The bleeding man in Pi (1997)

You wrote:

”Who is the bleeding man at the train station?”

One way to interpret your own dreams is that all of the characters are different facets of you. (Indeed, that is the truth of the matter, since you are creating the dream.) But we don’t need to get philosophic with this one because Max and the hat-guy bleeding in the subway are both played by Sean Gullette. (He turns around for a few frames and you can see clearly it is Max – both have squared earlobes.) So he is hallucinating seeing himself bleeding. He sees this twice while he’s waiting for the subway at 47-50 Rockefeller Center

”He is most likely just imagined, as is so many other things in the movie (e.g. the brain), but I can't imagine what it means.”

While hallucinating he runs around to the other side of the train tracks and follows the blood trail; it leads to the human brain you mention laying on the ground. Further investigation reveals it is his own brain, because as he probes it he hears and feels things. He repeats this multiple times. (This representation of probing the brain is actually based on fact, albeit with small electric pulses. This is an outstanding and approachable book on the subject ..matter.)

So the scene is another abstraction of his picking at his head to remove the source of the migraines. Indeed he sticks a pen into the brain on the pavement to try and kill the problem, which results in him being run over by a train even though he’s in the middle of the causeway and nowhere near the tracks. (These things can happen in hallucinations.) He also killed the brain in his sink, and Sol had two strokes and ultimately died exploring deeper numerical meaning within Pi. (Note: A hemorrhagic stroke is the type where a blood vessel in the brain bursts, and blood bleeds into the brain. This type of stroke can be caused by an aneurysm - a thin or weak spot in an artery that balloons out and can burst. This reminds me of the abstract scar that is revealed on the side of Max’s head, except external like a hernia.)

So the man on the other side of the tracks (Max) was reduced to just a brain (Max’s) within his own migraine induced hallucination. (Not shown, he ends up actually getting on the train, misses Chinatown, and wakes up with a bloody nose at the final stop down at Coney Island.)

To me the dress of the man in the hat represents an abstract combined character of a business suit Max, and a hat wearing orthodox Jew Max – the two camps that are courting him. A kind of paranoid mixed vision of him working for Marcy Dawson in the predictive strategy firm Lancet-Percy. and/or he being more like the orthodox Lenny Meyer character. That’s how I interpret that artistic decision. (Although it’s probably just the orthodox thing alone – but ultimately both camps want the same thing – the 216 character number. 216 being 6x6x6. We’re told only purified priests can handle its meaning for long, and he is not that, so can’t – nor could Sol.)

The hat guy in the subway is bleeding from his right side - matching Max’s eventual drill hole into the right side of his own head (which would run down his right arm), and also matching the dreamed image of him sticking the pen into his own brain with his right hand. In this sense the subway hallucination scene is a premonition.