[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.

A man was famous according as he had lifted up axes upon the thick trees.

Archimedes, who combined a genius for mathematics with a physical insight, must rank with Newton, who lived nearly two thousand years later, as one of the founders of mathematical physics. … The day (when having discovered his famous principle of hydrostatics he ran through the streets shouting Eureka! Eureka!) ought to be celebrated as the birthday of mathematical physics; the science came of age when Newton sat in his orchard.

His “Mathematical Games” column in Scientific American is one of the few bridges over C.P. Snow’s famous “gulf of mutual incomprehension’' that lies between technical and literary cultures.

In the Vienna of the late 1920s and 1930s there throve an internationally famous philosophical bunch called the logical positivists. … They said that a key ingredient of knowledge was “sense data,” and proclaimed emphatically, in the words of … J.S.L. Gilmour, that sense data are “objective and unalterable.” …Good guess, but no cigar!

It has been said by a distinguished philosopher that England is “usually the last to enter into the general movement of the European mind.” The author of the remark probably meant to assert that a man or a system may have become famous on the continent, while we are almost ignorant of the name of the man and the claims of his system. Perhaps, however, a wider range might be given to the assertion. An exploded theory or a disadvantageous practice, like a rebel or a patriot in distress, seeks refuge on our shores to spend its last days in comfort if not in splendour.

Laplace’s equation is the most famous and most universal of all partial differential equations. No other single equation has so many deep and diverse mathematical relationships and physical applications.

No matter how far you have wandered hitherto, or how many famous gorges and valleys you have seen, this one, the Grand Cañon of the Colorado, will seem as novel to you, as unearthly in the color and grandeur and quantity of its architecture, as if you have found it after death, on some other star.

Time will soon destroy the works of famous painters and sculptors, but the Indian arrowhead will balk his efforts and Eternity will have to come to his aid. They are not fossil bones, but, as it were, fossil thoughts, forever reminding me of the mind that shaped them… . Myriads of arrow-points lie sleeping in the skin of the revolving earth, while meteors revolve in space. The footprint, the mind-print of the oldest men.

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.

Western field-work conjures up images of struggle on horseback ... –toughing it out on one canteen a day as you labor up and down mountains. The value of a site is supposedly correlated with the difficulty of getting there. This, of course, is romantic drivel. Ease of access is no measure of importance. The famous La Brea tar pits are right in downtown Los Angeles. To reach the Clarkia lake beds, you turn off the main road at Buzzard’s Roost Trophy Company and drive the remaining fifty yards right up to the site.

When Faraday filled space with quivering lines of force, he was bringing mathematics into electricity. When Maxwell stated his famous laws about the electromagnetic field it was mathematics. The relativity theory of Einstein which makes gravity a fiction, and reduces the mechanics of the universe to geometry, is mathematical research.