Born on April 2, 1942, Singh had been suffering from schizophrenia for nearly four decades.
"Singh's condition deteriorated this morning. He was rushed to Patna Medical College Hospital (PMCH), where doctors declared him dead," said one of Singh's relatives.
Singh, a resident of Basantpur in Bhojpur district, was shifted to PMCH last month. However, he was discharged after treatment.
Expressing grief over his death, Bihar Chief Minister Nitish Kumar called it a "loss to the state and society".
"It's an irreparable loss to Bihar. He was a famous personality. I offer my tributes to him," said Kumar.
The mathematician is said to have challenged Einstein's theory of relativity.
Singh did his schooling from Netarhat Residential School. In 1962, he passed Class X.
Later, while studying at Patna Science College, he met American Professor Kelly, who invited him to Berkeley, US for research.
In 1963, he went to California University for research. In 1969, he received a Ph.D. degree from the varsity. His research on Cycle Vector Space Theory made him famous.
After completing his studies, he returned to India.
Later, he joined as a mathematics professor in Washington. In 1971, he came back to India. He worked at the Indian Institute of Technology (IIT), Kanpur and IIT, Kolkata.
In 1974, he began suffering from several critical illnesses.
( With inputs from IANS )