From the imaging work done so far on this important and unique manuscript, new discoveries have been made about Archimedes. He is considered the most important mathematician and engineer of ancient Greece, and his work resonates and remains relevant to this day. Archimedes, born in 287 B.C. in Syracuse on the island of Sicily, is famous for shouting “Eureka” (“I have found it”), and running naked from his bath through the streets of Syracuse declaring that he had discovered a method for determining the volume of bodies from the amount of water displaced when objects are submerged. He was also celebrated in his time—and is still celebrated in ours—for his practical applications of mathematics and physics to create war machines, used in the defense of the Greek city-state Syracuse from Roman invaders. (Syracuse eventually fell under the siege, and Archimedes was killed by a Roman soldier at age 75.)

But Archimedes remains scientifically relevant to this day for his concepts of abstract mathematics and his understanding of fundamental physical phenomena, which fuse together for the first time in Archimedes’s treatises and form the foundation for mathematical physics. In The Method of Mechanical Theorems, the most important essay known only by the Archimedes palimpsest, the Greek founder of physics shows the process he uses to derive geometrical properties from the ways in which objects can be balanced. Perhaps the most important insight into Archimedes mind is a passage in the Method in which he describes the concept of infinity. Infinity is a fundamental concept in all of mathematics, refined by Newton’s invention of calculus, but was previously considered a problem too difficult for ancient Greek mathematicians. From the palimpsest, we now know that infinity was understood and described by Archimedes twenty centuries before Newton.

Another unique passage contained in the palimpsest is the Stomachion , arguably the first-ever treatise on combinatorics , the branch of mathematics concerned with the selection, arrangement, and operation of elements within sets. In this passage, Archimedes describes a puzzle or game in which a square is cut into 14 pieces and shuffled. The game is to come up with the number of different ways the pieces can be arranged back into a square. It is not known whether Archimedes solved the puzzle—those pages have been lost—but modern “combinatorists” have tackled the problem and come up with the number 17,152, according to Greek scholar Reviel Netz, who has written extensively about the Archimedes palimpsest.