- I must study politics and war that my sons may have liberty to study mathematics and philosophy.

[ Liberty Mathematics May Must Philosophy Politics Sons Study War]

Topic: War

- Now being in such grace and favor by reason I learned him some points of geometry and understanding of the art of mathematics with other things, I pleased him so that what I said he would not contrary.

[ Art Being Contrary Favor Geometry Grace Him Learned Mathematics Now Other Pleased Points Reason Said Some Such Things Understanding Would]

Topic:

- When we were making the law, when we were writing the literature and the mathematics the grandfarthers of Blair and little Bush were scratching around in caves.

[ Around Blair Bush Caves Law Literature Little Making Mathematics Scratching Were Writing]

Topic:

- I could never accept findings based almost exclusively on mathematics. It ain't ignorance that causes all the trouble in this world. It's the things people know that ain't so.

[ Accept Almost Based Causes Could Exclusively Findings Ignorance Know Mathematics Never Things Trouble World]

Topic:

- Mathematics was hard, dull work. Geography pleased me more. For dancing I was quite enthusiastic.

[ Dancing Dull Enthusiastic Geography Hard Mathematics More Pleased Quite Work]

Topic:

- In mathematics we have long since drawn the rein, and given over a hopeless race.

[ Drawn Given Hopeless Long Mathematics Over Race Rein Since]

Topic:

- If a man's wit be wandering, let him study the mathematics.

[ Him Man Mathematics Study Wandering Wit]

Topic: Science

- All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.

[ Almost Brain Count Easiest Fact How Illiterate Innate Know Knowledge Mathematical Mathematics Obvious Reckon Rejects Requires Science Sciences Things Us Utterly Which]

Topic:

- For the things of this world cannot be made known without a knowledge of mathematics.

[ Cannot Knowledge Known Made Mathematics Things Without World]

Topic:

- If mathematics is to be understood widely, we need to emphasise its elegance and its applications. Sometimes it seems that universities want to emphasise how difficult it is!

[ Applications Difficult Elegance Emphasise How Mathematics Need Seems Sometimes Understood Universities Want Widely]

Topic:

- Mathematics is as old as Man.

[ Man Mathematics Old]

Topic:

- Mathematics is the most beautiful and most powerful creation of the human spirit.

[ Beautiful Creation Human Mathematics Most Powerful Spirit]

Topic:

- Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.

[ Any Art Creative Feeling Fitness Generality Guided Indefinable Inspired Mathematicians Mathematics Now Only Past Prospect Rather Sense Simplicity Symmetry Than Their Things Ultimate Usefulness]

Topic:

- If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

[ Asserted Experience Game Indeed Making Marks Mathematical Mathematics Meaningless Only Paper Played Refer Which]

Topic:

- It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.

[ Disconcerting Immortality Itself Marks Mathematics Off Other Perennial Sciences Which Youthfulness]

Topic:

- "Obvious" is the most dangerous word in mathematics.

[ Dangerous Mathematics Most Obvious Word]

Topic:

- The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.

[ Abstract Also Becomes Lives Longer Mathematics More Possibly Practical Therefore]

Topic:

- The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future.

[ Always Been Difficulties Future Mathematics Mistakes Opportunities Past Unresolved]

Topic:

- Apart from two periods of intense study, of music between the ages of 12 and 14 and of mathematics between the ages of 14 and 16, I coasted, daydreaming, through most of my school years.

[ Ages Apart Between Coasted Daydreaming Intense Mathematics Most Music Periods School Study Through Two Years]

Topic:

- It is not of the essence of mathematics to be conversant with the ideas of number and quantity.

[ Essence Ideas Mathematics Number Quantity]

Topic:

- If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.

[ Arithmetic Attempt Entirely Far Game Get Grasp Limited Logical Mathematics Might Our Physical Poker Probability Processes Reasoning Scientific Should Understanding Use Very Well Were World]

Topic:

- In mathematics the art of proposing a question must be held of higher value than solving it.

