Mathematical Quotations

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Mathematical QuotationsAbel, Niels H. (1802 - 1829)If you disregard the very simplest cases, there is in all of mathematics not a singleinfinite series whose sum has been rigorously determined. In other words,the mostimportant parts of mathematics stand without a foundation.

In G. F. Simmons, Calculus Gems, New York !cgraw "ill, Inc., #$$%, p. #&&.Abel, Niels H. (1802 - 1829)[A reply to a question about how he got his expertise:]'y studying the masters and not their pupils.Abel, Niels H. (1802 - 1829)[About Gauss' mathematical writing style]"e is like the fo(, who effaces his tracks in the sand with his tail.In G. F. Simmons, Calculus Gems, New York !cgraw "ill, Inc., #$$%, p. #)).Adams, Doulas (19!2 - 2001)'istromathics itself is simply a revolutionary new way of understanding the behaviorof numbers. *ust as +instein observed that space was not an absolute but depended

on the observers movement in space, and that time was not an absolute, butdepended on the observers movement in time, so it is now reali-ed that numbers arenot absolute, but depend on the observers movement in restaurants.Life, the ni!erse an" #!erything$New York "armony 'ooks, #$&%.Adams, Doulas (19!2 - 2001)

he first nonabsolute number is the number of people for whom the table is reserved.his will vary during the course of the first three telephone calls to the restaurant, andthen bear no apparent relation to the number of people who actually turn up, or tothe number of people who subse/uently 0oin them after the show1match1party1gig, orto the number of people who leave when they see who else has turned up.

he second nonabsolute number is the given time of arrival, which is now known tobe one of the most bi-arre of mathematical concepts, a recipriverse(cluson, a numberwhose e(istence can only be defined as being anything other than itself. In otherwords, the given time of arrival is the one moment of time at which it is impossiblethat any member of the party will arrive. 2ecipriverse(clusons now play a vital part inmany branches of math, including statistics and accountancy and also form the basice/uations used to engineer the Somebody +lses 3roblem field.

he third and most mysterious piece of nonabsoluteness of all lies in the relationshipbetween the number of items on the bill, the cost of each item, the number of peopleat the table and what they are each prepared to pay for. 4he number of people whohave actually brought any money is only a subphenomenon of this field.5

Life, the ni!erse an" #!erything$New York "armony 'ooks, #$&%.Adams, Doulas (19!2 - 2001)Numbers written on restaurant bills within the confines of restaurants do not followthe same mathematical laws as numbers written on any other pieces of paper in anyother parts of the 6niverse.

his single statement took the scientific world by storm. It completely revolutioni-edit. So many mathematical conferences got held in such good restaurants that many ofthe finest minds of a generation died of obesity and heart failure and the science ofmath was put back by years.Life, the ni!erse an" #!erything$New York "armony 'ooks, #$&%.Adams, "ohn (1#$! - 182%)

I must study politics and war that my sons may have liberty to study mathematicsand philosophy. !y sons ought to study mathematics and philosophy, geography,
http://math.furman.edu/mqs.htmlhttp://math.furman.edu/mqs.html


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natural history, naval architecture, navigation, commerce and agriculture in order togive their children a right to study painting, poetry, music, architecture, statuary,tapestry, and porcelain.7etter to 8bigail 8dams, !ay #%, #)&9.Adle&, Al'&ed+ach generation has its few great mathematicians, and mathematics would not evennotice the absence of the others. hey are useful as teachers, and their researchharms no one, but it is of no importance at all. 8 mathematician is great or he isnothing.:!athematics and ;reativity.: %he &ew or(er )aga*ine, February #$, #$)%.Adle&, Al'&ed

he mathematical life of a mathematician is short. B, p. #@>%.Anonmous7ike the crest of a peacock so is mathematics at the head of all knowledge.

D8n old Indian saying. 8lso, :Li(e the Crest of a .eacoc(: is the title of a book by G.G.*osephE


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Anonmous2eferees report his paper contains much that is new and much that is true.6nfortunately, that which is true is not new and that which is new is not true.In ".+ves +eturn to )athematical Circles, 'oston 3rindle, @.Aub&e, "ohn (1%2%-1%9#)

D8bout homas "obbesE"e was @9 years old before he looked on geometry which happened accidentally.


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'eing in a gentlemans library, +uclids +lements lay open, and :twas the @) +l. libri I:D3ythagoras heoremE. "e read the proposition :'y God:, sayd he, :this isimpossible: So he reads the demonstration of it, which referred him back to such aproposition which proposition he read. hat referred him back to another, which healso read. #t sic "einceps, that at last he was demonstratively convinced of thattrueth. his made him in love with geometry.In A. 7. Cick 4ed.5 rief Li!es, A(ford A(ford 6niversity 3ress, #$B9, p. [email protected], +. H. (190#-19#$)"ow happy the lot of the mathematician. "e is 0udged solely by his peers, and thestandard is so high that no colleague or rival can ever win a reputation he does notdeserve.%he ;yer's


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to be more kinds of them, as nature grows further disclosed.A"!ancement of Learningbook % ;e Augmentisbook ?./acon, oe&For the things of this world cannot be made known without a knowledge ofmathematics./pus )a?uspart @ ;istinctia .rima cap 0, #%B)./acon, oe&In the mathematics I can report no deficience, e(cept that it be that men do notsufficiently understand the e(cellent use of the pure mathematics, in that they doremedy and cure many defects in the wit and faculties intellectual. For if the wit betoo dull, they sharpen it if too wandering, they fi( it if too inherent in the sense, theyabstract it. So that as tennis is a game of no use in itself, but of great use in respect itmaketh a /uick eye and a body ready to put itself into all postures so in themathematics, that use which is collateral and intervenient is no less worthy than thatwhich is principal and intended.

*ohn Fauvel and *eremy Gray 4eds.5A #, p #B@./ell, 4&ic 5emle (188$-19%0)It is the perennial youthfulness of mathematics itself which marks it off with adisconcerting immortality from the other sciences./ell, 4&ic 5emle (188$-19%0)

he "andmaiden of the Sciences.D'ook by that title.E/ell, 4&ic 5emle (188$-19%0)8bstractness, sometimes hurled as a reproach at mathematics, is its chief glory and

its surest title to practical usefulness. It is also the source of such beauty as mayspring from mathematics.


