# Scientist of the Day - Pierre de Fermat

Linda Hall Library

Linda Hall Library

Linda Hall Library

Linda Hall Library

Linda Hall Library

Pierre Fermat, a French mathematician, was born Aug. 17, 1601. In 1631, as the result of a court appointment, he was allowed to change his name to Pierre *de* Fermat, which was pretty exciting. In the 1630s, Fermat was reading the *Six Books on Arithmetic* of the ancient Greek mathematician Diophantus, an edition printed in 1621. Next to a section where Diophantus showed that certain square numbers could be written as the sum of two smaller square numbers (Book 2, Question 8, to be precise), Fermat wrote in his copy that it is impossible to divide a cubic number into two smaller cubic numbers, or a quartic number (one that is raised to the fourth power) into two quartic numbers, or indeed, any numbers whatsoever except square numbers. And then he wrote in his copy the tantalizing words "I have discovered a truly marvelous proof of this, which this margin is too small to contain." This is the first statement of what is commonly called "Fermat's Last Theorem".

Fermat’s copy of the 1621 Diophantus, with his marginal notes, does not survive today, but it was extant in 1670, when Fermat’s son Samuel edited a new edition of Diophantus. When he came to Book 2, Question 8, Fermat junior added an editorial comment, stating that père Pierre had discovered that summing two squares to get a third square was a special case, only possible when the exponent was 2, and that he had a proof that the margin was too small to contain. This is indeed the source of the entire legend of Fermat’s last theorem. There is no good reason to doubt that Fermat made the comment about having a proof, although many doubt that he had such a proof. Many later mathematicians tackled the proof, but it did not get a general solution until 1994, almost 360 years after it was first scribbled down.

We have both editions of Diophantus’s *Six Books on Arithmetic* in our History of Science Collection. We see above the title pages of the two editions *(second and fourth images*); the page in the 1621 edition where Fermat supposedly wrote his marginal note (*third image*; one can see that the margins were indeed not very commodious); and the page in the 1670 edition where Samuel de Fermat printed Fermat’s last theorem for the very first time (*fifth image, with a detail of the theorem as our first image*). You can perhaps pick out the phrase *Hanc marginis exiguitas non caperet* in our first photo – not quite as famous in its original Latin as *Cogito ergo sum*, although perhaps it should be.** **

A statue of Fermat (*sixth image*), with his theorem carved onto the right side of the plinth (not visible here), was erected in his birthplace of Beaumont-de-Lomagne in southern France.*Dr. William B. Ashworth, Jr., Consultant for the History of Science, Linda Hall Library and Associate Professor, Department of History, University of Missouri-Kansas City. Comments or corrections are welcome; please direct to ashworthw@umkc.edu.*