A Beautiful MindGoofs
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As Nash walks on the Harvard campus on his way to the math conference (shortly before being chased by Rosen and his men), he drops his bag behind him to hug his roommate and the young girl. During his conversations with them, the bag remains on the ground. Within one second, just before Nash walks off, the bag goes from being on the ground to being clutched to his chest.
Errors in geography
Strictly speaking, John Nash didn't win the Nobel Prize because there isn't a prize for Economics or Mathematics. (Alfred Nobel who willed his estate to the Nobel foundation saw no need for a prize in mathematics.) In 1969 the Swedish Central Bank established the "The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel". This prize is presented in the same ceremony and is therefore often mistaken for a proper Nobel Prize. It is even often referred to as the "Nobel Prize in Economics" in daily conversation; the fictional character of President Jed Bartlet on The West Wing (1999) was also presented as a Nobel Prize winner (for economics) with the show also not making the real-world distinctions.
John Nash didn't receive the Nobel prize alone, but with colleague Reinhard Selten and Hungarian-born János Harsányi. "Game Theory" was initiated by Hungarian-born John von Neumann and Austrian-born Oskar Morgenstern in 1944.
At 1:36:52, in the dilapidated garage, there is a vintage Tektronix oscilloscope shown with the "phosphor" glowing, but the power switch and indicator light (center of bottom edge) are both off. Also, the color of the phosphor is wrong -- it would have been more of a pure green. From the oscilloscope to the right, light of the same hue as its (fake) phosphor is shining against the case to its side; in reality the only light coming from inside would be the dim orange glow of vacuum tube filaments.