These are random thoughts and quotes that I stumble upon here and there and have seemed thought provoking to me.

[in no particular order]

We do not choose mathematics as our profession, it chooses us.  [Yuri Marin]

I was lucky enough to attend a few lectures of S. S. Chern just before he retired from Berkeley in which he said that the cotangent bundle (differential forms) is the feminine side of analysis on manifolds, and the tangent bundle (vector fields) is the masculine side. Prom this perspective, Hamiltonian mechanics is the feminine side of classical physics, [and] its masculine side is Lagrangian mechanics. [Richard Montgomery ([83], p. 352)]

You do not need to leave your room. Remain sitting at your table and listen. Do not even listen, simply wait, be quiet still and solitary. The world will freely offer itself to you to be unmasked, it has no choice, it will roll in ecstasy at your feet.  [Kafka]

Study nature, love nature, stay close to nature. It will never fail you. [Frank Lloyd Wright]

I’ve made the most important discovery of my life. It’s only in the mysterious equation of love that any logic or reasons can be found. I’m only here tonight because of you. You are the only reason I am… you are all my reasons. [J Nash]

Suppose aliens invade the earth and threaten to obliterate it in a year’s time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world’s best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack. [Paul Erdos]

Every mathematician knows that it is impossible to understand any elementary course in thermodynamics. [V I Arnold]

Religion is an insult to human dignity. With or without it you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion. [Steven Weinberg]

Math is like love – a simple idea but it can get complicated. [R Drabek]

Nine times fall down, Nine times pick yourself up. [Tibetan Saying]

It’s hard to begin, harder is to keep going, and the hardest is to end. [NN]

Mathematics is a process of staring hard enough with enough perseverance at the fog of muddle and confusion to eventually break through to improved clarity. I’m happy when I can admit, at least to myself, that my thinking is muddled, and I try to overcome the embarrassment that I might reveal ignorance or confusion. Over the years, this has helped me develop clarity in some things, but I remain muddled in many others. I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication. – [Bill Thurston, MO]