Derbyshire has differed from his fellow writers at National Review on important subjects. For example, Derbyshire supported Michael Schiavo's position in the Terri Schiavo case, showed sympathy for class-warfare themes in movies such as Titanic, argued that Pope John Paul II was totally unable to stop the secularization of the West, ridiculed George W. Bush's "itty-bitty tax cut, paid for by dumping a slew of federal debt on your children and grandchildren", has derided Bush in general for being too sure of his religious convictions and for his "rich-kid-ness", dismisses small-government conservatism as unlikely to ever take hold (although he is not unsympathetic to it), has called for immediate U.S. withdrawal from Iraq (but favored the invasion), opposes market reforms or any other changes in Social Security, defended Michael Jackson as harmless, is pro-choice on abortion, supports euthanasia in a fairly wide range of circumstances, and has suggested that he might (in a time of international crisis) vote for Hillary Clinton as president. Derbyshire's views on the Schiavo case attracted harsh condemnation from fellow writers at National Review Online. NRO writer and frequent blogger, Ramesh Ponnuru, attacked Derbyshire in language far more forceful than customary in National Review's internal debates. The Derbyshire-Ponnuru dispute arose again over Ponnuru's recently published book, Party of Death. Derbyshire reviewed the book harshly in the New English Review, and Ponnuru replied on NRO with another strongly worded attack on Derbyshire as "wrong," "florid," "anti-intellectual," "gaseous" and "preposterous" among other terms.

Though Derbyshire broadly agrees with many other writers at National Review Online on immigration, he encountered strong opposition from former NRO blogger John Podhoretz, who described Derbyshire's comments on restricting immigration to maintain "ethnic balance" in severe terms: "But maintaining 'ethnic balance' is not fine. It is chillingly, horrifyingly not fine." In response, fellow Corner contributor Jonah Goldberg, who described himself as philosophically "in the middle" of the two, noted:

I should say that I think JPod is getting too hung up on the phrase "ethnic balance" as a codeword for all sorts of unlovely things. It seems to me that if you're going to sit down and have any immigration policy at all, it's unavoidable that you're going to address the issue of ethnic balance in one way or another, no matter what you call it. Ultimately, you have to choose where people come from if you have an immigration policy, even if you emphasize other factors like skills or family unification. So you can either look at it directly or you can skirt around it. But you can't avoid it.

Derbyshire's book, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics was first published in hardcover in 2003 and then paperback in 2004. It focuses on the Riemann hypothesis, one of the Millennium Problems. The book is aimed, as Derbyshire puts it in his prologue, "at the intelligent and curious but nonmathematical reader... I think I have pitched my book to the level of a person who finished high school math satisfactorily and perhaps went on to a couple of college courses...."

Prime Obsession explores such topics as complex numbers, field theory, the prime number theorem, the zeta function, the harmonic series, and others. The biographical sections give relevant information about the lives of mathematicians who worked in these areas, including Euler, Gauss, Dirichlet, Lobachevsky, Chebyshev, Vallée-Poussin, Hadamard, as well as Riemann himself.

In 2006, Joseph Henry Press published another Derbyshire book of popular mathematics: Unknown Quantity: A Real And Imaginary History of Algebra."John Derbyshire's Unknown Quantity is everything a popular mathematics book should be: gentle, chatty, anecdotal and full of mind-aching equations."

Derbyshire had an uncredited role in Meng long guojiang (released in the West as Way of the Dragon and Return of the Dragon), a 1972 martial arts film starring Bruce Lee. Of landing the part, Derbyshire says: "The casting director had obviously just trawled around the low-class guesthouses for unemployed foreigners of a sufficiently thuggish appearance."

Derbyshire is married and has two children. He lives in in Huntington, New York.

• Seeing Calvin Coolidge in a Dream (St. Martin's Griffin, 1997) ISBN 0-312-15649-9
• Fire From the Sun (Xlibris Corporation, 2000) ISBN 0-7388-4721-6
• Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (Plume Books, 2003) ISBN 0-452-28525-9
• Unknown Quantity: A Real And Imaginary History of Algebra (Joseph Henry Press, 2006) ISBN 0-309-09657-X
• We Are Doomed: Reclaiming Conservative Pessimism (Crown Forum, 2009) ISBN 0307409589, ISBN 978-0307409584

He has also written numerous articles for various publications, including National Review, The New Criterion, and The Washington Times. On the National Review website, he maintains a weekly audio commentary on current events.