There was a young fellow from Trinity, Who took the square root of infinity. But the number of digits, Gave him the fidgets; He dropped Math and took up Divinity.
How can you do 'New Math' problems with an 'Old Math' mind?
Factorials were someone's attempt to make math LOOK exciting.
The lottery is a tax on poor people and on people who can’t do math. Rich people and smart people would be in the line if the lottery were a real wealth-building tool, but the truth is that the lottery is a rip-off instituted by our government. This is not a moral position; it is a mathematical, statistical fact. Studies show that the zip codes that spend four times what anyone else does on lottery tickets are those in lower-income parts of town. The lottery, or gambling of any kind, offers false hope, not a ticket out.
"What I've done, of course, is total garbage."
The most important thing we can do is inspire young minds and to advance the kind of science, math and technology education that will help youngsters take us to the next phase of space travel.
For example, if \thinmskip = 3mu, this makes \thickmskip = 6mu. But if you also want to use \skip12 for horizontal glue, whether in math mode or not, the amount of skipping will be in points (e.g., 6pt). The rule is that glue in math mode varies with the size only when it is an \mskip; when moving between an mskip and ordinary skip, the conversion factor 1mu=1pt is always used. The meaning of '\mskip\skip12' and '\baselineskip=\the\thickmskip' should be clear. -- Donald Knuth, TeX 82 -- Comparison with TeX80
How can you do 'New Math' problems with an 'Old Math' mind? -- Charles Schulz
Several students were asked to prove that all odd integers are prime. The first student to try to do this was a math student. "Hmmm... Well, 1 is prime, 3 is prime, 5 is prime, and by induction, we have that all the odd integers are prime." The second student to try was a man of physics who commented, "I'm not sure of the validity of your proof, but I think I'll try to prove it by experiment." He continues, "Well, 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is... uh, 9 is... uh, 9 is an experimental error, 11 is prime, 13 is prime... Well, it seems that you're right." The third student to try it was the engineering student, who responded, "Well, to be honest, actually, I'm not sure of your answer either. Let's see... 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is... uh, 9 is... well, if you approximate, 9 is prime, 11 is prime, 13 is prime... Well, it does seem right." Not to be outdone, the computer science student comes along and says "Well, you two sort've got the right idea, but you'll end up taking too long! I've just whipped up a program to REALLY go and prove it." He goes over to his terminal and runs his program. Reading the output on the screen he says, "1 is prime, 1 is prime, 1 is prime, 1 is prime..."
-- R. Drabek
We come to bury DOS, not to praise it. -- Paul Vojta, vojta@math.berkeley.edu
We come to bury DOS, not to praise it. (Paul Vojta, vojta@math.berkeley.edu, paraphrasing a quote of Shakespeare)
Against his wishes, a math teacher's classroom was remodeled. Ever since, he's been talking about the good old dais. His students planted a small orchard in his honor; the trees all have square roots.
"What I've done, of course, is total garbage." -- R. Willard, Pure Math 430a
In California, Bill Honig, the Superintendent of Public Instruction, said he thought the general public should have a voice in defining what an excellent teacher should know. "I would not leave the definition of math," Dr. Honig said, "up to the mathematicians." -- The New York Times, October 22, 1985
Please, don't drink and derive.
Mathematicians
Against
Drunk
Deriving
"I think it is true for all _n. I was just playing it safe with _n >= 3 because I couldn't remember the proof." -- Baker, Pure Math 351a
Factorials were someone's attempt to make math LOOK exciting.
Do not worry about your difficulties in Mathematics. I can assure you, mine are still greater.
Love, and you shall be loved. All love is mathematically just, as much as the two sides of an algebraic equation.
This is the story of a family who didn’t fit in. A little girl who was a bit geeky and liked maths more than makeup. And a boy who liked makeup and didn’t fit into any tribes.
A mathematician is a device for turning coffee into theorems.
~Novels.~--Novels are sweet. All people with healthy literary appetites love them--almost all women; a vast number of clever, hard-headed men,--Judges, bishops, chancellors, mathematicians,--are notorious novel readers, as well as young boys and sweet girls, and their kind, tender mothers.--_Thackeray._
It was a common saying among the Puritans, "Brown bread and the Gospel is good fare."
The hope of all who suffer, The dread of all who wrong.
It is not fit the public trusts should be lodged in the hands of any, till they are first proved and found fit for the business they are to be entrusted with.
Better late than never.