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/ell, 4&ic 5emle (188$-19%0)Guided only by their feeling for symmetry, simplicity, and generality, and anindefinable sense of the fitness of things, creative mathematicians now, as in thepast, are inspired by the art of mathematics rather than by any prospect of ultimateusefulness./ell, 4&ic 5emle (188$-19%0):Abvious: is the most dangerous word in mathematics./ell, 4&ic 5emle (188$-19%0)

he pursuit of pretty formulas and neat theorems can no doubt /uickly degenerateinto a silly vice, but so can the /uest for austere generalities which are so verygeneral indeed that they are incapable of application to any particular.In ". +ves )athematical Circles 9quare", 'oston 3rindle,


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/e&noulli, "ohann'ut 0ust as much as it is easy to find the differential of a given /uantity, so it isdifficult to find the integral of a given differential. !oreover, sometimes we cannotsay with certainty whether the integral of a given /uantity can be found or not./esico3itch, A..8 mathematicians reputation rests on the number of bad proofs he has given.In *. +. 7ittlewoodA )athematician's )iscellany, !ethuen H ;o. 7td., #$>?./laeGod forbid that ruth should be confined to !athematical CemonstrationK&otes on +eynol"'s ;iscourses, c. #&9&./lae


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/&o:ne, i& 5homas (1%0!-1%82)8ll things began in Arder, so shall they end, and so shall they begin again, accordingto the Ardainer of Arder, and the mystical mathematicks of the ;ity of "eaven.B, p. #99#./uc, ea&l . (1892 - 19#$)No one really understood music unless he was a scientist, her father had declared,and not 0ust a scientist, either, oh, no, only the real ones, the theoreticians, whoselanguage mathematics. She had not understood mathematics until he had e(plainedto her that it was the symbolic language of relationships. :8nd relationships,: he had

told her, :contained the essential meaning of life.:%he Go""ess Abi"es, .t$ , #$)%./u&e, 4dmund

he age of chivalry is gone. hat of sophisters, economists and calculators hassucceeded.+eflections on the +e!olution in rance./utle&, /isho

o us probability is the very guide of life.3reface toAnalogy./utle&, amuel (1%12 - 1%80)... here can be no doubt about faith and not reason being the ultima ratio. +ven

+uclid, who has laid himself as little open to the charge of credulity as any writer whoever lived, cannot get beyond this. "e has no demonstrable first premise. "e re/uirespostulates and a(ioms which transcend demonstration, and without which he can donothing. "is superstructure indeed is demonstration, but his ground his faith. Noragain can he get further than telling a man he is a fool if he persists in differing fromhim. "e says :which is absurd,: and declines to discuss the matter further. Faith andauthority, therefore, prove to be as necessary for him as for anyone else.%he -ay of All lesh./&on


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suspicion on the part of a prudent man.;e Bita .ropria Liber$*a&lle, 5homas (1#9! - 1881)It is a mathematical fact that the casting of this pebble from my hand alters thecentre of gravity of the universe.9artor +esartus $*a&lle, 5homas (1#9!-1881)

eaching school is but another word for sure and not very slow destruction.In ". +ves n )athematical Circles, 'oston 3rindle,


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things.::he /uestion is,: said "umpty Cumpty, :which is to be master = thats all.:%hrough the Loo(ing Glass$*=line,


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decimals. I eventually arrived at the point where so many cows ate so much grass,and tanks filled with water in so many hours I found it /uite enthralling.

An Autobiography$*hu&chill, ?i&@ +inston ence& (18#-19%!)It is a good thing from an uneducated man to read books of /uotations.2oving ;ommission in )y #arly Life. #$?9.*hu&chill, i& +inston ence& (18#-19%!)I had a feeling once about !athematics = that I saw it all. Cepth beyond depth wasrevealed to me = the 'yss and 8byss. I saw = as one might see the transit of Menus oreven the 7ord !ayors Show = a /uantity passing through infinity and changing its signfrom plus to minus. I saw e(actly why it happened and why the tergiversation wasinevitable but it was after dinner and I let it go.In ". +ves +eturn to )athematical Circles, 'oston 3rindle,


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DAlembe&t, "ean


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undogmatic way.In %he )athematical ntelligencer, v. >, no. %, #$&?.De Mo&an, Auustus (180%-18#1)D


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too remote to be reached in the end, or to well hidden to be discovered.;iscours "e la )tho"e. #B?).Desca&tes, en= (1!9%-1%!0)


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beauty in ones e/uations that to have them fit e(periment. If Schroedinger had beenmore confident of his work, he could have published it some months earlier, and hecould have published a more accurate e/uation. It seems that if one is working fromthe point of view of getting beauty in ones e/uations, and if one has really a soundinsight, one is on a sure line of progress. If there is not complete agreement betweenthe results of ones work and e(periment, one should not allow oneself to be toodiscouraged, because the discrepancy may well be due to minor features that are notproperly taken into account and that will get cleared up with further development ofthe theory.9cientific American, !ay #$B?.Di&ac, aul Ad&ien Mau&ice (1902- )!athematics is the tool specially suited for dealing with abstract concepts of any kindand there is no limit to its power in this field.In 3. *. Cavis and 2. "ersh %he )athematical #xperience, 'oston 'irkhPuser, #$.Di&ac, aul Ad&ien Mau&ice (1902- )In science one tries to tell people, in such a way as to be understood by everyone,something that no one ever knew before. 'ut in poetry, its the e(act opposite.In ". +ves )athematical Circles A"ieu, 'oston 3rindle,


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In )echanisms of ;isco!eryin I. S. Gordon and S. Sorkin 4eds.5 %he Armchair 9cience+ea"er,New York Simon and Schuster, #$>$.Dunsan,


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4ddinton, i& A&thu& (1882-19)It is impossible to trap modern physics into predicting anything with perfectdeterminism because it deals with probabilities from the outset.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.4ddinton, i& A&thu& (1882-19)I believe there are#>,)@),)%@,#?B,%)>,99%,>)),B9>,B>?,$B#,#,>>>,@B&,9@@,)#),$#@,>%),##B,)9$,?BB,%?#,@%>,9)B,#&>,B?#,9?#,%$B protons in the universe and the same number ofelectrons.%he .hilosophy of .hysical 9cience. ;ambridge, #$?$.4ddinton, i& A&thu& (1882-19)

o the pure geometer the radius of curvature is an incidental characteristic = like thegrin of the ;heshire cat. o the physicist it is an indispensable characteristic. It wouldbe going too far to say that to the physicist the cat is merely incidental to the grin.3hysics is concerned with interrelatedness such as the interrelatedness of cats andgrins. In this case the :cat without a grin: and the :grin without a cat: are e/ually setaside as purely mathematical phantasies.

