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He gave us his "Curves and Functions", in the form of lectures; and sometimes, even while stating his propositions, he would be seized with some mathematical inspiration, would forget pupils, notes, everything, and would rapidly dash off equation after equation, following them out with smaller and smaller chalk-marks into the remote corners of the blackboard, forsaking his delightful task only when there was literally no more space to be covered, and coming back with a sigh to his actual students. There was a great fascination about these interruptions; we were present, as it seemed, at mathematics in the making; it was like peeping into a necromancer's cell, and seeing him at work; or as if our teacher were one of the old Arabian algebraists recalled to life.
--
Thomas Wentworth Higginson, as quoted in The Early Years of the Saturday Club, 1855-1870 (1918) by Edward Waldo Emerson

 

Benjamin Peirce

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One of the most frequently mentioned equations was Euler's equation, Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty"; and "mind-blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing?" The equation contains nine basic concepts of mathematics — once and only once — in a single expression. These are: e (the base of natural logarithms); the exponent operation; ?; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero.

 

Leonhard Euler

 

This is a mathematical universe. We are surrounded by equations and summations. Your life: the current state of your life and life itself is a direct summation of the equation you have created. Your life is a reflection of many choices you have made at the innumerable amount of choice-points you've crossed. Great endeavors are the summation of a great and deliberate equation.

 

Steve Maraboli

 

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

 

Nikola Tesla

 

Looking back over the space of fifty years since I entered Harvard College, Benjamin Peirce still impresses me as having the most massive intellect with which I have ever come in contact, and as being the most profoundly inspiring teacher I ever had. ... As soon as he had finished the problem or filled the blackboard he would rub everything out and begin again. He was impatient of detail, and sometimes the result would not come out right; but instead of going over his work to find the error, he would rub it out, saying that he had made a mistake in a sign somewhere, and that we should find it when we went over our notes. Described in this way it may seem strange that such a method of teaching should be inspiring; yet to us it was so to the highest degree. We were carried along by the rush of his thought, by the ease and grasp of his intellectual movement. The inspiration came, I think, partly from his treating us as highly competent pupils, capable of following his line of thought even through errors in transformations; partly from his rapid and graceful methods of proof, which reached a result with the least number of steps in the process, attaining thereby an artistic or literary character; and partly from the quality of his mind which tended to regard any mathematical theorem as a particular case of some more comprehensive one, so that we were led onward to constantly enlarging truths.

 

Benjamin Peirce

 

Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, . I hope that this will not scare off half of my potential readers.

 

Stephen Hawking