[3][4][5][6] Hoffmann was born in Złoczów, Poland (now Zolochiv, Ukraine), to a Polish-Jewish family, and was named in honor of the Norwegian explorer Roald Amundsen.

[7] After Germany invaded Poland and occupied the town, his family was placed in a labor camp where his father, who was familiar with much of the local infrastructure, was a valued prisoner.

When she received the news, his mother attempted to contain her sorrow by writing down her feelings in a notebook her husband had been using to take notes on a relativity textbook he had been reading.

[12] Hoffmann visited Zolochiv with his adult son (by then a parent of a five-year-old) in 2006 and found that the attic where he had hidden was still intact, but the storeroom had been incorporated, ironically enough, into a chemistry classroom.

They realized that chemical transformations could be approximately predicted from subtle symmetries and asymmetries in the electron orbitals of complex molecules.

[26] For this work Hoffmann received the 1981 Nobel Prize in chemistry, sharing it with Japanese chemist Kenichi Fukui,[27] who had independently resolved similar issues.

[29] Some of Hoffman's most recent work, with Neil Ashcroft and Vanessa Labet, examines bonding in matter under extreme high pressure.

[31][35] In 1981, Hoffmann received the Nobel Prize in Chemistry, which he shared with Kenichi Fukui "for their theories, developed independently, concerning the course of chemical reactions".

[64] In August 2007, the American Chemical Society held a symposium at its biannual national meeting to honor Hoffmann's 70th birthday.

In August 2017, another symposium was held at the 254th American Chemical Society National Meeting in Washington DC, to honor Hoffmann's 80th birthday.

[66] The Hoffmann Institute of Advanced Materials in Shenzhen, named after him, was founded in his honor in February 2018[67] and formally opened in his presence in May 2019.