%he #xpan"ing ni!erse$.4ddinton, i& A&thu& (1882-19)"uman life is proverbially uncertain few things are more certain than the solvency ofa life=insurance company.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.4d:a&ds, "onathon no. >, Cecember #$$%.4ien, Man'&ed (192# - )8 theory has only the alternative of being right or wrong. 8 model has a thirdpossibility it may be right, but irrelevant.

*agdish !ehra 4ed.5 %he .hysicist's Conception of &ature, #$)?.4instein, Albe&t (18#9-19!!)

DCuring a lectureEhis has been done elegantly by !inkowski but chalk is cheaperthan grey matter, and we will do it as it comes.D8ttributed by 3Tlya.E

*.+. 7ittlewood,A )athematician's )iscellany, !ethuen and ;o. 7td., #$>?.4instein, Albe&t (18#9-19!!)+verything should be made as simple as possible, but not simpler.+ea"er's ;igest. Act. #$)).4instein, Albe&t (18#9-19!!)I dont believe in mathematics.Juoted by ;arl Seelig.Albert #instein.4instein, Albe&t (18#9-19!!)

Imagination is more important than knowledge./n 9cience$


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4instein, Albe&t (18#9-19!!)he most beautiful thing we can e(perience is the mysterious. It is the source of alltrue art and science.-hat elie!e$4instein, Albe&t (18#9-19!!)

he bitter and the sweet come from the outside, the hard from within, from ones ownefforts./ut of )y Later ears$4instein, Albe&t (18#9-19!!)Gott wFrfelt nicht$4instein, Albe&t (18#9-19!!);ommon sense is the collection of pre0udices ac/uired by age eighteen.In +. . 'ell )athematics, @ueen an" 9er!ant of the 9ciences. #$>%.4instein, Albe&t (18#9-19!!)God does not care about our mathematical difficulties. "e integrates empirically.7. Infeld @uest, #$@%.4instein, Albe&t (18#9-19!!)"ow can it be that mathematics, being after all a product of human thought

independent of e(perience, is so admirably adapted to the ob0ects of reality4instein, Albe&t (18#9-19!!)D8bout NewtonENature to him was an open book, whose letters he could read without effort.In G. Simmons Calculus Gems, New York !cGraw "ill, #$$%.4instein, Albe&t (18#9-19!!)8s far as the laws of mathematics refer to reality, they are not certain and as far asthey are certain, they do not refer to reality.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.4instein, Albe&t (18#9-19!!)


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4instein, Albe&t (18#9-19!!)hese thoughts did not come in any verbal formulation. I rarely think in words at all. 8thought comes, and I may try to e(press it in words afterward.In ". +ves )athematical Circles A"ieu, 'oston 3rindle,


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4llis, Ha3elocIt is here Din mathematicsE that the artist has the fullest scope of his imagination.%he ;ance of Life$4&ath, E.God is a child and when he began to play, he cultivated mathematics. It is the mostgodly of mans games.;as blin"e 9piel. #$>@.4&dFs, aul!athematics is not yet ready for such problems.D8ttributed by 3aul "almos.E%he American )athematical )onthly, Nov. #$$%4&dFs, aul8 !athematician is a machine for turning coffee into theorems.4ule&,


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established on earth. here is one, however, of which he can boast the universaladoption of the "indu=8rabic numerals to record numbers. In this we perhaps havemans uni/ue worldwide victory of an idea.)athematical Circles 9quare", 'oston 3rindle,


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phantasmagoria disappear.


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from !r. 'ertrand 2ussell when the work was nearly through the press.In 9cientific American, !ay #$&@, p )).;alb&aith, "ohn >enneth

here can be no /uestion, however, that prolonged commitment to mathematicale(ercises in economics can be damaging. It leads to the atrophy of 0udgement andintuition...#conomics, .eace, an" Laughter$;alilei, ;alileo (1!% - 1%2)Dhe universeE cannot be read until we have learnt the language and become familiarwith the characters in which it is written. It is written in mathematical language, andthe letters are triangles, circles and other geometrical figures, without which means itis humanly impossible to comprehend a single word./pere l 9aggiatorep. #)#.;alilei, ;alileo (1!% - 1%2)!easure what is measurable, and make measurable what is not so.Juoted in ".


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;a&dne&, Ma&tin'iographical history, as taught in our public schools, is still largely a history ofboneheads ridiculous kings and /ueens, paranoid political leaders, compulsivevoyagers, ignorant generals == the flotsam and 0etsam of historical currents. he menwho radically altered history, the great scientists and mathematicians, are seldommentioned, if at all.In G. Simmons Calculus Gems, New York !cGraw "ill, #$$%.;a&dne&, Ma&tin!athematics is not only real, but it is the only reality. hat is that entire universe ismade of matter, obviously. 8nd matter is made of particles. Its made of electrons andneutrons and protons. So the entire universe is made out of particles. Now what arethe particles made out of heyre not made out of anything. he only thing you cansay about the reality of an electron is to cite its mathematical properties. So theres asense in which matter has completely dissolved and what is left is 0ust amathematical structure.Gardner on Gardner *3'! ;ommunications 8ward 3resentation. ocus1%he&ewsletter of the )athematical Association of Americav. #@, no. B, Cecember #$$@.;auss, >a&l &ied&ich (1###-18!!)I confess that Fermats heorem as an isolated

proposition has very little interest for me, because I could easily lay down a multitudeof such propositions, which one could neither prove nor dispose of.D8 reply to Albers attempt in #B to entice him to work on Fermats heorem.E In *.2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster, #$>B. p.?#%.;auss, >a&l &ied&ich (1###-18!!)If others would but reflect on mathematical truths as deeply and as continuously as Ihave, they would make my discoveries.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B. p. ?%B.;auss, >a&l &ied&ich (1###-18!!)

here are problems to whose solution I would attach an infinitely greater importancethan to those of mathematics, for e(ample touching ethics, or our relation to God, orconcerning our destiny and our future but their solution lies wholly beyond us andcompletely outside the province of science.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B. p. ?#@.;auss, >a&l &ied&ich (1###-18!!)

