It is given to us to live for the most part under the guidance of mathematics ... It is impossible to distinguish from other living creatures anyone who does not understand how to quantify.
A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?
Here is a quilted book about mathematical practice, each patch wonderfully prepared. Part invitation to number theory, part autobiography, part sociology of mathematical training, Mathematics without Apologies brings us into contemporary mathematics as a living, active inquiry by real people. Anyone wanting a varied, cultured, and penetrating view of today's mathematics could find no better place to engage.
A true soldier does not argue as he marches, how success is going to be ultimately achieved. But he is confident that if he only plays his humble part well, somehow or other the battle will be won. In is that spirit that every one of us should act. It is not given to us to know the future. But it is given to everyone of us to know how to do our own part well.
Most people have forgotten how to live with living creatures, with living systems and that, in turn, is the reason why man, whenever he comes into contact with nature, threatens to kill the natural system in which and from which he live.
How much is enough? How much does anyone require? Can I be both kind and tough? Can I put faith before desire? Right now, for all time, I vow to try . . . I volunteer to be simple, I volunteer to love, Every living thing like a mountain stream that flows out o'er the land. I volunteer for the journey from here to heaven's gate. I will do my part I place my heart in Your gracious hands . . . How then shall we live? Let us live lightly as a feather. How much shall we give? Let us give everything, together One heart, one mind, all humankind... I volunteer.
It's impossible to live a life totally free of feelings. God created all of us to be emotional creatures, and feelings are a big part of our lives.
So that, in effect, religion, which should most distinguish us from beasts, and ought most peculiarly to elevate us, as rational creatures, above brutes, is that wherein men often appear most irrational, and more senseless than beasts themselves.
The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.
Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.
How we live our lives does not,unfortunately depend on us alone.Circumstances,good or bad,constantly intervene.A person close to us die.A person not so close to us carries on living.All these things affect how we live.
Part of the problem is that we have become so dependent upon this system that is killing and exploiting us, it has become almost impossible for us to imagine living outside of it, and it's very difficult physically for us to live outside of it.
The mathematics is the odd one, odd because I'm not sure how to measure its effect. It is so fundamental to my outlook on everything and yet I'm not even sure how. It must be because in my formative years it was everything to me, the single place of beauty in my life, and of breathtaking beauty at that. I still believe that pure mathematics is the most creative thing that humanity does, though I am no longer a part of it.
Crucially we haven't been figuring out how to live in oneness, with the Earth & every other living thing; we have just been insanely trying to figure out how to live with each other, billions of each other, only we're not living with each other our crazy selves are living with each other, and perpetuating an epidemic of disconnection.
God has given us everything we need for life and godliness. And he's given us the indwelling strength and guidance of the Holy Spirit. The rest is up to us.
Like living creatures, automobiles expired when their environment became saturated with their own excreta. We ourselves are living creatures. We don't want the same to happen to us.
Consider the subtleness of the sea; how its most dreaded creatures glide under water, unapparent for the most part, and treacherously hidden beneath the loveliest tints of azure. Consider also the devilish brilliance and beauty of many of its most remorseless tribes, as the dainty embellished shape of many species of sharks. Consider, once more, the universal cannibalism of the sea; all whose creatures prey upon each other, carrying on eternal war since the world began.