Functional Analysis Quotes

“[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.”
― Paul R. Halmos

“I explain it to clients this way: “Sometimes it’s hard to know what our payoffs are for doing this stuff—­there could be so many different factors involved—­but basically all of our payoffs boil down to just four things: (1) we get away from something we don’t want; (2) we get something that we do want; (3) we get to escape unwanted feelings; (4) we get to feel good. Often our payoffs are a mixture of all those things.Do you think any of those apply to you in this case?”
[...] Remember, there will always be reinforcing consequences for any type of away move—­otherwise the behavior would cease. So the more entrenched the problematic behavior, the more important it is to raise clients’ awareness of these payoffs, and then validate them: “So there are real benefits to you, in the short term, such as…” After that, we can compassionately and respectfully help the client to contact the costs and explore if the behavior is “workable” (in other words, working to give her the life she wants in the long term).”
― Russ Harris, ACT Questions and Answers: A Practitioner's Guide to 150 Common Sticking Points in Acceptance and Commitment Therapy