David Cox - Collected Quotes

"Statistical methods of analysis are intended to aid the interpretation of data that are subject to appreciable haphazard variability." (David V. Hinkley & David Cox, "Theoretical Statistics", 1974)

"[…] it does not seem helpful just to say that all models are wrong. The very word model implies simplification and idealization. The idea that complex physical, biological or sociological systems can be exactly described by a few formulae is patently absurd. The construction of idealized representations that capture important stable aspects of such systems is, however, a vital part of general scientific analysis and statistical models, especially substantive ones, do not seem essentially different from other kinds of model." (David Cox, "Comment on ‘Model uncertainty, data mining and statistical inference’", Journal of the Royal Statistical Society, Series A 158, 1995)

"Besides being great history, Galois theory is also great mathematics. This is due primarily to two factors: first, its surprising link between group theory and the roots of polynomials, and second, the elegance of its presentation. Galois theory is often described as one of the most beautiful parts of mathematics." (David A Cox, "Galois Theory" 2nd Ed., [preface] 2012)

"In most courses on group theory, students usually study cosets and Lagrange's Theorem in one part of the course and group actions in another. Pedagogically, this makes sense, but it is also important to remember that historically, things are often more complicated. In considering resolvent polynomials, Lagrange had to deal with many issues all at once. It is a testament to his power as a mathematician that Lagrange could see what was important and thereby enable his successors to sort out the details of what he did." (David A Cox, "Galois Theory" 2nd Ed., 2012)

"Insolving the cubic and quartic equations, Cardan and Ferrari implicitly assumed the existence of roots [...]. Girard, in the early seventeenth century, was one of the first to assert the existence of roots, real or imaginary, though 'imaginary root' did not have a clear meaning in his work. As people became more comfortable with complex numbers, the existence of roots evolved into the existence of complex roots, which come in complex conjugate pairs when the coefficients are real. Thus the eighteenth-century version of the Fundamental Theorem of Algebra asserts that every nonconstant polynomial in R[x] factors into linear and quadratic factors with coefficients in R." (David A Cox, "Galois Theory" 2nd Ed., 2012)

"The early history of group theory and Galois theory are closely related - after all, Galois was the person who introduced the term 'group' into mathematics. So it is not surprising that notions like Abelian equations from Galois theory influenced the terminology of group theory." (David A Cox, "Galois Theory" 2nd Ed., 2012)

"The extension problem in group theory asks whether it is possible to classify all extensions of H by G. This is a difficult problem and is one of the reasons why groups are hard to classify. The extension problem is also related to group cohomology." (David A Cox, "Galois Theory" 2nd Ed., 2012)

"The moral is that cubic equations forced mathematicians to confront complex numbers. For quadratic equations, one could pretend that complex solutions don't exist. But for a cubic with real roots, we've seen that Cardan's formula must involve complex numbers. So it is impossible to ignore complex numbers in this case." (David A Cox, "Galois Theory" 2nd Ed., 2012)