He who would know what geometry is, must venture boldly into its depths and learn to think and feel as a geometer. I believe that it is impossible to do this, and to study geometry as it admits of being studied and am conscious it can be taught, without finding the reason invigorated, the invention quickened, the sentiment of the orderly and beautiful awakened and enhanced, and reverence for truth, the foundation of all integrity of character, converted into a fixed principle of the mental and moral constitution, according to the old and expressive adage “abeunt studia in mores”.

I will venture to say there is more learning and science within the circumference of ten miles from where we now sit [in London], than in all the rest of the kingdom.

If the views we have ventured to advance be correct, we may almost consider {greek words} of the ancients to be realised in hydrogen, an opinion, by the by, not altogether new. If we actually consider the specific gravities of bodies in their gaseous state to represent the number of volumes condensed into one; or in other words, the number of the absolute weight of a single volume of the first matter ({greek words}) which they contain, which is extremely probable, multiples in weight must always indicate multiples in volume, and vice versa; and the specific gravities, or absolute weights of all bodies in a gaseous state, must be multiples of the specific gravity or absolute weight of the first matter, ({Greek words}), because all bodies in the gaseous state which unite with one another unite with reference to their volume.

It seems to me that there is a good deal of ballyhoo about scientific method. I venture to think that the people who talk most about it are the people who do least about it. Scientific method is what working scientists do, not what other people or even they themselves may say about it. No working scientist, when he plans an experiment in the laboratory, asks himself whether he is being properly scientific, nor is he interested in whatever method he may be using as method.

Just as it will never be successfully challenged that the French language, progressively developing and growing more perfect day by day, has the better claim to serve as a developed court and world language, so no one will venture to estimate lightly the debt which the world owes to mathematicians, in that they treat in their own language matters of the utmost importance, and govern, determine and decide whatever is subject, using the word in the highest sense, to number and measurement.

Let him [the author] be permitted also in all humility to add … that in consequence of the large arrears of algebraical and arithmetical speculations waiting in his mind their turn to be called into outward existence, he is driven to the alternative of leaving the fruits of his meditations to perish (as has been the fate of too many foregone theories, the still-born progeny of his brain, now forever resolved back again into the primordial matter of thought), or venturing to produce from time to time such imperfect sketches as the present, calculated to evoke the mental co-operation of his readers, in whom the algebraical instinct has been to some extent developed, rather than to satisfy the strict demands of rigorously systematic exposition.

Melvin Calvin was a fearless scientist, totally unafraid to venture into new fields such as hot atom chemistry, carcinogenesis, chemical evolution and the origin of life, organic geochemistry, immunochemistry, petroleum production from plants, farming, Moon rock analysis, and development of novel synthetic biomembrane models for plant photosystems.

Miss Stevens’s work is characterized by its precision, and by a caution that seldom ventures far from the immediate observation. Her contributions are models of brevity—a brevity amounting at times almost to meagerness.

No national sovereignty rules in outer space. Those who venture there go as envoys of the entire human race. Their quest, therefore, must be for all mankind, and what they find should belong to all mankind.

On 17th July there came to us at Potsdam the eagerly-awaited news of the trial of the atomic bomb in the [New] Mexican desert. Success beyond all dreams crowded this sombre, magnificent venture of our American allies. The detailed reports ... could leave no doubt in the minds of the very few who were informed, that we were in the presence of a new factor in human affairs, and possessed of powers which were irresistible.

See with what force yon river’s crystal stream
Resists the weight of many a massy beam.
To sink the wood the more we vainly toil,
The higher it rebounds, with swift recoil.
Yet that the beam would of itself ascend
No man will rashly venture to contend.
Thus too the flame has weight, though highly rare,
Nor mounts but when compelled by heavier air.

The great truths with which it [mathematics] deals, are clothed with austere grandeur, far above all purposes of immediate convenience or profit. It is in them that our limited understandings approach nearest to the conception of that absolute and infinite, towards which in most other things they aspire in vain. In the pure mathematics we contemplate absolute truths, which existed in the divine mind before the morning stars sang together, and which will continue to exist there, when the last of their radiant host shall have fallen from heaven. They existed not merely in metaphysical possibility, but in the actual contemplation of the supreme reason. The pen of inspiration, ranging all nature and life for imagery to set forth the Creator’s power and wisdom, finds them best symbolized in the skill of the surveyor. "He meted out heaven as with a span;" and an ancient sage, neither falsely nor irreverently, ventured to say, that “God is a geometer”.

The personal adventures of a geologist would form an amusing narrative. He is trudging along, dusty and weather­beaten, with his wallet at his back, and his hammer on his shoulder, and he is taken for a stone-mason travelling in search of work. In mining-countries, he is supposed to be in quest of mines, and receives many tempting offers of shares in the ‘Wheel Dream’, or the ‘Golden Venture’;—he has been watched as a smuggler; it is well if he has not been committed as a vagrant, or apprehended as a spy, for he has been refused admittance to an inn, or has been ushered into the room appropriated to ostlers and postilions. When his fame has spread among the more enlightened part of the community of a district which he has been exploring, and inquiries are made of the peasantry as to the habits and pursuits of the great philosopher who has been among them, and with whom they have become familiar, it is found that the importance attached by him to shells and stones, and such like trumpery, is looked upon as a species of derangement, but they speak with delight of his affability, sprightliness, and good-humour. They respect the strength of his arm, and the weight of his hammer, as they point to marks which he inflicted on the rocks, and they recount with wonder his pedestrian performances, and the voracious appetite with which, at the close of a long day’s work he would devour the coarsest food that was set before him.

The thesis which I venture to sustain, within limits, is simply this, that the savage state in some measure represents an early condition of mankind, out of which the higher culture has gradually been developed or evolved, by processes still in regular operation as of old, the result showing that, on the whole, progress has far prevailed over relapse.

These specimens, which I could easily multiply, may suffice to justify a profound distrust of Auguste Comte, wherever he may venture to speak as a mathematician. But his vast general ability, and that personal intimacy with the great Fourier, which I most willingly take his own word for having enjoyed, must always give an interest to his views on any subject of pure or applied mathematics.

We do not live in a time when knowledge can be extended along a pathway smooth and free from obstacles, as at the time of the discovery of the infinitesimal calculus, and in a measure also when in the development of projective geometry obstacles were suddenly removed which, having hemmed progress for a long time, permitted a stream of investigators to pour in upon virgin soil. There is no longer any browsing along the beaten paths; and into the primeval forest only those may venture who are equipped with the sharpest tools.

We want greater venturesomeness. We have sat on the river bank and caught catfish with pin hooks. The time has come to harpoon a whale. And if we must gratify any human tendency to appropriate, let us take an empire.

When I first ventured into the Gulf of Mexico in the 1950s, the sea appeared to be a blue infinity too large, too wild to be harmed by anything that people could do. I explored powder white beaches, dense marshes, mangrove forests, and miles of sea grass meadows alive with pink sea urchins, tiny shrimps, and seahorses half the size of my little finger. … Then, in mere decades, not millennia, the blue wilderness of my childhood disappeared: biologic change in the space of a lifetime.

When the history of our galaxy is written, and for all any of us know it may already have been, if Earth gets mentioned at all it won’t be because its inhabitants visited their own moon. That first step, like a newborn’s cry, would be automatically assumed. What would be worth recording is what kind of civilization we earthlings created and whether or not we ventured out to other parts of the galaxy.