Continued from Part 1
William Dunham has some descriptions about Leonhard Euler's incredible abilities in his book Journey through Genius:
"Euler's collected works fill over 70 large volumes, a testament to the genius of this unassuming Swiss citizen who changed the face of mathematics so profoundly. Indeed, one's first inclination, upon encountering the volume and quality of his work, is to regard his story as an exaggerated piece of fiction rather than hard historical fact.
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Throughout his career, Euler was blessed with a memory that can only be called phenomenal. His number-theoretic investigations were aided by the fact that he had memorized not only the first 100 prime numbers but also all of their squares, their cubes, and their fourth, fifth, and sixth powers. While others were digging through tables or pulling out pencil and paper, Euler could simply recite from memory such quantities as 2414 or 3376. But this was the least of his achievements. He was able to do difficult calculations mentally, some of these requiring him to retain in his head up to 50 places of accuracy! The Frenchman Francois Arago said that Euler calculated without apparent effort, 'just as men breathe, as eagles sustain themselves in the air.' Yet this extraordinary mind still had room for a vast collection of memorized facts, orations, and poems, including the entire text of Virgil's Aeneid, which Euler had committed to memory as a boy and still could recite flawlessly half a century later. No writer of fiction would dare to provide a character with a memory of this caliber.
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Incredible as it sounds, it has been estimated that, if one were to collect all publications in the mathematical sciences produced over the last three-quarters of the eighteenth century, roughly one-third of these were from the pen of Leonhard Euler!
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Before he was done, Euler's number theory filled four large volumes of his Opera Omnia [Collected Works]. It has been observed that, had he done nothing else in his scientific career, these four volumes would place him among the greatest mathematicians of history."
From the way Euler wrote, it also seems like he solved problems in the act of writing about them. It should also be mentioned that Euler had 13 children and could work on mathematics with his children playing around him and Von Neumann could work well in loud, smoke-filled environments, so they didn't need quiet environments to concentrate.
Not only that, Euler became blind in one eye at age 31 and then completely blind at 59 and still he continued to churn out mathematics.
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