There is no certainty [in science] where one of the mathematical sciences cannot be applied, or in those [sciences] which are not in harmony with mathematics.
They that die by famine die by inches.
The computer can't tell you the emotional story. It can give you the exact
Mechanics are the paradise of scientific mathematics, because with them we arrive at the fruits of mathematics.
Let no man who is not a mathematician read the principles of my work.
Our world is in profound danger. Mankind must establish a set of positive values with which to secure its own survival. This quest for enlightenment must begin now. It is essential that all men and women become aware of what they are, why they are here on Earth and what they must do to preserve civilization before it is too late.
The bird is an instrument which operates by mathematical laws, and man can reproduce all {150} the movements of this instrument, but cannot attain to the intensity of its power; and can only succeed in acquiring balance. Thus we will say that such an instrument constructed by man lacks only the soul of the bird, and the soul of man must counterfeit the soul of the bird. The spirit in the frame of the bird doubtless would respond to needs of that frame better than would the spirit of man, whose frame is different, more especially in the almost insensible motions of balance; and since we see the bird make provision for the many sensible varieties of movement, we can conclude by such experience that man can acquire knowledge of the more markedly sensible of these movements, and that he will be able to make ample provision against the destruction of that instrument of which he has made himself the spirit and the guide.
We have more mathematics than ever, but less mathesis. Archimedes and Plato could not have read the "Mechanique Celeste;" but neither would the whole French Institute see aught in that saying, "God geometrises," but sentimental rhodomontade.
A boy is taught to read his own and other languages, in order that he may have access to infinitely wider stores of knowledge than could ever be opened to him by oral intercourse with his fellow men; he learns to write, that his means of communication with the rest of mankind may be indefinitely enlarged, and that he may record and store up the knowledge he acquires. He is taught elementary mathematics, that he may understand all those relations of number and form, upon which the transactions of men, associated in complicated societies, are built, and that he may have some practice in deductive reasoning.
None so blind as those that will not see.
Now seest thou not that the eye comprehends the beauty of the whole world? It is the head of astrology; it creates cosmography; it gives counsel and correction to all the human arts; it impels {84} men to seek diverse parts of the world; it is the principle of mathematics; its science is most certain; it has measured the height and the magnitude of the stars; it has discovered the elements and their abodes; it has been able to predict the events of the future, owing to the course of the stars; it has begotten architecture and perspective and divine painting. O most excellent above all the things created by God! What praise is there which can express thy nobility? What peoples, what tongues, are they who can perfectly describe thy true working? It is the window of the human body, through which the soul gazes and feasts on the beauty of the world; by reason of it the soul is content with its human prison, and without it this human prison is its torment; and by means of it human diligence has discovered fire by which the eye wins back what the darkness has stolen from it. It has adorned nature with agriculture and pleasant gardens. But what need is there for me to indulge in long and elevated discourse? What thing is there which acts not by reason of the eye? It impels men from the East to the West; it has discovered navigation; and in this it excels nature, because the simple products of the earth are finite and the works which the eye makes over to the hands are infinite, as the painter shows in his portrayal of countless forms of animals, herbs, plants and places.
Pater patri?=--The father of his country. [Greek: pathemata--mathemata]--We learn from the things we suffer.
The smallest natural point is larger than all mathematical points, and the proof of this is that the natural point has continuity, and everything which has continuity is infinitely divisible; but the mathematical point is indivisible because it is not a quantity. Every continuous quantity is mentally infinitely divisible. Among the magnitude of things which are among us, the chief of all is nothingness; and its function extends to matter that does not exist, and its essence is in time in the past or in the future, and it has nothing of the present. This nothingness has its part equal to the whole and the whole to the part, and the divisible to the indivisible, and produces the same result by addition or subtraction, or if it be divided or multiplied,--as is proved by arithmeticians by their tenth character, which represents nothing. And its power does not extend to the things of nature.
It is a mathematical fact that the casting of a pebble from my hand alters the centre of gravity of the universe.
If I would know the love of my friend, I must see what it can do in the winter. So with the divine love. It is very easy for me to worship in the summer sunshine, when the melodies of life are in the air and the fruits of life are on the tree. But let the song of the bird cease, and the fruit of the tree fall; and will my heart still go on to sing? Will I stand in God's house by night? Will I love Him in His own night? Will I watch with Him even one hour in His Gethsemane? Will I help to bear His cross up the Via Dolorosa? My love has come to Him in His humiliation. My faith has found Him in His lowliness. My heart has recognized His majesty through His mean disguise, and I know at last that I desire not the gift, but the Giver. When I can stand in His house by night, I have accepted Him for Himself alone.--_George Matheson._
Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; morals, grave; logic and rhetoric, able to contend.
