His patterns, like the painter’s or the poet’s must be beautiful the ideas, like the colors or the words, must fit together in a harmonious way.” - English mathematician G. If his patterns are more permanent than theirs, it is because they are made of ideas. “A mathematician, like a painter or a poet, is a maker of patterns. Schaaff, author and mathematics education professor “Mathematics is on the artistic side a creation of new rhythms, orders, designs, harmonies, and on the knowledge side, is a systematic study of various rhythms, orders, designs and harmonies.” - William L. “We do not listen with the best regard to the verses of a man who is only a poet, nor to his problems if he is only an algebraist īut if a man is at once acquainted with the geometric foundation of things and with their festal splendor, his poetry is exact and his arithmetic music.” -19 th century American philosopher/writer Ralph Waldo Emerson, Society and Solitude, Ch. 7, Works and Days van der Waerden , describing the beliefs of the followers of Pythagoras
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Whosoever acquires full understanding of this number harmony, he becomes himself divine and immortal.” –20 th century Dutch mathematician B. Harmony is divine, it consists of numerical ratios. “It is harmony which restores unity to the contrasting parts and which moulds them into a cosmos. We just have to put intelligence behind the entertainment.” - North Carolina State University’s James Lester, quoted at the 12th International Conference on College Teaching and Learning “In the future, we can expect that not much difference will exist between education and entertainment. “Educators have always known that learning and life are maximal where play and work coincide.” - L.
“Musical training is a more potent instrument than any other, because rhythm and harmony find their way into the inward places of soul, on which they mightily fasten, imparting grace, and making the soul of him who is rightly educated graceful…” - classical Greek philosopher Plato (428-348 BCE), The Republic, III “If all art aspires to the condition of music, all the sciences aspire to the condition of mathematics.” – Spanish philosopher/writer George Santayana (1863-1952) “May not music be described as mathematics of the sense, mathematics as music of the reason?” –19 th century English mathematician James Joseph Sylvester, On Newton’s Rule for the Discovery of Imaginary Roots Collected Mathematical Papers, Vol. “Mathematics and music, the most sharply contrasted fields of scientific activity which can be found, and yet related, supporting each other, as if to show forth the secret connection which ties together all the activities of our mind, and which leads us to surmise that the manifestations of the artist’s genius are but the unconscious expressions of a mysteriously acting rationality.” –19 th century German physician and physicist Hermann von Helmholtz, Vorträgeund Reden, Bd. “Music is the pleasure the human soul experiences from counting without being aware that it is counting.” - German mathematician and philosopher Gottfried Wilhelm von Leibniz (1646-1716) who co-discovered calculus
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