[ Art Held Higher Mathematics Must Proposing Question Solving Than Value]

Topic:

- The essence of mathematics lies in its freedom.

[ Essence Freedom Lies Mathematics]

Topic:

- Film is one of the three universal languages, the other two: mathematics and music.

[ Film Languages Mathematics Music Other Three Two Universal]

Topic:

- I was so pleased to be at university to do physics and mathematics.

[ Mathematics Physics Pleased University]

Topic:

- Even when I was studying mathematics, physics, and computer science, it always seemed that the problem of consciousness was about the most interesting problem out there for science to come to grips with.

[ Always Come Computer Consciousness Even Grips Interesting Mathematics Most Out Physics Problem Science Seemed Studying]

Topic:

- Well it was not exactly a dissertation in logic, at least not the kind of logic you would find in Whitehead and Russell's Principia Mathematica for instance. It looked more like mathematics; no formalized language was used.

[ Dissertation Exactly Find Instance Kind Language Least Logic Looked Mathematics More Russell Used Well Whitehead Would]

Topic:

- I sort of was good at writing essays. I was never very good at mathematics, and I was never very good at algebra. I loved science, but I wasn't sure of it.

[ Algebra Essays Good Loved Mathematics Never Science Sort Sure Very Writing]

Topic:

- The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.

[ Begins Ends Magnificence Mathematics Nile Study]

Topic:

- For the execution of the voyage to the Indies, I did not make use of intelligence, mathematics or maps.

[ Did Execution Indies Intelligence Make Maps Mathematics Use Voyage]

Topic:

- Mathematics is written for mathematicians.

[ Mathematicians Mathematics Written]

Topic:

- Not a few other very eminent and scholarly men made the same request, urging that I should no longer through fear refuse to give out my work for the common benefit of students of Mathematics.

[ Benefit Common Eminent Fear Few Give Longer Made Mathematics Men Other Out Refuse Request Same Scholarly Should Students Through Urging Very Work]

Topic:

- For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

[ Active Alike Alone Answer Experience Itself Mathematics Philosophy Question Scholars]

Topic:

- Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.

[ Active Aesthetic Analysis Basic Construction Contemplative Desire Elements Expression Generality Human Individuality Intuition Logic Mathematics Mind Perfection Reason Reflects Will]

Topic:

- It has become almost a cliche to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics.

[ Acceptable Almost Become Boast Boasts Claim Cliche Ignorance Incompetence Literature Mathematics Nobody Proudly Remark Science Socially]

Topic:

- The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.

[ Achieved Completely Concern Consensus Ethical Ever Mathematics Problem Science Source System Systems Unlike]

Topic:

- We in science are spoiled by the success of mathematics. Mathematics is the study of problems so simple that they have good solutions.

[ Good Mathematics Problems Science Simple Solutions Spoiled Study Success]

Topic:

- Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.

[ Applied Better Branches Difficult Had Mathematicians Mathematics Most Poorer Programming Pure Remain]

Topic:

- The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.

[ Appreciates Clumsy Consider Elegance Essential Further Go Ingredient Mathematical Mathematician Mathematics Propose Recognizes Sees Step Traditional]

Topic:

- There should be no such thing as boring mathematics.

[ Boring Mathematics Should Such Thing]

Topic:

- God used beautiful mathematics in creating the world.

[ Beautiful Creating God Mathematics Used World]

Topic:

- The mathematics is not there till we put it there.

[ Mathematics Put Till]

Topic:

- 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.

[ Certain Far Laws Mathematics Reality Refer]

Topic:

- To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.

[ Actually Answer Ask Believed Concept Hence Hidden Infinitely Many Mathematics Mysteries Quantity Small Those Usually Zero]

Topic:

- If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.

[ Advice Again Beginning Follow Mathematics Plato Start Studies Were Would]

Topic:

- It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.