O human folly! dost thou not perceive that thou hast been with thyself all thy life, and thou art not yet aware of the thing which more fully than any other thing thou dost possess, namely, thy own folly? And thou desirest with the multitude of sophists to deceive thyself and others, despising the mathematical sciences in which truth dwells and the knowledge of the things which they contain; and then thou dost busy thyself with miracles, and writest that thou hast attained to the knowledge of those things which the human mind cannot comprehend, which cannot be proved by any instance in nature, and thou deemest that thou hast wrought a miracle in spoiling the work of some speculative mind; and thou perceivest not that thy error is the same as that of a man who strips a plant of the ornament of its branches covered with leaves, mingled with fragrant flowers and fruits. Just as Justinius did when he abridged the stories written by Trogus Pompeius, who had written elaborately the noble deeds of his forefathers, which were full of wonderful beauties of style; and thus {19} he composed a barren work, worthy only of the impatient spirits who deem that they are wasting the time which they might usefully employ in studying the works of nature and mortal affairs. But let such men remain in company with the beasts; let dogs and other animals full of rapine be their courtiers, and let them be accompanied with these running ever at their heels! and let the harmless animals follow, which in the season of the snows come to the houses begging alms as from their master.
That which you believe becomes your world.
Thus I wish to say, in regard to these mathematical matters, that they who merely study the masters and not the works of nature are the grandchildren, and not the children, of nature, the mistress of good masters. I abhor the supreme folly of those who blame the disciples of nature in defiance of those masters who were themselves her pupils.
When we say that the ancestors of the Blacks, who today live mainly in Black Africa, were the first to invent mathematics, astronomy, the calendar, sciences in general, arts, religion, agriculture, social organization, medicine, writing, technique, architecture; that they were the first to erect buildings out of 6 million tons of stone (the Great Pyramid) as architects and engineers—not simply as unskilled laborers; that they built the immense temple of Karnak, that forest of columns with its famed hypostyle hall large enough to hold Notre-Dame and its towers; that they sculpted the first colossal statues (Colossi of Memnon, etc.)—when we say all that we are merely expressing the plain unvarnished truth that no one today can refute by arguments worthy of the name.
The eye, which is called the window of the soul, is the principal means by which the brain can most abundantly and splendidly contemplate the infinite works of nature; and the ear is the next in order, which is ennobled by hearing the recital of the things seen by the eye. If you, historians and poets, or mathematicians, had not seen things with the eyes, you could not report of them in writing. If thou, O poet, dost tell a story with thy painting pen, the painter will more easily give satisfaction in telling it with his brush and in a manner less tedious and more easily understood. And if thou callest painting mute poetry, the painter can call poetry blind painting. Now consider which is the greater loss, to be blind or dumb? Though the poet is as free as the painter in his creations and compositions, they are not so satisfactory to men as paintings, because if poetry is able to describe forms, actions and places in words, the painter deals with the very {65} semblance of forms in order to represent them. Now consider which is nearer to man, the name of man or the image of man? The name of man varies in diverse countries, but death alone changes his form. If thou wast to say that painting is more lasting, I answer that the works of a coppersmith, which time preserves longer than thine or ours, are more eternal still. Nevertheless there is but little invention in it, and painting on copper with colours of enamel is far more lasting.
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
The cup which our Father giveth us to drink is a cup for the will. It is easy for the lips to drain it when once the heart has accepted it. Not on the heights of Calvary, but in the shadows of Gethsemane is the cup presented; the act is easy after the choice. The real battle-field is in the silence of the spirit. Conquer there, and thou art crowned.--_George Matheson._
A mathematician is a device for turning coffee into theorems.
People should not be able to say of a man, he is a mathematician, or a preacher, or eloquent, but he is a gentleman; that universal quality alone pleases me.--When you think of a man's book as soon as you see himself, it is a bad sign. I would rather that none of his qualities should be recognised till you meet them, or have occasion to avail yourself of them. _Ne quid nimis_, for fear some one quality gain the mastery and stamp the man. Let not people think of him as an orator, unless oratory be in question, then let them think of it.
There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.
Angling may be said to be so like the mathematics that it can never be fully learnt.
It matters little whether a man be mathematically, or philologically, or artistically cultivated, so he be cultivated.
