Lofty Quotes (12 quotes)

Accurate and minute measurement seems to the non-scientific imagination, a less lofty and dignified work than looking for something new. But nearly all the grandest discoveries of science have been but the rewards of accurate measurement and patient long-continued labour in the minute sifting of numerical results.

I have enjoyed the trees and scenery of Kentucky exceedingly. How shall I ever tell of the miles and miles of beauty that have been flowing into me in such measure? These lofty curving ranks of lobing, swelling hills, these concealed valleys of fathomless verdure, and these lordly trees with the nursing sunlight glancing in their leaves upon the outlines of the magnificent masses of shade embosomed among their wide branches—these are cut into my memory to go with me forever.

Mathematics may, like poetry or music, “promote and sustain a lofty habit of mind.”

Men have called me mad; but the question is not yet settled, whether madness is or is not the loftiest intelligence—whether much that is glorious—whether all that is profound—does not spring from disease of thought—from moods of mind exalted at the expense of the general intellect.

Not in the ground of need, not in bent and painful toil, but in the deep-centred play-instinct of the world, in the joyous mood of the eternal Being, which is always young, science has her origin and root; and her spirit, which is the spirit of genius in moments of elevation, is but a sublimated form of play, the austere and lofty analogue of the kitten playing with the entangled skein or of the eaglet sporting with the mountain winds.

The ancients had a taste, let us say rather a passion, for the marvellous, which caused … grouping together the lofty deeds of a great number of heroes, whose names they have not even deigned to preserve, and investing the single personage of Hercules with them. … In our own time the public delight in blending fable with history. In every career of life, in the pursuit of science especially, they enjoy a pleasure in creating Herculeses.

The majority of mathematical truths now possessed by us presuppose the intellectual toil of many centuries. A mathematician, therefore, who wishes today to acquire a thorough understanding of modern research in this department, must think over again in quickened tempo the mathematical labors of several centuries. This constant dependence of new truths on old ones stamps mathematics as a science of uncommon exclusiveness and renders it generally impossible to lay open to uninitiated readers a speedy path to the apprehension of the higher mathematical truths. For this reason, too, the theories and results of mathematics are rarely adapted for popular presentation … This same inaccessibility of mathematics, although it secures for it a lofty and aristocratic place among the sciences, also renders it odious to those who have never learned it, and who dread the great labor involved in acquiring an understanding of the questions of modern mathematics. Neither in the languages nor in the natural sciences are the investigations and results so closely interdependent as to make it impossible to acquaint the uninitiated student with single branches or with particular results of these sciences, without causing him to go through a long course of preliminary study.

The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses …

The most part of leaves pour out the greatest quantity of this dephlogisticated air [oxygen] from their under surface, principally those of lofty trees.

The rudest numerical scales, such as that by which the mineralogists distinguish different degrees of hardness, are found useful. The mere counting of pistils and stamens sufficed to bring botany out of total chaos into some kind of form. It is not, however, so much from counting as from measuring, not so much from the conception of number as from that of continuous quantity, that the advantage of mathematical treatment comes. Number, after all, only serves to pin us down to a precision in our thoughts which, however beneficial, can seldom lead to lofty conceptions, and frequently descend to pettiness.

To the east was our giant neighbor Makalu, unexplored and unclimbed, and even on top of Everest the mountaineering instinct was sufficient strong to cause me to spend some moments conjecturing as to whether a route up that mountain might not exist. Far away across the clouds the great bulk of Kangchenjunga loomed on the horizon. To the west, Cho Oyu, our old adversary from 1952, dominated the scene and we could see the great unexplored ranges of Nepal stretching off into the distance. The most important photograph, I felt, was a shot down the north ridge, showing the North Col and the old route that had been made famous by the struggles of those great climbers of the 1920s and 1930s. I had little hope of the results being particularly successful, as I had a lot of difficulty in holding the camera steady in my clumsy gloves, but I felt that they would at least serve as a record. After some ten minutes of this, I realized that I was becoming rather clumsy-fingered and slow-moving, so I quickly replaced my oxygen set and experience once more the stimulating effect of even a few liters of oxygen. Meanwhile, Tenzing had made a little hole in the snow and in it he placed small articles of food – a bar of chocolate, a packet of biscuits and a handful of lollies. Small offerings, indeed, but at least a token gifts to the gods that all devoted Buddhists believe have their home on this lofty summit. While we were together on the South Col two days before, Hunt had given me a small crucifix that he had asked me to take to the top. I, too, made a hole in the snow and placed the crucifix beside Tenzing’s gifts.

What is mathematics? What is it for? What are mathematicians doing nowadays? Wasn't it all finished long ago? How many new numbers can you invent anyway? Is today’s mathematics just a matter of huge calculations, with the mathematician as a kind of zookeeper, making sure the precious computers are fed and watered? If it’s not, what is it other than the incomprehensible outpourings of superpowered brainboxes with their heads in the clouds and their feet dangling from the lofty balconies of their ivory towers?

Mathematics is all of these, and none. Mostly, it’s just different. It’s not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life.

Mathematics is all of these, and none. Mostly, it’s just different. It’s not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life.