[ Certain Equally Every Exclusive Fault Mathematicians Mathematics May Men Mere Occupation Other Shortcomings Specific True]

Topic:

- The abstract analysis of the world by mathematics and physics rests on the concepts of space and time.

[ Abstract Analysis Concepts Mathematics Physics Rests Space Time World]

Topic:

- How many of you have broken no laws this month? That's the kind of society I want to build. I want a guarantee - with physics and mathematics, not with laws - that we can give ourselves real privacy of personal communications.

[ Broken Build Communications Give Guarantee How Kind Laws Many Mathematics Month Ourselves Personal Physics Privacy Real Society Want]

Topic:

- I am interested in mathematics only as a creative art.

[ Am Art Creative Interested Mathematics Only]

Topic:

- Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

[ Above Applied Distinctly Mainly Mathematical Mathematics More Pure Taught Technique Than Through Useful Whole]

Topic:

- Beauty is the first test: there is no permanent place in the world for ugly mathematics.

[ Beauty First Mathematics Permanent Place Test Ugly World]

Topic:

- We are servants rather than masters in mathematics.

[ Masters Mathematics Rather Servants Than]

Topic:

- Mathematics is a game played according to certain simple rules with meaningless marks on paper.

[ According Certain Game Marks Mathematics Meaningless Paper Played Rules Simple]

Topic:

- Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

[ Boundaries Country Cultural Geographic Knows Mathematics Races World]

Topic:

- The art of doing mathematics consists in finding that special case which contains all the germs of generality.

[ Art Case Consists Contains Doing Finding Generality Germs Mathematics Special Which]

Topic:

- Poetry is a form of mathematics, a highly rigorous relationship with words.

[ Form Highly Mathematics Poetry Relationship Rigorous Words]

Topic:

- And they're also very good at math, these super boogers, and so they teach Billy the ways of mathematics.

[ Also Billy Good Math Mathematics Super Teach These Very Ways]

Topic:

- I had a liberal arts education at Amherst College where I had two majors, mathematics and philosophy.

[ Amherst Arts College Education Had Liberal Majors Mathematics Philosophy Two Where]

Topic:

- I read one or two other books which gave me a background in mathematics other than logic.

[ Background Books Gave Logic Mathematics Other Read Than Two Which]

Topic:

- I went to Princeton from Amherst, where I split my interests between mathematics and philosophy.

[ Amherst Between Interests Mathematics Philosophy Princeton Split Went Where]

Topic:

- Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

[ Become Confused Countless Curve Enough Everyone Exceptions Knows Mathematics Number Possible Studied Through Until]

Topic:

- Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

[ Advanced Been Distinguished Intuition Mathematics Most Proofs Rather Rigorous Sense Than Themselves Those Thus]

Topic:

- An early fascination with higher mathematics at the university level blossomed into speculative thinking that could provide a basis for dealing with economic issues.

[ Basis Blossomed Could Dealing Early Economic Fascination Higher Into Issues Level Mathematics Provide Speculative Thinking University]

Topic:

- My early education was in the public school system of Omaha, where, retrospectively, I realize that my high school training served me in good stead for the basic subjects of mathematics, English, foreign languages and history.

[ Basic Early Education English Foreign Good High History Languages Mathematics Omaha Public Realize School Served Stead Subjects System Training Where]

Topic:

- The completion of my undergraduate training at the University of California (Berkeley) provided just the needed touches of rigor at advanced levels in both economics and mathematics.

[ Advanced Berkeley Both California Completion Economics Just Levels Mathematics Needed Provided Rigor Touches Training Undergraduate University]

Topic:

- I was fortunate to find an extraordinary mathematics and applied mathematics program in Toronto.

[ Applied Extraordinary Find Fortunate Mathematics Program Toronto]

Topic:

- Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.

[ Amount Any Arid Arithmetic Confuse Consider Great Had However Imagination Knowing Many Mathematics More Opportunity Reality Requires Science Which]

Topic:

- We must always emphasize research and development of science and mathematics, and I can think of no better way to achieve this than through our future in space.