You know that I write slowly. his is chiefly because I am never satisfied until I havesaid as much as possible in a few words, and writing briefly takes far more time thanwriting at length.

In G. Simmons Calculus Gems, New York !cGraw "ill inc., #$$%.;auss, >a&l &ied&ich (1###-18!!)God does arithmetic.;auss, >a&l &ied&ich (1###-18!!)


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;auss, >a&l &ied&ich (1###-18!!)I have had my results for a long time but I do not yet know how I am to arrive atthem.In 8. 8rber %he )in" an" the #ye#$>@.;auss, >a&l &ied&ich (1###-18!!)D"is mottoEFew, but ripe.;auss, >a&l &ied&ich (1###-18!!)D"is second mottoE

hou, nature, art my goddess to thy laws my services are bound...a&l &ied&ich (1###-18!!)Dattributed to him by ".' 7UbsenE

heory attracts practice as the magnet attracts iron.Foreword of ".' 7Ubsens geometry te(tbook.;auss, >a&l &ied&ich (1###-18!!)It is not knowledge, but the act of learning, not possession but the act of gettingthere, which grants the greatest en0oyment.


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;ibbs, "osiah +illa&d (18$9-190$)!athematics is a language.;ilbe&t, +. . (18$% - 1911)Im very good at integral and differential calculus, I know the scientific names ofbeings animalculous In short, in matters vegetable, animal, and mineral, I am thevery model of a modern !a0or=General.%he .irates of .en*ance$8ct #.;laishe&, ".+.

he mathematician re/uires tact and good taste at every step of his work, and he hasto learn to trust to his own instinct to distinguish between what is really worthy of hisefforts and what is not.In ". +ves )athematical Circles 9quare", 'oston 3rindle, B, p. >@&.

;oedel, >u&tI dont believe in natural science.DSaid to physicist *ohn 'ahcall.E+d 2egis, -ho Got #instein's /fficeH8ddison


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Hadama&d, "ac6ueshe shortest path between two truths in the real domain passes through the comple(domain.Juoted in %he )athematical ntelligencer, v. #?, no. #,


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Halmos, aul .Cont 0ust read it fight itK 8sk your own /uestions, look for your own e(amples,discover your own proofs. Is the hypothesis necessary Is the converse true


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Ha&d, ;od'&e H. (18## - 19#)In great mathematics there is a very high degree of une(pectedness, combined withinevitability and economy.

A )athematician's Apology, 7ondon, ;ambridge 6niversity 3ress, #$@#.Ha&d, ;od'&e H. (18## - 19#)

here is no scorn more profound, or on the whole more 0ustifiable, than that of themen who make for the men who e(plain. +(position, criticism, appreciation, is workfor second=rate minds.


Young !en should prove theorems, old men should write books.Juoted by Freeman Cyson in Freeman Cyson !athematician, 3hysicist, and , No. #,

*anuary #[email protected]&d, ;od'&e H. (18## - 19#)8 science is said to be useful of its development tends to accentuate the e(istingine/ualities in the distribution of wealth, or more directly promotes the destruction ofhuman life.


he mathematicians patterns, like the painters or the poets must be beautiful theideas, like the colors or the words must fit together in a harmonious way. 'eauty isthe first test there is no permanent place in this world for ugly mathematics.

A )athematician's Apology, 7ondon, ;ambridge 6niversity 3ress, #$@#.Ha&d, ;od'&e H. (18## - 19#)I believe that mathematical reality lies outside us, that our function is to discover orobserve it, and that the theorems which we prove, and which we describegrandilo/uently as our :creations,: are simply the notes of our observations.

A )athematician's Apology, 7ondon, ;ambridge 6niversity 3ress, #$@#.

Ha&d, ;od'&e H. (18## - 19#)8rchimedes will be remembered when 8eschylus is forgotten, because languages dieand mathematical ideas do not. :Immortality: may be a silly word, but probably amathematician has the best chance of whatever it may mean.

A )athematician's Apology, 7ondon, ;ambridge 6niversity 3ress,#$@#.Ha&d, ;od'&e H. (18## - 19#)

he fact is that there are few more :popular: sub0ects than mathematics. !ost peoplehave some appreciation of mathematics, 0ust as most people can en0oy a pleasanttune and there are probably more people really interested in mathematics than inmusic. 8ppearances may suggest the contrary, but there are easy e(planations. !usic

can be used to stimulate mass emotion, while mathematics cannot and musicalincapacity is recogni-ed 4no doubt rightly5 as mildly discreditable, whereas mostpeople are so frightened of the name of mathematics that they are ready, /uiteunaffectedly, to e(aggerate their own mathematical stupidity.

A )athematician's Apology, 7ondon, ;ambridge 6niversity 3ress, #$@#.Ha&d, 5homas...he seemed to approach the grave as an hyperbolic curve approaches a line, lessdirectly as he got nearer, till it was doubtful if he would ever reach it at all.ar from the )a""ing Crow".Ha&ish-*hand&aI have often pondered over the roles of knowledge or e(perience, on the one hand,

and imagination or intuition, on the other, in the process of discovery. I believe thatthere is a certain fundamental conflict between the two, and knowledge, by


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advocating caution, tends to inhibit the flight of imagination. herefore, a certainnaivete, unburdened by conventional wisdom, can sometimes be a positive asset.2. 7anglands, :"arish=;handra,: iographical )emoirs of ellows of the +oyal 9ociety?# 4#$&>5 #$) = %%>.Ha&&is, dne ".

he real danger is not that computers will begin to think like men, but that men willbegin to think like computers.In ". +ves +eturn to )athematical Circles, 'oston 3rindle, B.Hemel, *a&l ;.he most distinctive characteristic which differentiates mathematics from the variousbranches of empirical science, and which accounts for its fame as the /ueen of thesciences, is no doubt the peculiar certainty and necessity of its results.:Geometry and +mpirical Science: in *. 2. Newman 4ed.5 %he -orl" of )athematics,New York Simon and Schuster, #$>B.Hemel, *a&l ;....to characteri-e the import of pure geometry, we might use the standard form of amovie=disclaimer No portrayal of the characteristics of geometrical figures or of thespatial properties of relationships of actual bodies is intended, and any similarities

between the primitive concepts and their customary geometrical connotations arepurely coincidental.


