as an automatic consequence. But the structure and dynamics of physical processes yield only more structure and dynamics, so structures and functions are all we can expect these processes to explain. The facts about experience cannot be an automatic consequence of any physical account, as it is conceptually coherent that any given process could exist without experience. Experience may arise from the physical, but it is not entailed by the physical.
With experience, on the other hand, physical explanation of the functions is not in question. The key is instead the conceptual point that the explanation of functions does not suffice for the explanation of experience. This basic conceptual point is not something that further neuroscientific investigation will affect. In a similar way, experience is disanalogous to the elan vital. The vital spirit was put forward as an explanatory posit, in order to explain the relevant functions, and could therefore be discarded when those functions were explained without it. Experience is not an explanatory posit but an explanandum in its own right, and so is not a candidate for this sort of elimination.
[emphasis added]

So there we have it. The ontological problem that consciousness presents to materialism and science is that its nature is insensible, private, and undetectable to everyone except the individual. Although, this may not be enough to classify consciousness as non-physical, but it is certainly unlike any other physical phenomenon that can be observed and measured. The epistemological problem is that simply explaining the structures and functions for consciousness, which is what scientists have been doing and probably all that they can do w/ a third-person perspective, does not fully account for the subjective experience itself. These facts that scientists discover do not tell us about the qualitative nor subjective aspects of the experience (first-person facts?). Some thought experiments that illustrate this is Frank Jackson's Knowledge argument, or showing how the same neural states can be present without a particular conscious state or without consciousness at all, etc.

I'm sure many other aspects of consciousness can be brought up as presenting a problem to science.

For Debate:
1. Do you agree that consciousness presents a problem to science and materialism?
2. What can we do to solve the problem?
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How would scientists even know about subjective experience of others, if no one had a way to report their experience?

If consciousness were physical, then scientists would be able to discover it or deduce it from knowledge of neural activity (which are physical). That has not happened, and part of the Hard Problem, is to show why it's inconceivable that it could happen. That's especially the case when you consider that we can't even observe subjective experiences, and a lot of neural activity occurs without any subjective experience anyway. So again, just how would scientists have discovered conscious experience just by looking at physical neural activity?

Scientists know about conscious experience when we report it to them, and even then they still can't explain it.