[ Achieve Always Better Development Emphasize Future Mathematics Must Our Research Science Space Than Think Through Way]

Topic:

- Consequently he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics.

[ Attain Branches Consequently First Human Lastly Logic Mathematics Metaphysics Must Next Order Perfection Physics Proper Study Their Then Therefore Various Wishes]

Topic:

- But however measurable, there is much more life in music than mathematics or logic ever dreamed of.

[ Dreamed Ever However Life Logic Mathematics Measurable More Much Music Than]

Topic:

- Music at times is more like perfume than mathematics.

[ Mathematics More Music Perfume Than Times]

Topic:

- Being exposed to theory, stimulated by a basic love of concepts and mathematics, was a marvelous experience.

[ Basic Being Concepts Experience Exposed Love Marvelous Mathematics Stimulated Theory]

Topic:

- My interest in the sciences started with mathematics in the very beginning, and later with chemistry in early high school and the proverbial home chemistry set.

[ Beginning Chemistry Early High Home Interest Later Mathematics Proverbial School Sciences Set Started Very]

Topic:

- The mathematics of rhythm are universal. They don't belong to any particular culture.

[ Any Belong Culture Mathematics Particular Rhythm Universal]

Topic:

- It is now quite lawful for a Catholic woman to avoid pregnancy by a resort to mathematics, though she is still forbidden to resort to physics or chemistry.

[ Avoid Catholic Chemistry Forbidden Lawful Mathematics Now Physics Pregnancy Quite Resort She Still Though Woman]

Topic: Religion

- We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry.

[ Beauty Especially Imagination Logic Mathematics Need Nor Poetry Science Somewhat]

Topic:

- I did not have a very literary background. I came to poetry from the sciences and mathematics, and also through an interest in Japanese and Chinese poetry in translation.

[ Also Background Came Chinese Did Interest Japanese Literary Mathematics Poetry Sciences Through Translation Very]

Topic:

- But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius.

[ Arts Genius Madness Mathematics Same Servant Sister Touched Well]

Topic:

- Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.

[ Beauty Chooses Designs Down Earth Important Infinity Mathematician Mathematics Must Mysterious Out Part Pattern Play Powers Pulls Recognition Result Sake Unconscious Understands Which]

Topic:

- Chess, like mathematics and music, is a nursery for child prodigies.

[ Chess Child Mathematics Music Nursery]

Topic:

- I was on the mathematics faculty at M.I.T. from 1951 through until I resigned in the spring of 1959.

[ Faculty Mathematics Resigned Spring Through Until]

Topic:

- Language is remarkable, except under the extreme constraints of mathematics and logic, it never can talk only about what it's supposed to talk about but is always spreading around.

[ Always Around Constraints Except Extreme Language Logic Mathematics Never Only Remarkable Spreading Supposed Talk Under]

Topic:

- As the existence of a corps of professors of mathematics is peculiar to our navy, as well as an apparent, perhaps a real, anomaly, some account of it may be of interest.

[ Account Anomaly Apparent Corps Existence Interest Mathematics May Navy Our Peculiar Perhaps Professors Real Some Well]

Topic:

- I finally reached the conclusion that mathematics was the study I was best fitted to follow, though I did not clearly see in what way I should turn the subject to account.

[ Account Best Clearly Conclusion Did Finally Fitted Follow Mathematics Reached See Should Study Subject Though Turn Way]

Topic:

- It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer.

[ Discourse Half Hard Know Mathematics Other Queer Questions Realm Say Talking Validity Yet]

Topic:

- The infinite in mathematics is alway unruly unless it is properly treated.

[ Infinite Mathematics Properly Treated Unless Unruly]

Topic:

- The most painful thing about mathematics is how far away you are from being able to use it after you have learned it.

