Dahlquist began to study mathematics at Stockholm University in 1942 at the age of 17, where he cites the Danish mathematician Harald Bohr (who was living in exile after the occupation of Denmark during World War II) as a profound influence.
He has won numerous awards, including the 1989 Leslie Fox Prize for Numerical Analysis, and the SIAM James Wilkinson and Germund Dahlquist Prizes in 1997.