One time we had a math problem: multiply 26 times 40, and it had the 40 on the top and the 26 on the bottom. So I flipped it over to do the multiplying. The principal game me a very hard time about that: "You do the problem the way it is given to you. Put the 40 on top, and you must have the 26 on the bottom."
Jean Taylor, quoted in "Still Questioning Authority: An Interview with Jean Taylor," by D.J. Albers, College Mathematics Journal, vol. 27, no. 4, Sept. 1996.
595
 
There lives more faith in honest doubt, believe me, than in half the creeds.
Alfred Lord Tennyson,
1692
 
I am a part of all that I have met.
Alfred Lord Tennyson, from Ulysses.
1441
 
I went to see the doctor of philosophy;
With a poster of Rasputin and a beard down to his knee;
He never did marry or see a B-grade movie;
He graded my performance, he said he could see through me;
I spent four years prostrate to the higher mind, got my paper;
And I was free.
The Indigo Girls, from "Closer to fine" on the album "Indigo Girls"
1186
 
The most famous of all hexagonal conformations, and one of the most beautiful, is the bee's cell.
D'Arcy Wentworth Thompson, On Growth and Form, Vol 2, page 525, second edition, 1952.
1231
 
The harmony of the world is made manifest in Form and Number and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.
Sir D'Arcy Wentworth Thompson, from "On Growth and Form."
371
 
Myths and legends die hard in America. We love them for the extra dimension they provide, the illusion of near-infinite possibility to erase the narrow confines of most men's reality. Weird heroes and mould-breaking champions exist as living proof to those who need it that the tyranny of "the rat race" is not yet final.
Hunter S. Thompson,
802
 
When the going gets weird, the weird turn pro.
Hunter S. Thompson,
804
 
Every now and then when your life gets complicated and the weasels start closing in, the only cure is to load up on heinous chemicals and then drive like a bastard from Hollywood to Las Vegas ... with the music at top volume and at least a pint of ether.
Hunter S. Thompson, from Fear and Loathing in Las Vegas
803
 
The question is not what you look at, but what you see.
Henry David Thoreau,
1332
 
I went to the woods because I wished to live deliberately, to front only the essential facts of life and see if I could not learn what it had to teach, and not, when I came to die, discover that I had not lived.
Henry David Thoreau, from Walden; Or, Life in the Woods
806
 
Books are the treasured wealth of the world and the fit inheritance of generations and nations.
Henry David Thoreau,
1005
 
How full of the creative genius is the air in which these [snowflakes] are generated! I should hardly admire them more if real stars fell and lodged on my coat. Nature is full of genius. Full of the divinity. So that not a snowflake escapes its fashioning hand.
Henry David Thoreau,
1464
 
We have heard much about the poetry of mathematics, but very little of it has as yet been sung. The ancients had a juster notion of their poetic value than we. The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both.
H.D. Thoreau, quoted in The American Mathematical Monthly, vol. 103, no. 2, February, 1996.
604
 
There must be the...generating force of love behind every effort destined to be successful.
Henry David Thoreau, quoted in Listening to Nature by Joseph Cornell.
766
 
The question is not what you look at, but what you see.
Henry David Thoreau,
1654
 
What does education often do? It makes a straight-cut ditch of a free meandering brook.
Henery David Thoreau, quoted in A Teacher's Treasury of Quotations, by Bernard E. Farber.
373
 
I did not wish to live what was not life, living is so dear; nor did I wish to practice resignation, unless it was quite necessary. I wanted to live deep and suck out all the marrow of life, to live so sturdily and Spartan-like as to put to rout all that was not life.
Henry David Thoreau, from Walden; Or, Life in the Woods
807
 
Don't ask what the world needs. Ask what makes you come alive, and go do it. Because what the world needs is people who have come alive.
Howard Thurman,
1042
 
