Is there proof of the mind as a separate entity?
It's all in your skull...
You, and everything about you, are indistinguishable from this arrangement of organic materials. Regardless of what you think, feel, believe, or assert about this proposition, it fundamentally reduces humanity to a machine.
If we examine a computer, we'll find plenty of similarities. Our brain operates like a CPU, processing, prioritizing, and facilitating communication and interpretation of signals. Our circulatory system is the motherboard, providing life-giving power to the rest of the system. Occasionally, the memory storage unit (hard drive) gets flaky and data is lost (amnesia, Alzheimer's, etc).
Everything about who we are is the operating system: all our likes, habits, traits, dreams, and so forth are all certain files and folders stored in our brain. We pick and choose which items to save, much as we do with computers today; we collect data and information based on pre-disposed traits determined by random configuration.
You are who you are because you're wired the way you're wired and that's it. The human brain-body is the case, machine, fan, power supply, and components necessary to load and run the human operating system.
Maybe it's something else...
People believe they may be just animals, motivated only by biochemical reactions and determined attributes brought about by random processes operating over a vast amount of time, but what we experience seems to indicate otherwise. We certainly don't feel like we're just a machine, do we?
How much does our interpretation, our feeling, our belief, matter in terms of what we really are? Since reality is unequivocally the "world as we see it", it would seem our belief about what we are is, quite literally, what we are and will be.
But there are ways we can examine the Mind using basic sense, logic, etc. We presume we have a mind because we think; our thoughts provide that constant presence about ourselves; these thoughts create a personality, a particular expression or arrangement of thought. Without these thoughts, this feedback, is there any way to express who or what we are?
Assuming the answer is "no", we are left with the bare fact that thought and personality, thought and being, are the same thing--e.g. you are your thoughts. When saying "I", we are referring to our thoughts and the Mind that has them. Again assuming that is an acceptable concept, we can rationally conclude that Mind and thought are the same, as one without the other is impossible to understand or express.
At this point, we are left with the possibility that we are our Mind; our thoughts represent us as people, and people know us by the thoughts we express. All human interaction is Mind to Mind on a fundamental level.
If you refer to yourself as "the signals in my brain", then maybe you will disagree with this proposition. Most of us, when saying "I" or referring to oneself, do not think we are just our physical brain; we believe we are individuals, people, and we deserve to be respected, to live, and to grow.
Why want these things if we're just animals? The inner life is intrinsically different than the survival-based exterior one. Thoughts, ideas, dreams, and so forth represent a different sphere of being; the needs of the body, or of basic neurological functioning, operate efficiently for many other living creatures without the need for art, writing, expression, and all the mind stuff.
The simple fact that we are conscious of being conscious, aware of ourselves, and have a desire to express this realization points to the Mind and its contents being fundamentally different than the natural world in which our body operates.
The Experience of Mind...
Perhaps our mental existence, our thoughts and dreams, and all the things we ponder throughout our life (including the end of life) are the result of accumulated survival strategies, random processes, and natural selection. Perhaps that is true; perhaps our animal life ends and everything it was or represented ends in decay, recycling the animal back into the ecosystem.
Experentially, this has no value at all. What need would self-consciousness, belief, art, dreams, and so forth fulfill in a materialistic reality? The emotional trauma caused by mental interaction with the physical world is profound; people kill themselves because someone doesn't love them, and the unloved can't stop thinking about their sadness. What is the natural goal of Mind and thought in terms of survival?
Humans are capable of tremendous waste and destruction. Animal life finds an equilibrium with the environment. Much of our destructive tendency comes from ideas, invention, and the things of the Mind. What other creatures study electricity and built a network of power, satellites, and so forth? Why would they need to? Why do we need to?
Bringing our thoughts into being is profound. Please stop and think about it. Something which does not exist outside of someone's mind is created in the natural world. Often this requires many intermediary steps, transforming materials, making tools, and much more that must be considered before the thought can come to life.
We have done this on a global scale in a very short period of time. Our Mind accumulates knowledge at an exponential rate, building technology so vast that many of us don't understand how complicated it is or exactly how to work everything we've created.
So what is Mind?
It seems rational to conclude that the Mind serves a different purpose than physical survival. Whatever is at work generating and interpreting thoughts is fundamentally different and more complex that the systems that control our biological functions. Mind seems to require expression, interaction, and things that have little or no impact on our ability to physically survive.
This indicates that Mind, the "I" inside, cannot be a result of the physical--i.e. cannot originate or be caused by the body. If that were true (the Mind and thoughts are just physical), then we would see more of it in other life forms on Earth. Denoting the Mind as part of evolution doesn't fit; dreams and thoughts would run counter to a survivalist system (hive minds would make more sense).
Mind craves more than body; its needs are all together different, beyond the reach of the material world.