Scientists have found a 2000-year-old math book that could have changed history. Written by the Greek mathematician Archimedes, who was born about 287 BC, it contains essential concepts that weren’t rediscovered until centuries later.

“The manuscript was heavily damaged by mold,” says manuscript conservator Abigail Quandt. “The parchment is perforated where the fungi have actually gone through and digested the collagen, and it means that the Archimedes text is just totally missing in these areas.”

The book was hidden away 800 years ago by a medieval monk who needed paper for the prayer book he was writing. The monk took pages out of the Archimedes book, turned them sideways, washed away the ink, and wrote over it. But modern science can detect a faint trace of the original text.

“We are trying to take advantage of the very slight differences in color of the two inks, of the inks from the Archimedes text and the later ink,” says optical scientist Roger Easton. “So we did that by taking images at a wide variety of wavelengths.”

Pages were scanned into a computer and then looked at in blue and red light. The computer came up with an image in which the two different texts appeared as different colors that were easier to tell apart. “I was amazed by the fact that now for the first time I can look at pages that look hopeless with the naked eye and begin to use them as text from which you just read,” says classicist Reviel Netz. “We are able to recover the original text of Archimedes where it appears to have been lost. I think we will be able to read everything there for the first time.”

We once thought that calculus, the basis of 21st century technology, was invented in the 17th century, but we now know that Archimedes was approaching that crucial discovery. He talked about infinity, which is an essential concept of calculus. “We always knew that Archimedes was making a step in the direction leading to modern calculus,” says Netz. “What we have found right now is that, in a sense, Archimedes was already there. He already did develop a special tool with which you can sum up infinitely many objects and measure a volume.”

“If the mathematicians and scientists of the Renaissance had been aware of these discoveries of Archimedes, this could have had a tremendous impact on the development of mathematics,” says mathematician Chris Rorres. “We could have been on Mars today. We could have accomplished all of the things that people are predicting for a century from now. You would basically be raising the tide by increasing the knowledge of mathematics several hundred years ago.”

There’s a lot we need to know?how much of it is things we knew in the past but have now forgotten?

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