At the dawn of the twentieth century, it was already clear that, chemically speaking, you and I are not much different from cans of soup. And yet we can do many complex and even fun things we do not usually see cans of soup doing.
Artin very wisely identifies these matrix groups as more fundamental–and they are. They come up much more in mathematics. Linear algebra is the central subject of mathematics. You cannot learn too much linear algebra. That’s the basic principle for all of you going on in mathematics.
Linear algebra is presented as sort of stupid stuff, [but] you cannot learn too much linear algebra.
Benedict Gross, Ph.D., George Vasmer Leverett Professor of Mathematics, Harvard University
in Abstract Algebra, Lecture 2 at 14:25 via Harvard Extension
Quite often in science we get a bit ahead of ourselves and begin theorizing wildly, which can very often be an excellent thought experiment in and of itself. But without some data to give proof to our theorems, we can be easily sidedtracked. Never have I read a statement so poetically phrased to admonish against it as I have recently:
So, we’d better bridle our speculations, lest we run the risk that someone like LeCarre’s Smiley asks us one day: ‘What dreams did you cherish that had so little of the world in them?’
Possibly one of the oddest closing sentences of a technical book–and a very good one at that–I’ve ever read:
This pressure can be calculated by minimizing the Helmholtz function of the system. Details can be found in Fermi’s textbook on thermodynamics (Fermi 1956). But why does osmosis explain the behavior of a salted cucumber? This question is left to the reader as a parting gift.
To establish a place of work where engineers can feel the joy of technical innovation, be aware of their mission to society, and work to their heart’s content.
Masara Ibuka (—), co-founder of Sony Corporation
on the first “Purposes of Incorporation” of Sony
Nominated for quote of the week, which I encountered while reading Matt Ridley’s The Rational Optimist:
He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.
Thomas Jefferson (—), American Founding Father and the principal author of the Declaration of Independence (1776)
in a letter to Isaac McPherson
The chessboard is the world; the pieces are the phenomena of the universe; the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake or makes the smallest allowance for ignorance.
…[the reader] should not be discouraged, if on first reading of section 0, he finds that he does not have the prerequisites for reading the prerequisites.
Paul Halmos (1916 – 2006, Hungarian-born American mathematician
in Measure Theory (1950)
This is essentially the mathematician’s equivalent of the adage “Fake it ’til you make it.”
