When you think, focus on thinking with the part of your brain that forms thoughts, not the part that says them aloud in your head. When that filter is removed in times of extreme meditation, psychedelic experiences, etc. you will find that thoughts can flow like a turbulent river, whereas before it was only a trickle. But such a skill can be cultivated in the sober mind as well. This, I believe, is a key to human genius. It exists in all of us, regardless of if we know it or not. 
In normal times of sober reflection, we notice that we think in 2 stages, first we know what we are going to say in our mind, and then we say it aloud in our head. Focus on that part that spontaneously brings thoughts into being. Listen to it, and it alone when you need inspiration, or to think quickly.
Thoughts arise naturally, independent of language. This is the realization that comes from such thinking. We imagine first the essence of what we want to think, then the words. The essence forms in our minds 50x quicker than it takes to say the thought aloud. If we focus on the essence, and not the time consuming process of putting it into words, we will find the genius of the human mind, regardless of who is thinking.
I believe such thinking can only be fully unleashed during spiritual and psychedelic experiences, when the filter between the essence of our thoughts coming into being, and it’s translation, is removed. In such a state we think of 50 thoughts per second. Incredible realizations about life, language, ordinary phenomena, inventions, being, etc. These experiences of completely unfiltered thinking under the influence of psychedelics have led to incredible innovations and discovery. I will give you several examples.
The shape of DNA was discovered on LSD. A group of scientists had been working for many months on trying to figure out the shape of DNA. They all dropped acid one day, and within several hours had discovered that the double helix was the best shape to bring the molecules of life together in a functioning pattern. Steve Jobs and Bill Gated both attribute LSD to their success. And most of the music on your phone without doubt came from someone on some form of psychedelic. 
I too have experienced the profound realizations that come under psilocybin, I speak from experience alone. Unfiltered thinking can be cultivated, I believe, in a mind that has not had such an experience. Unfiltered thinking is natural thinking, divorced entirely from language. I believe it, along with psychedelic drugs, to be keys of human genius.