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   James M. Vaughn Jr., president of the Vaughn Foundation Fund and a   
   philanthropist whose financial support may have led to a mathematician   
   solving Fermat’s last theorem.   
      
   The Texas Oil Heir Who Took On Math’s Impossible Dare   
      
   James M. Vaughn Jr., wielding a fortune, argues that he brought about the   
   Fermat breakthrough after the best and brightest had failed for centuries   
   to solve the puzzle.   
      
   James M. Vaughn Jr., president of the Vaughn Foundation Fund and a   
   philanthropist whose financial support may have led to a mathematician   
   solving Fermat’s last theorem.Credit...Brandon Thibodeaux for The New York   
   Times   
      
   By William J. Broad   
   Jan. 31, 2022   
      
   Fermat’s last theorem, a riddle put forward by one of history’s great   
   mathematicians, had baffled experts for more than 300 years. Then a genius   
   toiled in secret for seven years to solve it, according to the usual   
   narrative. That shy Englishman, Andrew Wiles, made his feat public in the   
   early 1990s and amassed a glittering array of tributes. In 2016, he won   
   the Abel Prize, math’s top award. It came with a $700,000 purse.   
      
   Now, a wealthy Texas philanthropist is recounting how his financial   
   support created a community of Fermat innovators that, over decades, lent   
   moral and mathematical support to Dr. Wiles. That patronage drew top   
   mathematicians to the puzzle after great minds had given up, succeeded in   
   bringing the moribund field back to life, and may have helped make Dr.   
   Wiles’s breakthrough possible.   
      
   “We solved the problem,” the philanthropist, James M. Vaughn Jr., 82,   
   president of the Vaughn Foundation Fund, said in an interview. “If we   
   hadn’t put the program together as we did, it would still be unsolved.”   
      
   In interviews, top experts described Mr. Vaughn’s foundation and its early   
   financial support as sparks that had lit an intellectual fire, although   
   they stopped short of saying that his backing had been responsible for Dr.   
   Wiles’s Fermat breakthrough. Dr. Wiles did not respond to inquiries.   
      
   Recently, Mr. Vaughn gave the University of Texas a collection of 125 rare   
   and foundational books in the history of mathematics, and the gift has   
   prompted him to speak publicly of other foundation projects that have gone   
   largely unheralded.   
      
   While gregarious, Mr. Vaughn, heir to a Texas oil fortune, is an extremely   
   private man who has never before claimed publicly that his philanthropy   
   begot the mathematical feat. Even so, he takes immense pride in what he   
   characterizes as his legacy. Mr. Vaughn said that he and his wife had no   
   children and that the Fermat triumph was how he hoped he would be   
   remembered.   
      
   “It was very important to have someone like Vaughn doing this,” said   
   Dorian Goldfeld, a professor of mathematics at Columbia University who   
   worked closely with Mr. Vaughn. “It made the problem more visible to more   
   people.” Mr. Vaughn’s financial aid, he added, eventually led to wide   
   Fermat collaborations, including an early gathering that Dr. Wiles helped   
   organize.   
      
   “It’s really great to have people like Vaughn,” said Neal I. Koblitz, a   
   professor of mathematics at the University of Washington who edited a   
   Fermat book for the Vaughn Foundation. “Nobody was working on the problem.   
   Vaughn had the money and the interest.”   
      
   It seems unlikely that Mr. Vaughn had a direct impact on what turned out   
   to be the Byzantine math of the Fermat proof. But in science, private   
   donors often act as pathfinders for government investment in difficult   
   research. So it was with Mr. Vaughn. He led, and Washington followed. In   
   the 1970s and 1980s, he directed millions of dollars to Fermat   
   conferences, authors and researchers, giving the old field new life and   
   social acceptability.   
      
   Subsequently, in the early 1990s, the National Science Foundation, a   
   federal agency, lent its support. It provided Dr. Wiles, then at Princeton   
   University, with math research grants totaling nearly a half-million   
   dollars.   
      
   It turns out that both men sought to advance an arcane branch of   
   mathematics known as elliptic curves. The field’s equations build up sets   
   of simple geometric forms that can lead to infinite runs of subsidiary   
   equations and, when solved, solutions to problems of blinding complexity.   
   The exotic forms led Dr. Wiles to the Fermat breakthrough.   
      
   Dr. Wiles, now 68 and known as Sir Andrew after being named a knight   
   commander of the British Empire, made no response to repeated emails   
   asking his view on Mr. Vaughn’s claim of having made his feat possible.   
   According to his biographer, Dr. Wiles comes across as a “diffident” man   
   who dislikes publicity.   
      
   While historians of science may one day debate whether Mr. Vaughn should   
   share a measure of credit for the Wiles breakthrough, the body of   
   developing evidence already makes the Texan’s blunt declaration seem less   
   like a yarn than a reasonable possibility.   
      
   “He really deserves the recognition,” Dr. Goldfeld said of Mr. Vaughn.   
      
   Pierre de Fermat, the French mathematician, penned his riddle around 1637,   
   early in his career.Credit...via Science Source   
      
   A page from the 1670 edition of “Arithmetica” by the Greek mathematician   
   Diophantus, in whose margins Fermat wrote his puzzle.   
      
   Pierre de Fermat was a French lawyer of the 17th century who pursued math   
   as a hobby. After his death, appraisals of his work revealed him to be a   
   giant. He helped lay the foundations of calculus and probability theory.   
      
   Fermat also left behind a large body of what he called theorems. The   
   general claims rest on chains of logic. Fermat, however, was something of   
   a tease. He often asserted the truth of a proposition but gave no details.   
   Skeptical experts found to their surprise that many of his sketchy claims   
   were, in fact, true.   
      
   The Great Read   
   More fascinating tales you can’t help but read all the way to the end.   
   A German climber is attempting to be the first to scale Mount Everest in   
   winter alone without supplemental oxygen. There’s nobody else out there.   
   An heir to a Texas oil fortune was fascinated with one of the greatest   
   enigmas in the history of mathematics. His private support for research   
   may have been a critical factor in the puzzle’s solution.   
      
   Behind the wildly popular “Trump coin” lies an entire disinformation   
   supply chain. Complete with fake social media profiles and fake news, it   
   all exists to help someone, somewhere, make a buck.   
      
   The exception came to be known as Fermat’s last theorem. Early in his   
   career, around 1637, he had scribbled the equation in a book’s margins,   
   claiming a marvelous proof, but called the space too small for   
   particulars. Over time, his reputation drove thousands of mathematicians   
   to take on the problem.   
      
   Part of the appeal was basic. The simple equation had just three elements   
   but an infinite number of possible solutions. The challenge was to find   
   ways of bounding the infinite.   
      
   Leonhard Euler was an 18th-century Swiss mathematician who solved hundreds   
      
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