[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 garden requires patient labor and attention. Plants do not grow merely to satisfy ambitions or to fulfill good intentions. They thrive because some one expended effort on them.

A man may fulfill the object of his existence by asking a question he cannot answer, and attempting a task he cannot achieve.

But we shall not satisfy ourselves simply with improving steam and explosive engines or inventing new batteries; we have something much better to work for, a greater task to fulfill. We have to evolve means for obtaining energy from stores which are forever inexhaustible, to perfect methods which do not imply consumption and waste of any material whatever.

For science, God is simplythe stream of tendency in which all things seek to fulfil the law of their being.

Great spirits have always found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageously uses his intelligence and fulfills the duty to express the results of his thoughts in clear form.

In fulfilling the wants of the public, a manufacturer should keep as far ahead as his imagination and his knowledge of his buying public will let him. One should never wait to see what it is a customer is going to want. Give him, rather, what he needs, before he has sensed that need himself.

In the case of a Christian clergyman, the tragic-comical is found in this: that the Christian religion demands love from the faithful, even love for the enemy. This demand, because it is indeed superhuman, he is unable to fulfill. Thus intolerance and hatred ring through the oily words of the clergyman. The love, which on the Christian side is the basis for the conciliatory attempt towards Judaism is the same as the love of a child for a cake. That means that it contains the hope that the object of the love will be eaten up.

Is science visionary? Is it not the hardest-headed intellectual discipline we know? How, then, does science look at this universe? Always as a bundle of possibilities. Habitually the scientist looks at this universe and every area in it as a bundle of possibilities, with no telling what might come if we fulfilled the conditions. Thomas Edison was no dreamer. He was a seer. The possibilities that he brought out were factually there. They were there before he saw them. They would have been there if he never had seen them. Always the possibilities are part of the actualities in any given situation.

Looking at the thunder machine which had been set up, I saw not the slightest indication of the presence of electricity. However, while they were putting the food on the table, I obtained extraordinary electric sparks from the wire. My wife and others approached from it, for the reason that I wished to have witnesses see the various colors of fire about which the departed Professor Richmann used to argue with me. Suddenly it thundered most violently at the exact time that I was holding my hand to the metal, and sparks crackled. All fled away from me, and my wife implored that I go away. Curiosity kept me there two or three minutes more, until they told me that the soup was getting cold. By that time the force of electricity greatly subsided. I had sat at table only a few minutes when the man servant of the departed Richmann suddenly opened the door, all in tears and out of breath from fear. I thought that some one had beaten him as he was on his way to me, but he said, with difficulty, that the professor had been injured by thunder… . Nonetheless, Mr. Richmann died a splendid death, fulfilling a duty of his profession.

Most of his [Euler’s] memoirs are contained in the transactions of the Academy of Sciences at St. Petersburg, and in those of the Academy at Berlin. From 1728 to 1783 a large portion of the Petropolitan transactions were filled by his writings. He had engaged to furnish the Petersburg Academy with memoirs in sufficient number to enrich its acts for twenty years—a promise more than fulfilled, for down to 1818 [Euler died in 1793] the volumes usually contained one or more papers of his. It has been said that an edition of Euler’s complete works would fill 16,000 quarto pages.

Relatively few benefits have flowed to the people who live closest to the more than 3,000 protected areas that have been established in tropical countries during the past 50 years. For this reason, the preservation of biodiversity is often thought of as something that poor people are asked to do to fulfill the wishes of rich people living in comfort thousands of miles away.

The adequate study of culture, our own and those on the opposite side of the globe, can press on to fulfillment only as we learn today from the humanities as well as from the sciences.

The average English author [of mathematical texts] leaves one under the impression that he has made a bargain with his reader to put before him the truth, the greater part of the truth, and nothing but the truth; and that if he has put the facts of his subject into his book, however difficult it may be to unearth them, he has fulfilled his contract with his reader. This is a very much mistaken view, because effective teaching requires a great deal more than a bare recitation of facts, even if these are duly set forth in logical order—as in English books they often are not. The probable difficulties which will occur to the student, the objections which the intelligent student will naturally and necessarily raise to some statement of fact or theory—these things our authors seldom or never notice, and yet a recognition and anticipation of them by the author would be often of priceless value to the student. Again, a touch of humour (strange as the contention may seem) in mathematical works is not only possible with perfect propriety, but very helpful; and I could give instances of this even from the pure mathematics of Salmon and the physics of Clerk Maxwell.

The experience was more fulfilling than I could have ever imagined. I have a newfound sense of wonder seeing the Earth and stars from such an incredible perspective. Certainly, through my training I was prepared for the technical aspects, but I had no idea that I would be flooded with such amazement and joy after seeing my first sunrise and sunset from space.

The infinite variations in the ways creatures fulfill the same requirement—to fuel energy needs—constantly astound me. Booby birds and pelicans … actually performed underwater dives, descending some twenty feet below the surface and then flapping their wings to fly through water. Totally encrusted with tiny diamond bubbles—like the jeweled nightingales of Asian emperors—they soared around below for nearly half a minute.

The major gift of science to the world is a mighty increase of power. Did science then create that power? Not a bit of it! Science discovered that power in the universe and set it free. Science found out the conditions, fulfilling which, the endless dynamic forces of the cosmos are liberated. Electricity is none of man’s making, but man has learned how to fulfill the conditions that release it. Atomic energy is a force that man did not create, but that some day man may liberate. Man by himself is still a puny animal; a gorilla is much the stronger. Man's significance lies in another realm—he knows how to fulfill conditions so that universal power not his own is set free. The whole universe as man now sees it is essentially a vast system of power waiting to be released.

The United States this week will commit its national pride, eight years of work and $24 billion of its fortune to showing the world it can still fulfill a dream. It will send three young men on a human adventure of mythological proportions with the whole of the civilized world invited to watch—for better or worse.

To fulfill a dream, to be allowed to sweat over lonely labor, to be given a chance to create, are the meat and potatoes of life. The money is the gravy.