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:Geometry and +mpirical Science: in *. 2. Newman 4ed.5 %he -orl" of )athematics,New York Simon and Schuster, #$>B.Henin,


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Hilbe&t, Da3id (18%2-19$)3hysics is much too hard for physicists.;. 2eid B.Hi&st, 5homas A&cheth 8ugust #&># An uesday evening at !useum, at a ball in the gardens. he nightwas chill, I dropped too suddenly from Cifferential ;alculus into ladies society, andcould not give myself freely to the change. 8fter an hours attempt so to do, Ireturned, cursing the mode of life I was pursuing ne(t morning I had already shaken

hands, however, with Ciff. ;alculus, and forgot the ladies....*. "elen Gardner and 2obin *.


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Hobbes, 5homasGeometry, which is the only science that it hath pleased God hitherto to bestow onmankind.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.Hobbes, 5homas

he errors of definitions multiply themselves according as the reckoning proceedsand lead men into absurdities, which at last they see but cannot avoid, withoutreckoning anew from the beginning.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.Holmes, li3e& +endellCescartes commanded the future from his study more than Napoleon from thethrone.In G. Simmons Calculus Gems, New York !cGraw "ill Inc., #$$%.Holmes, li3e& +endell;ertitude is not the test of certainty.


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HuBle, AldousI admit that mathematical science is a good thing. 'ut e(cessive devotion to it is abad thing.Interview with *.


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of the world.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.

"acobi, *a&lGod ever arithmeti-es.In ". +ves )athematical Circles +e!isite", 'oston 3rindle, B.

"ames, +illiam (182 - 1910)he union of the mathematician with the poet, fervor with measure, passion withcorrectness, this surely is the ideal.Collecte" #ssays$

"eans, i& "ameshe essential fact is that all the pictures which science now draws of nature, andwhich alone seem capable of according with observational facts, are mathematicalpictures.

In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.

"eans, i& "amesFrom the intrinsic evidence of his creation, the Great 8rchitect of the 6niverse nowbegins to appear as a pure mathematician.)ysterious ni!erse.

"e''e&son, 5homas...the science of calculation also is indispensable as far as the e(traction of the s/uareand cube roots 8lgebra as far as the /uadratic e/uation and the use of logarithmsare often of value in ordinary cases but all beyond these is but a lu(ury a delicious

lu(ury indeed but not be in indulged in by one who is to have a profession to followfor his subsistence.In *. 2obert Appenheimer :he +ncouragement of Science: in I. Gordon and S. Sorkin4eds.5 %he Armchair 9cience +ea"er, New York Simon and Schuster, #$>$.

"e3ons, +illiam tanleIt is clear that +conomics, if it is to be a science at all, must be a mathematicalscience.%heory of .olitical #conomy$

"ohnson, amuel (1#09-1#8)Sir, I have found you an argument. I am not obliged to find you an understanding.

*. 'oswell %he Life of 9amuel ohnson, #)&@.

"o:ett, /enCamin (181# - 189$)7ogic is neither a science or an art, but a dodge.


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In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.>ant, 4mmanual (1#2 - 180)

he science of mathematics presents the most brilliant e(ample of how pure reasonmay successfully enlarge its domain without the aid of e(perience.%he )athematical ntelligencer, v. #?, no. #, ant, 4mmanual (1#2 - 180)8ll human knowledge thus begins with intuitions, proceeds thence to concepts, andends with ideas.Juoted in "ilberts oun"ations of Geometry.>alan, Ab&aham!athematics is not yet capable of coping with the naivete of the mathematicianhimself.9ociology Learns the Language of )athematics.>alans, G&3in


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securely and confidently it must first set its affairs in order at home.)athematics an" the magination, New York Simon and Schuster, #$@9.>asne&, 4. and Ne:man, ". .

he testament of science is so continually in a flu( that the heresy of yesterday is thegospel of today and the fundamentalism of tomorrow.+. asner and *. 2. Newman, )athematics an" the magination, Simon and Schuster,#$@9.>elle&, Helen (1880 - 19%8)Now I feel as if I should succeed in doing something in mathematics, although Icannot see why it is so very important... he knowledge doesnt make life any sweeteror happier, does it%he 9tory of )y Life$#$9?.>elle, "ohn8 topologist is one who doesnt know the difference between a doughnut and a coffeecup.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.>ele&, "ohannes (1!#1-1%$0)8 mind is accustomed to mathematical deduction, when confronted with the faulty

foundations of astrology, resists a long, long time, like an obstinate mule, untilcompelled by beating and curses to put its foot into that dirty puddle.In G. Simmons Calculus Gems, New York !cGraw "ill Inc., #$$%.>ele&, "ohannes (1!#1-1%$0)enes, "ohn Mana&dIt has been pointed out already that no knowledge of probabilities, less in degree thancertainty, helps us to know what conclusions are true, and that there is no directrelation between the truth of a proposition and its probability. 3robability begins andends with probability.%he Application of .robability to Con"uct.>leinhen, obe&t ".line, Mo&&is8 proof tells us where to concentrate our doubts.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.>line, Mo&&isStatistics the mathematical theory of ignorance.

In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.


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>line, Mo&&is7ogic is the art of going wrong with confidence.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.>line, Mo&&is6niversities hire professors the way some men choose wives = they want the ones theothers will admire.-hy the .rofessor Can't %each$St. !artins 3ress, #$)). p $%.>oestle&, A&thu& (190!- )In the inde( to the si( hundred odd pages of 8rnold oynbees 8 Study of "istory,abridged version, the names of ;opernicus, Galileo, Cescartes and Newton do notoccur yet their cosmic /uest destroyed the medieval vision of an immutable socialorder in a walled=in universe and transformed the +uropean landscape, society,culture, habits and general outlook, as thoroughly as if a new species had arisen onthis planet.In G. Simmons Calculus Gems, New York !cGraw "ill Inc., #$$%.>oestle&, A&thu& (190!- )Nobody before the 3ythagoreans had thought that mathematical relations held thesecret of the universe. wenty=five centuries later, +urope is still blessed and cursed

with their heritage. o non=+uropean civili-ations, the idea that numbers are the keyto both wisdom and power, seems never to have occurred.%he 9leepwal(ers$#$>$.>o3ale3s, onCaSay what you know, do what you must, come what may.D!otto on her paper :An the 3roblem of the 2otation of a Solid 'ody about a Fi(ed3oint.:E>&a't, &in u Hohlenlohe-Gnel'inen (182# - 1892)!athematics is indeed dangerous in that it absorbs students to such a degree that itdulls their senses to everything else.8ttributed by arl Schellbach. In ". +ves )athematical Circles A"ieu, 'oston 3rindle,

&onece&,


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reproduce it.". +vesAn ntro"uction to the


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!an follows only phantoms.Ce!organs u"get of .ara"oxes.de


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by many philosophers.9cientific American, %##, September #$B@, p. #%$.


