Quotes About Mathematics

Derivatives're just trig with some imagination.

But what G. Cantor posits as the defining formal property of an infinite set is that such a set can be put in a 1-1C with at least one of its proper subsets. Which is to say that an infinite set can have the same cardinal number as its proper subset, as in Galileo's infinite set of all positive integers and that set's proper subset of all perfect squares, which latter is itself an infinite set.

Möbius Strips. Year of the Whopper. Latrodectus Mactans Productions. 'Hugh G. Section,' Pam Heath, 'Bunny Day,' 'Taffy Appel'; 35 mm.; 109 minutes black and white; sound. Pornography-parody, possible parodic homage to Fosse's All That Jazz, in which a theoretical physicist ('Reaction'), who can only achieve mathematical insight during coitus, conceives of Death as a lethally beautiful woman (Heath). INTERLACE TALENT FEATURE CARTRIDGE #357-65-32 (Y.W.)

Specifically, Aristotle claims that no spatial extension (e.g. the intercurb interval AB) is 'actually infinite,' but that all such extensions are 'potentially infinite' in the sense of being infinitely divisible.

Like most religious mathematicians from Pythagoras to Godel, Bolzano believes that math is the Language of God and that profound metaphysical truths can be derived and proved mathematically.

The extreme mathematical weirdness of (infinity), which Galileo spends a lot of time in TNS giving examples of, is rather presciently attributed to epistemology instead of metaphysics. Paradoxes arise, according to G.G.'s mouthpiece, only when we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited.

but let's emphasize once more here that G. Cantor is, like R. Dedekind, a mathematical Platonist; i.e., he believes that both infinite sets and transfinite numbers really exist, as in metaphysically, and that they are reflected in actual real-world infinities.....

In other words, Cantor is able to show that real numbers themselves can serve as the limits of fundamental sequences of reals, meaning his system of definitions is self-enclosed and VIR-proof.

Mathematical thinking is abstract, but it's also thoroughly private-sector and results-oriented.

The closest conventional analogue I could derive for this figure was a cycloid, L'Hôpital's solution to Bernoulli's famous Brachistochrone Problem, the curve traced by a fixed point on the circumference of a circle rolling along a continuous plane.

One of the great Greek contributions to the very concept of mathematics was the conscious recognition and emphasis of the fact that mathematical entities are abstractions, ideas entertained by the mind and sharply distinguished from physical objects or pictures.

It may be that mathematics is not generally recognized as one of the arts precisely because so much pyramidal training and practice is required in order to appreciate its aesthetics; math is perhaps the ultimate in acquired tastes.

We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences.

Naturally, the significant results that legitimize a mathematical theory take time to derive, and then even more time to be fully accepted, and of course throughout this time the Insanity-v.-Genius question remains undecided, probably even for the mathematician himself, so that he's developing his theory and cooking his proofs under conditions of enormous personal stress and doubt, and sometimes isn't even vindicated in his own lifetime, etc.

The work that interests me is done with a pencil and a sheet of paper. Rarely even a calculator. At the cutting edge of electrical engineering, almost everything interesting is resolved via the manipulation of variables.

Chesterton above is wrong in one respect. Or at least imprecise. The danger he's trying to name is not logic. Logic is just a method, and methods can't unhinge people. What Chesterton's really trying to talk about is one of logic's main characteristics—and mathematics'. Abstractness. Abstraction.

Mathematical thinking is abstract, but it's also thoroughly private-sector and results-oriented. The difference between a brilliant, revolutionary mathematical theory and a wacko one lies, therefore, in what-all can be done with it, in whether or not it yields significant results.

I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.

I had a feeling once about Mathematics, that I saw it all—Depth beyond depth was revealed to me—the Byss and the Abyss.

Der Satz der Mathematik drückt keinen Gedanken aus.

She wore a short skirt and a tight sweater and her figure described a set of parabolas that could cause cardiac arrest in a yak.

Like Bertrand Russell, I feel a great sadness for the human race. Unlike Bertrand Russell, I can't do long division.

No es acaso el amor una asombrosa, y a veces milagrosa, conjunción de patrañas? ¿No es exacto que menos por menos da más?

And so, in that Greek letter that looks like a shack with a corrugated tin roof, in that elusive, irrational number with which scientists try to understand the universe, I found refuge.