Mathematics is a huge and highly interconnected structure... Think of a tinkertoy set. The key is the pieces which have holes, allowing you to join them with rods to form interesting and highly interconnected structures. No interesting mathematical topic is self-contained or complete: rather it is full of "holes," or natural questions and ideas not readily answered by techniques native to the topic. These holes often give rise to connections between the given topic and other topics that seem at first unrelated. Mathematical exposition often conceals these holes, for the sake of smoothness--but what good is a tinkertoy set if the holes are all filled in with modeling clay?
William P. Thurston, from Three-Dimensional Geometry and Topology.
715
 
As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure.
William P. Thurston, from Three-Dimensional Geometry and Topology.
714
 
How often might a man, after he had jumbled a set of letters in a bag, fling them out upon the ground before they would fall into an exact poem, yea, or so much as make a good discourse in prose. And may not a little book be as easily made by chance as this great volume of the world.
Archbishop Tillatron, quoted in The World of Mathematics, by J.R. Newman.
372
 
I met a man once who told me that far from believing in the square root of minus one, he didn't believe in minus one. This is at any rate a consistent attitude.
Edward Titchmarsch,
1369
 
There are certainly many people who regard the square root of two as something perfectly obvious, but jib at the square root of negative one. This is because they think they can visualize the former as something in physical space, but not the latter. Actually the square root of negative one is a much simpler concept.
E.C. Titschmarch, quoted in Glimpses of Algebra and Geometry, by Gabor Toth.
633
 
Our job as teachers is to lead people out of their comfort zones.
Shelia Tobias, at Westfield State College, Spring 2009.
1315
 
There is a difference between not knowing and not knowing yet.
Shelia Tobias, quoted in Garbage Pizzas, Patchwork Quilts and Math Magic, by Susan Ohanian.
579
 
The illiterate of the future will not be the person who cannot read. It will be the person who does not know how to learn.
Alvin Toffler.,
1161
 
Not all who wander are lost.
J.R.R. Tolkien,
1008
 
The movement of humanity, arising as it does from innumerable arbitrary human wills, is continuous.
To understand the laws of this continuous movement is the aim of history...
Only by taking infinitesimally small units for observation (the differential of history, that is, the individual tendencies of men) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
Leo Tolstoy, from War and Peace.
1290
 
Historical science in its endeavor to draw nearer to truth continually takes smaller and smaller units for examination. But however small the units it takes, we feel that to take any unit disconnected from others, or to assume a beginning , of any phenomenon, or to say that the will of many men is expressed by the actions of any one historical personage, is in itself false.
Leo Tolstoy, from War and Peace.
1291
 
A modern branch of mathematics having achieved the art of dealing with the infinitely small can now yield solutions in other more complex problems of motions which used to appear insoluble.
This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion admits the conception of the infinitely small, and so conforms to the chief conditions of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when it deals with separate elements of motion instead of examining continuous motion.
Leo Tolstoy, from War and Peace.
1292
 
Everyone thinks of changing the world, but no one thinks of changing himself.
Leo Tolstoy,
1365
 
Some mathematician, I believe, has said that true pleasure lies not in the discovery of truth, but in the search for it.
Tolstoy, from Anna Kerenina.
750
 
Almost every American who has a degree, however ignorant, can live better than even competent people in much poorer countries around the world... But this cannot last long in the situation when "competence" and a diploma tautologically mean each other. The advantages enjoyed by Americans are the results of real competence and real efforts of previous generations...And someday ignorant people with degrees and diplomas may want power according to their papers rather than real competence. We Russians have some experience of this sort...It is clear to me right now that the winners in the modern world will be those countries which will really teach their students to think and solve problems. I sincerely wish America to be among these.
Andre Toom,
374
 
The Geometer has the special privilege to carry out, by abstraction, all constructions by means of the intellect. Who, then, would wish to prevent me from freely considering figures hanging on a balance imagined to be at an infinite distance beyond the confines of the world?
Evangelista Torricelli, quoted in "Torricelli"s Infinitely Long Solid and Its Philosophical Reception in the Seventeenth Century," by P. Mancosu and E. Vailati, Isis, vol. 82, 1991.
622
 
Books are the carriers of civilization. Without books, history is silent, literature dumb, science crippled, thought and speculation at a standstill.
Barbara Tuchman,
990
 
On the day before the launch of the Challenger, the rocket engineers and managers needed a quick, smart analysis of evidence about the threat of cold to the O-rings, as well as an effective presentation of evidence in order to convince NASA officials not to launch. Engineers at Thiokol prepared 13 charts to make the case that the Challenger should not be launched the next day, given the forecast of very chilly weather. Drawn up in a few hours, the charts were faxed to NASA and discussed in two long telephone conferences between Thiokol and NASA on the night before the launch. The charts were unconvincing; the arguments against the launch failed; the Challenger blew up.
Edward R. Tufte, from 'Visual and Statistical Thinking: Displays of Evidence for Making Decisions,' p. 18.
1596
 
Data graphics visually display measured quantities by means of the combined use of points, lines, a coordinate system, numbers, symbols, words, shading, and color... At their best, graphics are instruments for reasoning about quantitative information... Of all methods for analyzing and communicating statistical information, well-designed data graphics are usually the simplest and at the same time the most powerful.
Edward Tufte, from the Introduction to The Visual Display of Quantitative Information
1677
 
To envision information- and what bright and splendid visions can result- is to work at the intersection of image, word, number, and art.
Edward Tufte, from the Introduction to Envisioning Information
1676
 
Even though we navigate daily through a perceptual world of three spatial dimensions and reason occasionally about higher dimensional arenas with mathematical ease, the world portrayed on our information displays is caught up in the two-dimensionality of the endless flatlands of paper and video screen. All communication between the readers of an image and the makers of an image must now take place on a two-dimensional surface. Escaping this flatland is the essential task of envisioning information- for all interesting worlds (physical, biological, imaginary, human) that we seek to understand are inevitably and happily multivariate in nature. Not flatlands.
Edward Tufte, from Envisioning Information
1675
 
Displays of evidence implicitly but powerfully define the scope of the relevant, as presented data are selected from a larger pool of material. Like magicians, chart makers reveal what they choose to reveal. That selection of data- whether partisan, hurried, haphazard, uninformed, thoughtful, wise- can make all the different, determining the scope of the evidence and thereby setting the analytic agenda that leads to a particular decision.
Edward R. Tufte, from 'Visual and Statistical Thinking: Displays of Evidence for Making Decisions,' p. 21.
1597
 
In the 13 charts prepared for making the decision to launch [the space shuttle Challenger], there is a scandalous discrepancy between the intellectual tasks at hand and the images created to serve those tasks.
Edward R. Tufte, from 'Visual and Statistical Thinking: Displays of Evidence for Making Decisions,' p. 23.
1598
 
We can only see a short distance ahead, but we can see plenty there that needs to be done.
Alan Turing,
1722
 
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
A. Turing, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
375
 
A computer would deserve to be called intelligent if it could deceive a human into believing that it was human.
Alan Turing,
1704
 
Science is a differential equation. Religion is a boundary condition.
Alan Turing,
1705
 
Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do.
So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails.
Explore. Dream. Discover.
Mark Twain,
1439
 
The man who does not read good books has no advantage over the man who can't read them.
Mark Twain,
995
 
When I was 14, I couldn't believe how ignorant my father was. By the time I turned 21 I was astounded at how much the old man had learned in just seven years.
Mark Twain,
1438
 
Great people are those who make others feel that they, too, can become great.
Mark Twain,
797
 
It is the longest river in the world - 4,300 miles... It is also the crookedest river in the world, since in one part of its journey it uses up 1,100 miles to cover the same ground that a crow would fly over in 675.
Mark Twain, from "Life on the Mississippi."
378
 
I have never let my schooling interfere with my education.
Mark Twain,
377
 
Out of the public schools comes the greatness of the nation.
Mark Twain,
376
 
Courage is resistance to fear, mastery of fear, not absence of fear.
Mark Twain,
1328
 
When you are dissatisfied and would like to go back to youth, think of Algebra.
Mark Twain,
816
 
If we accept the four-color theorem as a theorem, then we are committed to changing the sense of "theorem," or more to the point, to changing the sense of the underlying concept of "proof."
Stephen Tymoczko, quoted in The Mathematical Experience, by Philip Davis and Reuben Hersh.
581
 

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