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da Einci,


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?.


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said that I wish I had.: In the ne(t proof=sheets I read 4what now stands5, :It was7ittlewood who said...:

A )athematician's )iscellany, !ethuen ;o. 7td, #$>?.


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to number, the cry becomes a song, noise ac/uires rhythm, the spring is transformedinto a dance, force becomes dynamic, and outlines figures.Mann, 5homas (18#!-19!!)8 great truth is a truth whose opposite is also a great truth.#ssay on reu". #$?).Mann, 5homas (18#!-19!!)I tell them that if they will occupy themselves with the study of mathematics they willfind in it the best remedy against the lusts of the flesh.%he )agic )ountain. #$%).Mann, 5homas (18#!-19!!)Some of the men stood talking in this room, and at the right of the door a little knothad formed round a small table, the center of which was the mathematics student,who ws eagerly talking. "e had made the assertion that one could draw through agiven point more than one parallel to a straight line Frau "agenstrVm had cried outthat this was impossible, and he had gone on to prove it so conclusively that hishearers were constrained to behave as though they understood.Little


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mathematicians what is even more annoying is that by doing so they often come upwith the right answer.ulletin of the American )athematical 9ociety, v. B$, p. B##, #$B?.Mencen, H.


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In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.Mins, Ma&3in


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Nebeuts, 4. >im8 good preparation takes longer than the delivery.In ". +ves +eturn to )athematical Circles, 'oston 3rindle,


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of mathematicians for the 0ob of transforming delectable ingredients into a dish thattastes like a damp blanket.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.Ne:ton, Gsaac (1%2-1#2#)...from the same principles, I now demonstrate the frame of the System of the


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in mental acrobatics and contribute nothing to society.Complete -or(s on apan's .hilosophical %hought. #$>B.enheime&, "ulius obe&t (190 - 19%#)

oday, it is not only that our kings do not know mathematics, but our philosophers donot know mathematics and == to go a step further == our mathematicians do not knowmathematics.:he ree of nowledge: in


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ascal, /laise (1%2$-1%%2)Nature is an infinite sphere of which the center is everywhere and the circumferencenowhere..ensees$ 084$ascal, /laise (1%2$-1%%2)


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shorter.Lettres pro!inciales$ascal, /laise (1%2$-1%%2)

he last thing one knows when writing a book is what to put first..ensees$ 084$ascal, /laise (1%2$-1%%2)?.ascal, /laise (1%2$-1%%2)

here are two types of mind ... the mathematical, and what might be called theintuitive. he former arrives at its views slowly, but they are firm and rigid the latteris endowed with greater fle(ibility and applies itself simultaneously to the diverse

lovable parts of that which it loves.;iscours sur les passions "e l'amour. #B>?.assano,


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ei&ce, /enCamin (1809-1880)!athematics is the science which draws necessary conclusions.!emoir read before the National 8cademy of Sciences in B.ei&ce, *ha&les ande&s (18$9-191)8mong the minor, yet striking characteristics of mathematics, may be mentioned the

fleshless and skeletal build of its propositions the peculiar difficulty, complication,and stress of its reasonings the perfect e(actitude of its results their broaduniversality their practical infallibility.:he +ssence of !athematics: in *. 2. Newman 4ed.5 %he -orl" of )athematics, New

York Simon and Schuster, #$>B.ei&ce, *ha&les ande&s (18$9-191)

he pragmatist knows that doubt is an art which hs to be ac/uired with difficulty.Collecte" .apers$ede&sen, "eanGeometry is a skill of the eyes and the hands as well as of the mind.lato (ca 29-$# /*)

"e who can properly define and divide is to be considered a god.lato (ca 29-$# /*)

he ludicrous state of solid geometry made me pass over this branch. +epublic, MII,>%&.lato (ca 29-$# /*)"e is unworthy of the name of man who is ignorant of the fact that the diagonal of as/uare is incommensurable with its side.lato (ca 29-$# /*)!athematics is like checkers in being suitable for the young, not too difficult,amusing, and without peril to the state.

lato (ca 29-$# /*)he knowledge of which geometry aims is the knowledge of the eternal.2epublic, MII, >%.lato (ca 29-$# /*)I have hardly ever known a mathematician who was capable of reasoning.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.lato (ca 29-$# /*)

here still remain three studies suitable for free man. 8rithmetic is one of them.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.luta&ch (ca %-12#)

Dabout 8rchimedesE... being perpetually charmed by his familiar siren, that is, by his geometry, he


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neglected to eat and drink and took no care of his person that he was often carriedby force to the baths, and when there he would trace geometrical figures in the ashesof the fire, and with his finger draws lines upon his body when it was anointed with oil,being in a state of great ecstasy and divinely possessed by his science.In G. Simmons Calculus Gems, New York !cGraw "ill Inc., #$$%.oe, 4da& Allen

o speak algebraically, !r. !. is e(ecrable, but !r. G. is 4( W #5= ecrable.DCiscussing fellow writers ;ornelius !athews and


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strangers to one another.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.oinca&=, "ules Hen&i (18!-1912)!athematicians do not study ob0ects, but relations between ob0ects. hus, they arefree to replace some ob0ects by others so long as the relations remain unchanged.;ontent to them is irrelevant they are interested in form only.oinca&=, "ules Hen&i (18!-1912)

hought is only a flash between two long nights, but this flash is everything.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.oinca&=, "ules Hen&i (18!-1912)

he mind uses its faculty for creativity only when e(perience forces it to do so.oinca&=, "ules Hen&i (18!-1912)!athematical discoveries, small or greatare never born of spontaneous generation

hey always presuppose a soil seeded with preliminary knowledge and well preparedby labour, both conscious and subconscious.oinca&=, "ules Hen&i (18!-1912)8bsolute space, that is to say, the mark to which it would be necessary to refer the

earth to know whether it really moves, has no ob0ective e(istence.... he twopropositions :he earth turns round: and :it is more convenient to suppose the earthturns round: have the same meaning there is nothing more in the one than in theother.La 9cience et l'hypothMse$oinca&=, "ules Hen&i (18!-1912)...by natural selection our mind has adapted itself to the conditions of the e(ternalworld. It has adopted the geometry most advantageous to the species or, in otherwords, the most convenient. Geometry is not true, it is advantageous.9cience an" )etho"$oisson, im=on (1#81-180)

7ife is good for only two things, discovering mathematics and teaching mathematics.)athematics )aga*ine, v. B@, no. #, Feb. #$$#.ol, ;eo&e (188#, 198!)!athematics consists of proving the most obvious thing in the least obvious way.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.ol, ;eo&e (188#, 198!)

he traditional mathematics professor of the popular legend is absentminded. "eusually appears in public with a lost umbrella in each hand. "e prefers to face theblackboard and to turn his back to the class. "e writes a, he says b, he means c but itshould be d. Some of his sayings are handed down from generation to generation.

