A million years is a short time—the shortest worth messing with for most problems. You begin tuning your mind to a time scale that is the planet’s time scale. For me, it is almost unconscious now and is a kind of companionship with the earth.

At this very minute, with almost absolute certainty, radio waves sent forth by other intelligent civilizations are falling on the earth. A telescope can be built that, pointed in the right place, and tuned to the right frequency, could discover these waves. Someday, from somewhere out among the stars, will come the answers to many of the oldest, most important, and most exciting questions mankind has asked.

Chess problems are the hymn-tunes of mathematics.

Chief Seattle, of the Indians that inhabited the Seattle area, wrote a wonderful paper that has to do with putting oneself in tune with the universe. He said, “Why should I lament the disappearance of my people! All things end, and the white man will find this out also.” And this goes for the universe. One can be at peace with that. This doesn’t mean that one shouldn’t participate in efforts to correct the situation. But underlying the effort to change must be an “at peace.” To win a dog sled race is great. To lose is okay too.

Counting stars by candlelight all are dim but one is bright; the spiral light of Venus rising first and shining best, from the northwest corner of a brand-new crescent moon crickets and cicadas sing a rare and different tune.

Everything is determined … by forces over which we have no control. It is determined for the insect as well as the star. Human beings, vegetables, or cosmic dust—we all dance to a mysterious tune, intoned in the distance by an invisible piper.

For the world was built in order,
And the atoms march in tune.

Good, old-fashioned common sense iz one ov the hardest things in the world to out-wit, out-argy, or beat in enny way, it iz az honest az a loaf ov good domestik bread, alwus in tune, either hot from the oven or 8 days old.

If Mozart, instead of playing the pianoforte at three years old with wonderfully little practice, had played a tune with no practice at all, he might truly have been said to have done so instinctively.

It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.

Life is water, dancing to the tune of solids.

Our world is not an optimal place, fine tuned by omnipotent forces of selection. It is a quirky mass of imperfections, working well enough (often admirably); a jury-rigged set of adaptations built of curious parts made available by past histories in different contexts ... A world optimally adapted to current environments is a world without history, and a world without history might have been created as we find it. History matters; it confounds perfection and proves that current life transformed its own past.

The discovery of the conic sections, attributed to Plato, first threw open the higher species of form to the contemplation of geometers. But for this discovery, which was probably regarded in Plato’s tune and long after him, as the unprofitable amusement of a speculative brain, the whole course of practical philosophy of the present day, of the science of astronomy, of the theory of projectiles, of the art of navigation, might have run in a different channel; and the greatest discovery that has ever been made in the history of the world, the law of universal gravitation, with its innumerable direct and indirect consequences and applications to every department of human research and industry, might never to this hour have been elicited.

The fact is that there are few more “popular” subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.

The living world is a unique and spectacular marvel. Billions of individuals, and millions of kinds of plants and animals …. Working together to benefit from the energy of the sun and the minerals of the earth. Leading lives that interlock in such a way that they sustain each other. We rely entirely on this finely tuned life-support machine. And it relies on its biodiversity to run smoothly. Yet the way we humans live on Earth now is sending biodiversity into a decline.

The poets did well to conjoin music and medicine, in Apollo, because the office of medicine is but to tune the curious harp of man's body and reduce it to harmony.

The wind makes music in the woods, but the tune changes with the seasons.

There once was a brainy baboon,
Who always breathed down a bassoon,
For he said, “It appears
That in billions of years
I shall certainly hit on a tune”.

There's antimony, arsenic, aluminium, selenium,
And hydrogen and oxygen and nitrogen and rhenium,
And nickel, neodymium, neptunium, germanium,
And iron, americium, ruthenium, uranium,
Europium, zirconium, lutetium, vanadium,
And lanthanum and osmium and astatine and radium,
And gold and protactinium and indium and gallium,
And iodine and thorium and thulium and thallium.
There's yttrium, ytterbium, actinium, rubidium,
And boron, gadolinium, niobium, iridium,
And strontium and silicon and silver and samarium,
And bismuth, bromine, lithium, beryllium and barium.
There's holmium and helium and hafnium and erbium,
And phosphorus and francium and fluorine and terbium,
And manganese and mercury, molybdenum, magnesium,
Dysprosium and scandium and cerium and cesium,
And lead, praseodymium and platinum, plutonium,
Palladium, promethium, potassium, polonium,
And tantalum, technetium, titanium, tellurium,
And cadmium and calcium and chromium and curium.
There's sulfur, californium and fermium, berkelium,
And also mendelevium, einsteinium, nobelium,
And argon, krypton, neon, radon, xenon, zinc and rhodium,
And chlorine, cobalt, carbon, copper, tungsten, tin and sodium.
These are the only ones of which the news has come to Harvard,
And there may be many others, but they haven't been discarvard.
[To the tune of I am the Very Model of a Modern Major General.]

Two extreme views have always been held as to the use of mathematics. To some, mathematics is only measuring and calculating instruments, and their interest ceases as soon as discussions arise which cannot benefit those who use the instruments for the purposes of application in mechanics, astronomy, physics, statistics, and other sciences. At the other extreme we have those who are animated exclusively by the love of pure science. To them pure mathematics, with the theory of numbers at the head, is the only real and genuine science, and the applications have only an interest in so far as they contain or suggest problems in pure mathematics.
Of the two greatest mathematicians of modern tunes, Newton and Gauss, the former can be considered as a representative of the first, the latter of the second class; neither of them was exclusively so, and Newton’s inventions in the science of pure mathematics were probably equal to Gauss’s work in applied mathematics. Newton’s reluctance to publish the method of fluxions invented and used by him may perhaps be attributed to the fact that he was not satisfied with the logical foundations of the Calculus; and Gauss is known to have abandoned his electro-dynamic speculations, as he could not find a satisfying physical basis. …
Newton’s greatest work, the Principia, laid the foundation of mathematical physics; Gauss’s greatest work, the Disquisitiones Arithmeticae, that of higher arithmetic as distinguished from algebra. Both works, written in the synthetic style of the ancients, are difficult, if not deterrent, in their form, neither of them leading the reader by easy steps to the results. It took twenty or more years before either of these works received due recognition; neither found favour at once before that great tribunal of mathematical thought, the Paris Academy of Sciences. …
The country of Newton is still pre-eminent for its culture of mathematical physics, that of Gauss for the most abstract work in mathematics.