Fischer died Aug. 26 in hospice care in Montgomery County, Md., the university announced. A cause was not given.
And he was an early target of the Unabomber, the name that had been given to a perpetrator who had killed three people and wounded at least 23 from 1978 to 1995. The bomber was later identified as Ted Kaczynski.
On May 5, 1982, Fischer's secretary, Janet Smith, opened a package addressed to the professor and a pipe bomb stuffed with smokeless powder and match heads exploded in her hands. She was hospitalized for three weeks with burns and cuts to her chest, arms and hands.
Fischer, who was attending a conference in Puerto Rico at the time, said he could not recall meeting Kaczynski.
Authorities eventually linked the incident to Kaczynski, who is now serving a life sentence. He was not charged in the Vanderbilt incident because the statute of limitations for such a crime had expired by the time he was arrested in 1996.
For years afterward, Fischer wondered how the mail bomber had chosen him.
"For a while I thought he opened up 'Who's Who' and threw a dart until he got a computer scientist," Fischer told The Times in 1996. "That's probably wrong. There has to be a link."
Fischer did notice odd coincidences. His father was a math professor at the University of Michigan when Kaczynski was a graduate student there. And Fischer was a math student at the Massachusetts Institute of Technology while Kaczynski was studying across town at Harvard University.
"The thing is, yes, we knew a lot of the same people," Fischer told the Dallas Morning News in 1996. "But I don't think I know him directly. I didn't recognize the face, either the shaven face or the bearded face. I don't recognize the name at all."
Patrick Carl Fischer was born Dec. 3, 1935, in St. Louis. He received a bachelor's degree from the University of Michigan in 1957 and a doctorate in math from MIT in 1962.
He taught at Harvard, Cornell University, the University of Waterloo in Canada and Penn State before moving to Vanderbilt.
Kaczynski originally addressed the package to Fischer to Penn State, and it was forwarded to him at his new position in Nashville.
Fischer never again assumed a package would be safe to open, telling the Times in 1996: "I will be careful for the rest of my life."
Survivors include his second wife, Charlotte Froese Fischer, a professor of computer science at Vanderbilt; a son and a daughter.