:In order to solve this differential e/uation you look at it till a solution occurs to you.::his principle is so perfectly general that no particular application of it is possible.::Geometry is the science of correct reasoning on incorrect figures.::!y method to overcome a difficulty is to go round it.::.


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ol, ;eo&e (188#, 198!)here are many /uestions which fools can ask that wise men cannot answer.In ". +ves +eturn to )athematical Circles, 'oston 3rindle,


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to avoid doing any real work.In ". +ves +eturn to )athematical Circles, 'oston 3rindle,


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and are correspondingly useless.)athematics of -ar an" oreign .olitics$isin, Ad&ian4after +dna St. Mincent !illay5...+uclid alone"as looked on 'eauty bare."e turned away at onceFar too polite to stare.%he )athematical ntelligencer, M. #B, no. @ 4Fall #$$@5, p. %9.. i3est, A. hami&, and


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mathematics was my chief interest and my chief source of happiness.%he Autobiography of ertran" +ussell .ussell, /e&t&and (18#2-19#0)8 good notation has a subtlety and suggestiveness which at times make it almostseem like a live teacher.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.ussell, /e&t&and (18#2-19#0)If I were a medical man, I should prescribe a holiday to any patient who consideredhis work important.%he Autobiography of ertran" +ussell .ussell, /e&t&and (18#2-19#0)Ardinary language is totally unsuited for e(pressing what physics really asserts, sincethe words of everyday life are not sufficiently abstract. Anly mathematics andmathematical logic can say as little as the physicist means to say.%he 9cientific /utloo(, #$?#.ussell, /e&t&and (18#2-19#0)


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o think I have spent my life on absolute muck.*.+. 7ittlewood,A )athematician's )iscellany,!ethuen and ;o. ltd., #$>?.ussell, /e&t&and (18#2-19#0):'ut,: you might say, :none of this shakes my belief that % and % are @.: You are /uiteright, e(cept in marginal cases == and it is only in marginal cases that you are doubtfulwhether a certain animal is a dog or a certain length is less than a meter. wo mustbe two of something, and the proposition :% and % are @: is useless unless it can beapplied. wo dogs and two dogs are certainly four dogs, but cases arise in which youare doubtful whether two of them are dogs. :


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engines of progress.)arriage an" )orals$ussell, /e&t&and (18#2-19#0)It can be shown that a mathematical web of some kind can be woven about anyuniverse containing several ob0ects. he fact that our universe lends itself tomathematical treatment is not a fact of any great philosophical significance.


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sum of his desires.In ". +ves +eturn to )athematical Circles, 'oston 3rindle,


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and of the religious spirit :God eternally geometri-es.:In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.mith, Hen& "ohn tehen (182% - 188$)D"is toastE3ure mathematics, may it never be of any use to anyone.In ". +ves )athematical Circles 9quare", 'oston 3rindle,


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epler for this. It is instructive to compare this with the current attempts to :e(plain:the -oology of elementary particles in terms of irreducible representations of 7iegroups.te:a&t, Gan

he successes of the differential e/uation paradigm were impressive and e(tensive.!any problems, including basic and important ones, led to e/uations that could besolved. 8 process of self=selection set in, whereby e/uations that could not be solvedwere automatically of less interest than those that could.;oes Go" .lay ;iceH %he )athematics of Chaos$'lackwell, ;ambridge, !8, #$&$, p.?$.ulli3an, "ohn +illiam Na3in (188% - 19$#)

he mathematician is entirely free, within the limits of his imagination, to constructwhat worlds he pleases. .

ulli3an, "ohn +illiam Na3in (188%-19$#)!athematics, as much as music or any other art, is one of the means by which we riseto a complete self=consciousness. he significance of mathematics resides precisely inthe fact that it is an art by informing us of the nature of our own minds it informs usof much that depends on our minds.

Aspects of 9cience, #$%>.un 5e (!th - %th centu&)

he control of large numbers is possible, and like unto that of small numbers, if wesubdivide them.9un %*e .ing a$:i't, "onathan

If they would, for +(ample, praise the 'eauty of a


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l3este&, ".". (181 - 189#)Don graph theory...E

he theory of ramification is one of pure colligation, for it takes no account ofmagnitude or position geometrical lines are used, but these have no more realbearing on the matter than those employed in genealogical tables have in e(plainingthe laws of procreation.In ". +ves )athematical Circles A"ieu, 'oston 3rindle,


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5ietehe story was told that the young Cirichlet had as a constant companion all histravels, like a devout man with his prayer book, an old, worn copy of the;isquisitiones Arithmeticaeof Gauss.In G. Simmons Calculus Gems, New York !cGraw "ill Inc., #$$%.5illotson, A&chbisho"ow often might a man, after he had 0umbled a set of letters in a bag, fling them outupon the ground before they would fall into an e(act poem, yea, or so much as makea good discourse in prose. 8nd may not a little book be as easily made by chance asthis great volume of the world.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.5itchma&sh, 4. *.3erhaps the most surprising thing about mathematics is that it is so surprising. herules which we make up at the beginning seem ordinary and inevitable, but it isimpossible to foresee their conse/uences. hese have only been found out by longstudy, e(tending over many centuries. !uch of our knowledge is due to acomparatively few great mathematicians such as Newton, +uler, Gauss, or 2iemann

few careers can have been more satisfying than theirs. hey have contributedsomething to human thought even more lasting than great literature, since it isindependent of language.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.5itchma&sh, 4. *.It can be of no practical use to know that 3i is irrational, but if we can know, it surelywould be intolerable not to know.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.5odhunte&, Gsaac (1820 - 1910)D8sked whether he would like to see an e(perimental demonstration of conicalrefractionE

No. I have been teaching it all my life, and I do not want to have my ideas upset.5olsto, ?*ount@


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new.)athematical +e!iews#%, p>B#.5u&ene3, G3an e&eie3ich (1818 - 188$)B.Eoltai&e (1%9-1##8)"e who has heard the same thing told by #%,999 eye=witnesses has only #%,999probabilities, which are e/ual to one strong probability, which is far from certain.In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.Eoltai&e (1%9-1##8)

here are no sects in geometry.


