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The Gaussian-School of Higher-Arithmetic (1831, updated 2022); tutorial #19.

The founding father of the Gaussian School of Higher-Arithmetic was presumably blocked by radian fixation, this prevented him from completing his ideas.

In fact, Gauss almost hid his great breakthrough for two possible reasons; 1) he was upset that Sophie Germain (his doctoral student) was dying without her well-deserved doctorate in math's (for her thesis on the Strong Primes) and 2) he wished to retain his huge lead. In any case, he did not make himself that clear.

JCF Gauss; 2nd letter to the Royal Society, 1831.  C. NOTICE ON THE THEORY OF BIQUADRACTIC RESIDUES.

Paragraph 24, the first three sentences of his last paragraph in a long tedious paper.


[24] "We have believed that we were doing the friends of mathematics a favour by this account of the principal parts of a new theory of so-called imaginary quantities. If one formerly contemplated this subject from a false point of view and therefore found a mystery darkness, this is in large part attributable to clumsy terminology. Had one not called +1, -1, square-root of -1, positive, negative, or imaginary (or even impossible) units, but instead, say, direct, inverse, or lateral units, then there could scarcely have been talk of such darkness".

The text shown in blue font above was translated from the Latin by William Ewald within his masterwork; From Kant to Hilbert, A Source Book in the Foundations of Mathematics VOLUME 1, OUP 1999. This appears on page 313 of the paperback edition. Try to follow that little lot when read out in Latin. By 1831, almost no mathematicians, other than say Gauss, were still fluent in Latin, but in 1831 no lofty academic could dare to admit to that.


We (as in "the Royal We") are the mathematicians here; you others are merely "the friends". Clearly, Gauss was just "taking the Mickey" and being as unhelpful as his great sense of mathematical-fun and conscience could permit him. Had the great man ever deigned to leave his observatory to speak at the Royal Society, then there would have been flags, trumpets and a packed house, but this was read out to a handful of half-asleep math's fellows who were too tired to retire to the bar (blink, and you missed it).

Continue with your pre-qualification tutorial required for qr-physics; level-101; GUT.
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