The portrait of Euler that emerges from his publications and letters is that of a genial man of simple tastes and conventional religious faith. He was even wealthy, at least in the second half of his life, but ostentation was not part of his lifestyle. His memory was prodigious, and contemporary accounts have emphasized this. He would delight relatives, friends, and acquaintances with a literal recitation of any song from Virgil’s Aenesis, and he would remember minutes of Academy meetings years after they were held. He was not given to envy, and when someone made an advance on his work his happiness was genuine. For example, when he learnt of Lagrange’s improvements on his work on elliptic integrals, he wrote to him that his admiration knew no bounds and then proceeded to improve upon Lagrange!
But, what is most characteristic of his work is its clarity and openness. He never tries to hide the difficulties from the reader. This is in stark contrast to Newton, who was prone to hide his methods in obscure anagrams, and even from his successor, Gauss, who very often erased his steps to present a monolithic proof that was seldom illuminating. In Euler’s writings there are no comments on how profound his results are, and in his papers one can follow his ideas step by step with the greatest of ease. Nor was he chary of giving credit to others; his willingness to share his summation formula with Maclaurin, his proper citations to Fuguano when he started his work on algebraic integrals, his open admiration for Lagrange when the latter improved on his work in calculus of variations are all instances of his serene outlook. One can only contrast this with Gauss’s reaction to Bolyai’s discovery of non-Euclidean postulates. Euler was secure in his knowledge of what he had achieved but never insisted that he should be the only one on top of the mountain.
Perhaps, the most astounding aspect of his scientific opus is its universality. He worked on everything that had any bearing on mathematics. For instance, his early training under Johann Bernoulli did not include number theory; nevertheless, within a couple of years after reaching St. Petersburg he was deeply immersed in it, recreating the entire corpus of Fermat’s work in that area and then moving well beyond him. His founding of graph theory as a separate discipline, his excursions in what we call combinatorial topology, his intuition that suggested to him the idea of exploring multizeta values are all examples of a mind that did not have any artificial boundaries. He had no preferences about which branch of mathematics was dear to him. To him, they were all filled with splendour, or Herrlichkeit, to use his own favourite word.
Hilbert and Poincare were perhaps last of the universalists of modern era. Already von Neumann had remarked that it would be difficult even to have a general understanding of more than a third of the mathematicians of his time. With the explosive growth of mathematics in the twentieth century we may never see again the great universalists. But who is to say what is and is not possible for the human mind?
It is impossible to read Euler and not fall under his spell. He is to mathematics what Shakespeare is to literature and Mozart to music: universal and sui generis.
Reference:
Euler Through Time: A New Look at Old Themes by V S Varadarajan:
Hindustan Book Agency;
http://www.hindbook.com/index.php/euler-through-time-a-new-look-at-old-themes;
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up to a million digits and these ways are used to test the efficiency and efficacy of supercomputers.