“Were you born inhuman, or did you grow so by degrees — M. S., M. D., Ph. D…”

Vorkosigan Saga, Falling Free (1988)

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Lois McMaster Bujold 383
Science Fiction and fantasy author from the USA 1949

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“My dissertation for the Ph. D. degree at the University of Michigan was on applications of vectorial methods to metric geometry (in the sense of the Menger school), especially with a view to the merging of metric geometry in that sense with differential geometry. Professor S B Myers at the University of Michigan sponsored my dissertation, but I was particularly close to R L Wilder there.”

Leonard Jimmie Savage (1917–1971) American mathematician

Leonard Jimmie Savage, cited in: W.A. Wallis, "Leonard Jimmie Savage 1917-1971," in E Shils (ed.), Remembering the University of Chicago: teachers, scientists, and scholars. (University of Chicago Press, Chicago, 1991), 436-451; Quoted in: J J O'Connor and E F Robertson, " Leonard Jimmie Savage http://www-history.mcs.st-and.ac.uk/Biographies/Savage.html," at history.mcs.st-and.ac.uk, November 2010.

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“Lety5 - ay4 + by3 - cy2 + dy - e = 0be the general equation of the fifth degree and suppose that it can be solved algebraically,—i. e., that y can be expressed as a function of the quantities a, b, c, d, and e, composed of radicals. In this case, it is clear that y can be written in the formy = p + p1R1/m + p2R2/m +…+ pm-1R(m-1)/m,m being a prime number, and R, p, p1, p2, etc. being functions of the same form as y. We can continue in this way until we reach rational functions of a, b, c, d, and e. [Note: main body of proof is excluded]
…we can find y expressed as a rational function of Z, a, b, c, d, and e. Now such a function can always be reduced to the formy = P + R1/5 + P2R2/5 + P3R3/5 + P4R4/5, where P, R, P2, P3, and P4 are functions or the form p + p1S1/2, where p, p1 and S are rational functions of a, b, c, d, and e. From this value of y we obtainR1/5 = 1/5(y1 + α4y2 + α3y3 + α2y4 + α y5) = (p + p1S1/2)1/5,whereα4 + α3 + α2 + α + 1 = 0.Now the first member has 120 different values, while the second member has only 10; hence y can not have the form that we have found: but we have proved that y must necessarily have this form, if the proposed equation can be solved: hence we conclude that
It is impossible to solve the general equation of the fifth degree in terms of radicals.
It follows immediately from this theorem, that it is also impossible to solve the general equations of degrees higher than the fifth, in terms of radicals.”

Niels Henrik Abel (1802–1829) Norwegian mathematician

A Memoir on Algebraic Equations, Proving the Impossibility of a Solution of the General Equation of the Fifth Degree (1824) Tr. W. H. Langdon, as quote in A Source Book in Mathematics (1929) ed. David Eugene Smith

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“There would be cases where we would not want to accept an hypothesis even though the evidence gives a high d. c. [degree of confirmation] score, because we are fearful of the consequences of a wrong decision.”

C. West Churchman (1913–2004) American philosopher and systems scientist

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“Every one, though born of God in an instant, yet undoubtedly grows by slow degrees.”

John Wesley (1703–1791) Christian theologian

Letter (27 June 1760), published in The Works of the Rev. John Wesley (1813) Vol. XVI, p. 109
As quoted in an 1856 edition of Works
General sources
Variant: Every one, though born of God in an instant, yea, and sanctified in an instant, yet undoubtedly grows by slow degrees.

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