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+alton, Gaa8ngling may be said to be so like mathematics that it can never be fully learned.%he Compleat Angler, #B>?.+a&ne&, l3ia 5o:nsendFor twenty pages perhaps, he read slowly, carefully, dutifully, with pauses for self=e(amination and working out e(amples. hen, 0ust as it was working up and thepauses should have been more scrupulous than ever, a kind of swoon and ecstasywould fall on him, and he read ravening on, sitting up till dawn to finish the book, asthough it were a novel. 8fter that his passion was stayed the book went back to the7ibrary and he was done with mathematics till the ne(t bout. Not much remained withhim after these orgies, but something remained a sensation in the mind, aworshiping acknowledgment of something isolated and unassailable, or aremembered mental 0oy at the rightness of thoughts coming together to a conclusion,accurate thoughts, thoughts in 0ust intonation, coming together like unaccompaniedvoices coming to a close.)r$ ortune's )aggot.+a&ne&, l3ia 5o:nsend

heology, !r. Fortune found, is a more accommodating sub0ect than mathematics its

techni/ue of e(position allows greater latitude. For instance when you are gravelledfor matter there is always the moral to fall back upon. ;omparisons too may bedrawn, leading cases cited, types and antetypes analysed and anecdotes introduced.+(cept for 8rchimedes mathematics is singularly naked of anecdotes.)r$ ortune's )aggot$+a&ne&, l3ia 5o:nsend"e resumed:In order to ascertain the height of the tree I must be in such a position that the top ofthe tree is e(actly in a line with the top of a measuring stick or any straight ob0ectwould do, such as an umbrella which I shall secure in an upright position between myfeet. nowing then that the ratio that the height of the tree bears to the length of the

measuring stick must e/ual the ratio that the distance from my eye to the base of thetree bears to my height, and knowing 4or being able to find out5 my height, the lengthof the measuring stick and the distance from my eye to the base of the tree, I can,therefore, calculate the height of the tree.::


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+eil, imone (1909 - 19$)8lgebra and money are essentially levelers the first intellectually, the secondeffectively.


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:!athematics and the 7aws of Nature: in %he Armchair 9cience +ea"er, New YorkSimon and Schuster, #$>$.+el, He&mann (188! - 19!!)9 years.DSaid in #$>9E%he American )athematical )onthly, v. #99. p. $?.+el, He&mann (188! - 19!!)7ogic is the hygiene the mathematician practices to keep his ideas healthy andstrong.%he American )athematical )onthly, November, #$$%.+he:ellNobody since Newton has been able to use geometrical methods to the same e(tentfor the like purposes and as we read the 3rincipia we feel as when we are in anancient armoury where the weapons are of gigantic si-e and as we look at them wemarvel what manner of man he was who could use as a weapon what we can scarcelylift as a burden.

In +. N. Ca ;. 8ndrade :Isaac Newton: in *. 2. Newman 4ed.5 %he -orl" of)athematics, New York Simon and Schuster, #$>B.+hitehead, Al'&ed No&th (18%1 - 19#)

he science of pure mathematics ... may claim to be the most original creation of thehuman spirit.9cience an" the )o"ern -orl"$+hitehead, Al'&ed No&th (18%1 - 19#)!athematics as a science, commenced when first someone, probably a Greek, provedpropositions about :any: things or about :some: things, without specifications ofdefinite particular things.+hitehead, Al'&ed No&th (18%1 - 19#)

So far as the mere imparting of information is concerned, no university has had any0ustification for e(istence since the populari-ation of printing in the fifteenth century.%he Aims of #"ucation.+hitehead, Al'&ed No&th (18%1 - 19#)No 2oman ever died in contemplation over a geometrical diagram.D8 reference to the death of 8rchimedes.EIn ". +ves )athematical Circles 9quare", 'oston 3rindle,


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what we are doing. he precise opposite is the case. ;ivili-ation advances bye(tending the number of important operations which we can perform without thinkingabout them.

An ntro"uction to )athematics$+hitehead, Al'&ed No&th (18%1 - 19#)Aur minds are finite, and yet even in these circumstances of finitude we aresurrounded by possibilities that are infinite, and the purpose of life is to grasp asmuch as we can out of that infinitude.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.+hitehead, Al'&ed No&th (18%1 - 19#)In modern times the belief that the ultimate e(planation of all things was to be foundin Newtonian mechanics was an adumbration of the truth that all science, as it growstowards perfection, becomes mathematical in its ideas.In N. 2ose )athematical )axims an" )inims, 2aleigh N;2ome 3ress Inc., #$&&.+hitehead, Al'&ed No&th (18%1 - 19#)8lgebra reverses the relative importance of the factors in ordinary language. It isessentially a written language, and it endeavors to e(emplify in its written structuresthe patterns which it is its purpose to convey. he pattern of the marks on paper is a

particular instance of the pattern to be conveyed to thought. he algebraic method isour best approach to the e(pression of necessity, by reason of its reduction ofaccident to the ghostlike character of the real variable.


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In *. 2. Newman 4ed.5 %he -orl" of )athematics, New York Simon and Schuster,#$>B.+hitehead, Al'&ed No&th (18%1 - 19#)Familiar things happen, and mankind does not bother about them. It re/uires a veryunusual mind to undertake the analysis of the obvious.9cience an" the )o"ern -orl"$+hitman, +alt (1819-1892)Co I contradict myself Mery well then I contradict myself. 4I am large, I containsmultitudes5.9ong of )yself, #$?$.+hitman, +alt (1819-1892)


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+ilson, "ohn (1#1 - 1#9$)8 monument to NewtonK a monument to ShakespeareK 7ook up to "eaven look intothe "uman "eart. ill the planets and the passionsthe affections and the fi(ed starsare e(tinguishedtheir names cannot die.+ittenstein,

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