PRINCETON -- More than a year after his death, Princeton University mathematician John Forbes Nash Jr. is bidding farewell to the academic world with a new book about the biggest mysteries of mathematics.
Nash, the brilliant-but-troubled subject of the film "A Beautiful Mind," was in the final stages of co-editing the book on unsolved mathematical problems when he was killed in a car crash on the New Jersey Turnpike last year.
"Open Problems in Mathematics" was completed by his co-author and released Saturday by the scientific publisher Springer.
The book is a collection of essays about "beautiful mathematical questions," according to the introduction written by Nash and co-author Michael Th. Rassias.
Rassias and the mathematicians who contributed to the book dedicated the 543-page volume to Nash and his "rich mathematical legacy."
"In history, one can say that among the mathematicians who have reached greatness, there are some -- a selected few -- who have gone beyond greatness to become legends. John Nash was one such legend," Rassias wrote in a tribute to Nash included in the book.
Rassias, a former postdoctoral researcher in Princeton's math department, said the idea for the book began in 2014 when Nash walked into the common room of Fine Hall on Princeton's campus, poured himself a cup of decaf coffee and sat silently by himself. Rassias approached the reclusive Nobel Prize winner and the pair chatted about game theory, Nash's specialty.
Though the researcher was nearly 60 years younger than Nash, the pair began to speak frequently about math. They eventually decided to write a book together on the biggest unsolved mathematical problems.
"The day we made this decision, he turned to me and said with his gentle voice, 'I don't want to be just a name on the cover though. I want to be really involved,'" Rassias wrote in an essay at the beginning of the book.
The pair met almost daily to decide which mathematical problems to include in the book, Rassias said. They recruited other experts to write chapters about each mathematical mystery, including unsolved problems in algebraic geometry, number theory, discrete mathematics and differential geometry.
Nash helped pick the Albert Einstein quote that opens the book and decided to include the co-authors' signatures at the end of the introduction to give the volume a "vintage" feel, Rassias said.
The book was nearly complete in May 2015 when Nash and his wife left for Oslo, Norway, where the mathematician received the Abel Prize for Mathematics from King Harald V for his work on nonlinear partial differential equations.
Nash and his wife, Alicia, were headed home from Newark Liberty International Airport when their taxi crashed into a guardrail on the New Jersey Turnpike.
Nash, 86, and Alicia, 82, were pronounced dead at the scene.
The couple had been portrayed in the 2001 Academy Award-winning film "A Beautiful Mind" by Russell Crowe and Jennifer Connelly. The film was about how Nash struggled with paranoid schizophrenia, but went on to win the 1994 Nobel Prize in Economics for his pioneering work on game theory.
The mathematician and his wife, who lived in a modest home in Princeton Junction, also became advocates for improved mental health care.
Rassias had grown close to the couple.
"What was certainly true though was the dear love between John and Alicia Nash, who together faced and overcame the tremendous challenges of John Nash's life. It is somehow a romantic tragedy that fate bound them to even leave this life together," Rassias wrote.
Nash was scheduled to write a chapter for the book on an unsolved problem in game theory when he returned from his trip to Norway, Rassias said. But he never got the chance. Harvard University professor Eric Maskin, also a Nobel Prize winner in economics, stepped in to write the chapter instead.
The book, which retails for $149 in print through the publisher, is written for an academic audience. Individual chapters can be purchased for $29.95, the publisher said.
Kelly Heyboer may be reached at kheyboer@njadvancemedia.com. Follow her on Twitter @KellyHeyboer. Find her at KellyHeyboerReporter on Facebook.