To their own second thoughts.
But if I regard it closely, a curious reflection arises. I suppose that, fifteen hundred years ago, the child of any well-to-do Roman citizen was taught just these same things; reading and writing in his own, and, perhaps, the Greek tongue; the elements of mathematics; and the religion, morality, history, and geography current in his time. Furthermore, I do not think I err in affirming that, if such a Christian Roman boy, who had finished his education, could be transplanted into one of our public schools, and pass through its course of instruction, he would not meet with a single unfamiliar line of thought; amidst all the new facts he would have to learn, not one would suggest a different mode of regarding the universe from that current in his own time.
I tell them to turn to the study of mathematics, for it is only there that
O my soul, wouldst thou have thy life glorified, beautified, transfigured to the eyes of men? Get thee up into the secret place of God's pavilion, where the fires of love are burning. Thy life shall shine gloriously to the dwellers on the plain. Thy prayers shall be luminous; they shall light thy face like the face of Moses when he wist not that it shone. Thy words shall be burning; they will kindle many a heart journeying on the road to Emmaus. Thy path shall be lambent; when thou hast prayed in Elijah's solitude thou shalt have Elijah's chariot of fire.--_George Matheson._
The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of hell.
Those that are above business.
To fish in troubled waters.
I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.
The better day, the worse deed.
Saying and doing are two things.
I passed a long time in the study of the abstract sciences, and was much discouraged at finding how few were my fellow-students. When I began the study of man I saw that these abstract sciences were not fit for him, and that I was wandering more from my true state in investigating them, than others in ignoring them. I forgave their scanty knowledge. But I thought at least to find many fellow-students in the study of man, and that this was the real study which befits us. I was deceived, for there are still fewer than those who study mathematics. It is only for want of knowing how to pursue this study that we seek others. But is it not that even here is not the knowledge that man should have, and that it is better for him to be ignorant of himself in order to be happy?
The reason that every major university maintains a department of
After a storm comes a calm.
Not lost, but gone before.
Man is full of wants, and cares only for those who can satisfy them all. "Such an one is a good mathematician," it is said. But I have nothing to do with mathematics, he would take me for a proposition. "This other is a good soldier." He would treat me as a besieged city. I need then an honourable man who can lend himself generally to all my wants.
Nemo mathematicus genium indemnatus habebit=--No astronomer will be held a genius until he is condemned.
Many a dangerous temptation comes to us in fine gay colours that are but skin-deep.
I must study politics and war, that my sons may have liberty to study mathematics and philosophy, geography, natural history and naval architecture, navigation, commerce, and agriculture, in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry and porcelain. [Letter to his wife Abigail; edited by Charles Francis Adams. May 12, 1780.]
As far as the laws of mathematics refer to reality, they are not
There is no human experience that can be termed true science unless it can be mathematically demonstrated. And if thou sayest that the sciences which begin and end in the mind are true, this cannot be conceded, but must be denied for many reasons, and firstly because in such mental discourses experience is eliminated, and without experience there can be no certainty.
Robert Neville looked out over the new people of the earth. He knew he did not belong to them; he knew that, like the vampires, he was anathema and black terror to be destroyed. And, abruptly, the concept came, amusing to him even in his pain. … Full circle. A new terror born in death, a new superstition entering the unassailable fortress of forever. I am legend.
The poet says that his science consists of {78} invention and rhythm, and this is the simple body of poetry, invention as regards the subject matter and rhythm as regards the verse, which he afterwards clothes with all the sciences. To which the painter rejoins that he is governed by the same necessities in the science of painting, that is to say, invention and measure (fancy as regards the subject matter which he must invent, and measure as regards the matters painted), so that they may be in proportion, but that he does not make use of three sciences; on the contrary it is rather the other sciences that make use of painting, as, for instance, astrology, which effects nothing without the aid of perspective, the principal link of painting,--that is, mathematical astronomy and not fallacious astrology (let those who by reason of the existence of fools make a profession of it, forgive me). The poet says he describes an object, that he represents another full of beautiful allegory; the painter says he is capable of doing the same, and in this respect he is also a poet. And if the poet says he can incite men to love, which is the most important fact among every kind of animal, the painter can do the same, all the more so because he presents the lover with the image of his beloved; and the lover often does with it what he would not do with the writer's delineation of the same charms, i.e. talk with it and kiss it; so great is the painter's influence on the minds of men that he incites them to love and {79} become enamoured of a picture which does not represent any living woman.