Mathematical mystery of ancient Babylonian clay tablet solved
Rene Descartes (0:40:35 – 0:41:31) [Inventor of Cartesian coordinate system]
“We see that the old geometers have made use of a kind of an analysis which they extended to the solution of all problems. Albeit they have hidden it from posterity. I well realize that they must have known a kind of mathematics that was very different from today’s common one, not that I think they knew it perfectly. And indeed some traces of this true mathematics seem to me still to appear in Pappus, who, though not belonging to the most ancient ages, lived many centuries before our times. I would also think that later on it was suppressed by its very authors because of a certain wicked slyness.”
Gottfried Leibniz: (0:46:18 – 0:46:55) [Inventor of calculus]
“The ancients seem to have recognized and possessed such an analysis proper to geometry, for in their works I think I can make out some vestiges of it, namely of an algebra in which numbers are not the issue. Certainly it is by this art that they unfolded those propositions otherwise we would not have had them for such a long time which only with difficulty would we find by using our modern methods. I think I have attained and discovered the foundation and first lineaments of this art with which, once we have found the right symbols and established some principles, we can obtain everything else by an imitation of calculating, and with no need to follow the lines with our imagination, the result which I’m not sure even the ancients have ever attained.”
Isaac Newton (0:43:39 - 0:44:18) [Inventor of calculus]
“To be sure, the ancients’ method is more elegant by far than the Cartesian one, for Descartes achieved the result by an algebraic calculus which when transfused into words, following the practice of the ancients in their writings, would prove to be so tedious and entangled as to provoke nausea; nor might it be understood. But they accomplished it by certain simple proportions, judging that nothing written in a different style is willing to be read, and in consequence concealing the analysis by which they found their construction.”
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