[ Able After Away Being Far How Learned Mathematics Most Painful Thing Use]

Topic:

- The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.

[ Branch Compares Does Doing Else Groups Mathematics Obtained Result Same Something Then Theory Thing Which]

Topic:

- We do not learn by inference and deduction and the application of mathematics to philosophy, but by direct intercourse and sympathy.

[ Application Deduction Direct Inference Intercourse Learn Mathematics Philosophy Sympathy]

Topic:

- Life has obliged him to remember so much useful knowledge that he has lost not only his history, but his whole original cargo of useless knowledge; history, languages, literatures, the higher mathematics, or what you will - are all gone.

[ Cargo Gone Higher Him His History Knowledge Languages Life Lost Mathematics Much Obliged Only Original Remember Useful Useless Whole Will]

Topic:

- Modern bodybuilding is ritual, religion, sport, art, and science, awash in Western chemistry and mathematics. Defying nature, it surpasses it.

[ Art Awash Bodybuilding Chemistry Defying Mathematics Modern Nature Religion Ritual Science Sport Surpasses Western]

Topic:

- This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.

[ Book Explore Extent How Intimately Mathematics Physics Related Relationship Seem Trust]

Topic:

- I read everything: fiction, history, science, mathematics, biography, travel.

[ Biography Everything Fiction History Mathematics Read Science Travel]

Topic:

- Whatever the course, whether the course was boring or interesting to me, whether I was talented in mathematics or not talented in languages, my parents expected A's.

[ Boring Course Expected Interesting Languages Mathematics Parents Talented Whatever Whether]

Topic:

- Logic and mathematics are nothing but specialised linguistic structures.

[ Linguistic Logic Mathematics Nothing Specialised Structures]

Topic:

- How is an error possible in mathematics?

[ Error How Mathematics Possible]

Topic:

- Mathematics is the art of giving the same name to different things.

[ Art Different Giving Mathematics Name Same Things]

Topic:

- One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

[ Completely Constant Desire Development Forgotten Had Happiest History Influence Know Mathematics Most Nature Remember Science Would]

Topic:

- Life is good for only two things, discovering mathematics and teaching mathematics.

[ Discovering Good Life Mathematics Only Teaching Things Two]

Topic:

- At the age of 12, I developed an intense interest in mathematics. On exposure to algebra, I was fascinated by simultaneous equations and read ahead of the class to the end of the book.

[ Age Ahead Algebra Book Class Developed End Equations Exposure Fascinated Intense Interest Mathematics Read Simultaneous]

Topic:

- I abandoned chemistry to concentrate on mathematics and physics. In 1942, I travelled to Cambridge to take the scholarship examination at Trinity College, received an award and entered the university in October 1943.

[ Abandoned Award Cambridge Chemistry College Concentrate Entered Examination Mathematics October Physics Received Scholarship Take Travelled Trinity University]

Topic:

- I had changed from being a mathematician to a practicing scientist. I was increasingly embarassed that I could no longer follow some of the more modern branches of pure mathematics.

[ Being Branches Changed Could Follow Had Increasingly Longer Mathematician Mathematics Modern More Practicing Pure Scientist Some]

Topic:

- Reading music is something that's inherently hateful to me. It makes music like mathematics.

[ Hateful Inherently Makes Mathematics Music Reading Something]

Topic:

- In my schooling through high school, I excelled mainly in chemistry, physics and mathematics.

[ Chemistry Excelled High Mainly Mathematics Physics School Schooling Through]

Topic:

- I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza's God, it won't love us in return.

[ Accidental Because God Human Love Mathematics Nothing Particular Planet Return Spinoza Universe Us Whole Won]

Topic:

- Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

[ Defined Know Mathematics May Never Nor Saying Subject Talking True Whether Which]

Topic:

- Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.

[ Absolute Actual Conform Every Into Mathematics Must Necessity Only Possible Region Takes Us Which Word]

Topic:

- The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

[ Being Delight Exaltation Excellence Found Highest Man Mathematics More Poetry Sense Spirit Surely Than Touchstone True Which]

Topic:

- I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded.

[ Based Began Caesar Chose Codes Cryptography Deal Decided Designed Developed Even Mathematical Mathematics Number Principles Science Theory Those Time Use Were Work]

Topic:

- What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.

[ Affected Cryptography Elegant Ends Found Less Mathematics Most Profoundly Pure Realization Sciences These Used Very Which]

Topic:

- I stayed away from mathematics not so much because I knew it would be hard work as because of the amount of time I knew it would take, hours spent in a field where I was not a natural.

[ Amount Away Because Field Hard Hours Knew Mathematics Much Natural Spent Stayed Take Time Where Work Would]

Topic:

- Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry.

[ Art Arts Logic Mathematics Music Philosophy Plastic Poetry Relates Sensuous Were]

Topic:

- Mathematics allows for no hypocrisy and no vagueness.

[ Allows Hypocrisy Mathematics Vagueness]

Topic:

- Mathematics is the music of reason.

[ Mathematics Music Reason]

Topic:

- May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.

[ Described Dream Feels Life Mathematician Mathematics May Music Musician Reason Sense Thinks Working]

Topic:

- The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence.

[ Human Intelligence Intelligible Laws Mathematics Object Physics Pure Unfolding World]

Topic:

- Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

[ After Build Equation Eventually Experiments Mathematics Off Reality Relation Scientists Structure Substituted Through Today Wander Which]

Topic:

- James Brown is important because he decorates the clock correctly and he's good with lower mathematics. Don't get me wrong - he's good.

[ Because Brown Clock Correctly Get Good Important James Lower Mathematics Wrong]

Topic:

- Angling may be said to be so like the mathematics that it can never be fully learned.

[ Angling Fully Learned Mathematics May Never Said]

Topic:

- God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

[ Cannot Consistent Devil Exists God Mathematics Prove Since]

Topic:

- You can not apply mathematics as long as words still becloud reality.

[ Apply Long Mathematics Reality Still Words]

Topic:

- I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.

[ Cambridge Childhood Dates Days Early England Grew Love Mathematics Those Up]

Topic:

- I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.

[ Challenging Excitement Future Going Hope Just Lots Make Mathematicians Mathematics Other Problem Problems Realize Seeing Solving Which Will Young]

Topic:

- I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.

[ Broad Clarify Conceptual Fit Mathematics Part Particular Previous Problem Some Thinking Tried Understanding Would]

Topic:

- I'm sure that some of them will be very hard and I'll have a sense of achievement again, but nothing will mean the same to me - there's no other problem in mathematics that could hold me the way that this one did.

[ Achievement Again Could Did Hard Hold Mathematics Mean Nothing Other Problem Same Sense Some Sure Them Very Way Will]

Topic:

- It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years.

[ Beyond Complete Could Day Hundred Invented Mathematics May Methods Needed Next Perhaps Present Proof Simply Step Take Would Years]

Topic:

- It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.

[ Along Any Day End Even Fine Generates Interesting Long Mathematics Problem Solve Way Work]

Topic:

- The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

[ Definition Generates Good Itself Mathematical Mathematics Problem Rather Than]

Topic:

- We've lost something that's been with us for so long, and something that drew a lot of us into mathematics. But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention.

[ Always Attention Been Capture Drew Find Into Just Long Lost Lot Math Mathematics New Ones Our Perhaps Problems Something Us Way]

Topic:

- Well, some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve.

[ Extremely Hard Hundred Look Mathematics Out Problems Simple Solve Some Them Then Try Turns Well Year Years]

Topic:

- In some parts of life, like mathematics and science, yeah, I was a genius. I would top all the top scores you could ever measure it by.

[ Could Ever Genius Life Mathematics Measure Parts Science Scores Some Top Would Yeah]

Topic: