As for mathematicians themselves: don't expect too much help. Most of them are too far removed in their ivory towers to take up such challenges. And anyway, they are not competent. After all, they are just mathematicians-what we need is paramathematicians, like you... It is you who can be the welding force, between mathematicians and stories, in order to achieve the synthesis.

**Apostolos Doxiadis**

as-for-mathematicians-themselves-dont-expect-too-much-help-most-them-are-too-far-removed-in-their-ivory-towers-to-take-up-such-challenges-and-anyway-apostolos-doxiadis

Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.

**William Thurston**

mathematicians-can-do-fill-in-gaps-correct-errors-supply-more-detail-more-careful-scholarship-when-they-are-called-on-motivated-to-do-our-system-william-thurston

Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.

**Freeman Dyson**

now-as-mandelbrot-points-out-nature-has-played-joke-on-mathematicians-the-19thcentury-mathematicians-may-not-have-been-lacking-in-imagination-but-freeman-dyson

programming-is-one-most-difficult-branches-applied-mathematics-poorer-mathematicians-had-better-remain-pure-mathematicians

when-i-told-my-son-that-i-had-to-give-talk-about-my-work-to-nonmathematicians-he-warned-me-that-regular-people-dont-think-like-mathematicians-richard-a-falk

Whenever I want to represent or depict the official version, I will refer to them as 'mathematicians' or 'mathematical physicists' or idiots or something like that. There are no physicists in mainstream 'Physics.' From Newton to Einstein to Hawking, they are all just mathematicians as far as Science and Physics are concerned.

**Bill Gaede**

whenever-i-want-to-represent-depict-official-version-i-will-refer-to-them-as-mathematicians-mathematical-physicists-idiots-something-like-that-bill-gaede

the-physicists-defer-only-to-mathematicians-mathematicians-defer-only-to-god-leon-m-lederman

Sure, some [teachers] could give the standard limit definitions, but they [the students] clearly did not understand the definitions - and it would be a remarkable student who did, since it took mathematicians a couple of thousand years to sort out the notion of a limit, and I think most of us who call ourselves professional mathematicians really only understand it when we start to teach the stuff, either in graduate school or beyond.

**Keith Devlin**

sure-some-teachers-could-give-standard-limit-definitions-but-they-students-clearly-did-not-understand-definitions-it-would-be-remarkable-student-keith-devlin

Mathematics may be likened to a large rock whose interior composition we wish to examine. The older mathematicians appear as persevering stone cutters slowly attempting to demolish the rock from the outside with hammer and chisel. The later mathematicians resemble expert miners who seek vulnerable veins, drill into these strategic places, and then blast the rock apart with well placed internal charges.

**Howard Whitley Eves**

mathematics-may-be-likened-to-large-rock-whose-interior-composition-we-wish-to-examine-the-older-mathematicians-appear-as-persevering-stone-cutters-howard-whitley-eves

I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.

**G. H. Hardy**

i-am-obliged-to-interpolate-some-remarks-on-difficult-subject-proof-its-importance-in-mathematics-all-physicists-good-many-quite-respectable-g-h-hardy

Silicon Valley, "the largest legal creation of wealth in history," was built largely by unprofessional amateurs using math, sand, and the institutions of freedom. The Soviet Union had the greatest mathematicians on earth, and plenty of sand, but without the institutions of freedom their brilliant mathematicians were not empowered to create those devices that are changing the world.

**Michael Strong**

silicon-valley-largest-legal-creation-wealth-in-history-was-built-largely-by-unprofessional-amateurs-using-math-sand-institutions-freedom-the-michael-strong

Outside observers often assume that the more complicted a piece of mathematics is, the more mathematicians admire it. Nothing could be further from the truth. Mathematicians admire elegance and simplicity above all else, and the ultimate goal in solving a problem is to find the method that does the job in the most efficient manner. Though the major accolades are given to the individual who solves a particular problem first, credit (and gratitude) always goes to those who subsequently find a simpler solution.

**Keith Devlin**

outside-observers-often-assume-that-more-complicted-piece-mathematics-is-more-mathematicians-admire-it-nothing-could-be-further-from-truth-keith-devlin

In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century could say without exaggeration, "Abel has left mathematicians enough to keep them busy for five hundred years." Asked how he had done all this in the six or seven years of his working life, Abel replied, "By studying the masters, not the pupils."

**Eric Temple Bell**

in-his-wretched-life-less-than-twentyseven-years-abel-accomplished-much-highest-order-that-one-leading-mathematicians-nineteenth-century-could-eric-temple-bell

All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They're adults in the crystalline world, infants in the real one.

**Sylvain Cappell**

all-mathematicians-live-in-two-different-worlds-they-live-in-crystalline-world-perfect-platonic-forms-an-ice-palace-but-they-also-live-in-common-world-where-things-are-transient-

Most of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.

**Cornelius Lanczos**

most-arts-as-painting-sculpture-music-have-emotional-appeal-to-general-public-this-is-because-these-arts-can-be-experienced-by-some-one-more-our-cornelius-lanczos

We find sects and parties in most branches of science; and disputes which are carried on from age to age, without being brought to an issue. Sophistry has been more effectually excluded from mathematics and natural philosophy than from other sciences. In mathematics it had no place from the beginning; mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly, we find no parties among mathematicians, and hardly any disputes.

**Thomas Reid**

we-find-sects-parties-in-most-branches-science-disputes-which-are-carried-on-from-age-to-age-without-being-brought-to-issue-sophistry-has-been-thomas-reid

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

**G. H. Hardy**

it-is-melancholy-experience-for-professional-mathematician-to-find-himself-writing-about-mathematics-the-function-mathematician-is-to-do-something-g-h-hardy

In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, "this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." He immediately protested: "No, no. These concepts were not dreamed up. They were natural and real."

**Chen-Ning Yang**

in-1975-speaking-with-shiing-shen-chern-i-told-him-i-had-finally-learned-beauty-fiberbundle-theory-profound-chernweil-theorem-i-said-i-found-it-chenning-yang

programmers-are-not-mathematicians-no-matter-how-much-we-wish-wish-for-it-richard-p-gabriel

unfortunately-world-has-not-been-designed-for-convenience-mathematicians-benoit-mandelbrot

it-would-be-better-for-the-true-physics-if-there-were-no-mathematicians-on-earth

the-computers-are-not-replacing-mathematicians-they-are-breeding-them-martin-gardner

i-like-to-move-among-painters-mathematicians-psychologists-people-who-can-tell-me-something

mathematicians-deal-with-large-numbers-sometimes-but-never-in-their-income-isaac-asimov

mathematicians-are-like-frenchmen-whatever-you-say-to-them-they-translate-into-their-own-language-forthwith-it-is-something-entirely-different-johann-wolfgang-von-goethe

the-mathematicians-this-world-regard-themselves-as-physicists-yet-they-know-next-to-nothing-about-physics-bill-gaede

nature-is-probably-quite-indifferent-to-aesthetic-preferences-mathematicians-alfred-north-whitehead

since-mathematicians-have-invaded-theory-relativity-i-do-not-understand-it-myself-any-more-albert-einstein

abel-has-left-mathematicians-enough-to-keep-them-busy-for-five-hundred-years-charles-hermite

abel-has-left-mathematicians-something-to-keep-them-busy-for-five-hundred-years-charles-hermite

there-have-been-only-three-epochmaking-mathematicians-archimedes-newton-eisenstein-carl-friedrich-gauss

mathematicians-use-intuition-conjecture-guesswork-all-time-except-when-they-are-in-classroom-joseph-warren

are-not-most-professional-mathematicians-spared-all-trouble-incident-to-income-tobias-dantzig

since-mathematicians-have-invaded-theory-relativity-i-do-not-understand-it-myself-anymore-albert-einstein

the-only-way-to-comprehend-what-mathematicians-mean-by-infinity-is-to-contemplate-the-extent-of-human-stupidity

artists-realise-that-mathematicians-have-way-looking-at-world-that-can-make-them-see-things-differently

any-false-value-is-gonna-be-fairly-boring-in-perl-mathematicians-notwithstanding-larry-wall

thirtyfive-craters-on-moon-are-named-for-jesuit-scientists-mathematicians-thomas-e-woods-jr

mathematicians-for-what-they-do-are-really-poorly-rewarded-and-its-competitive-field-almost-as-bad-as-being-concert-pianist-giancarlo-rota

it-is-obvious-that-mathematics-needs-both-sorts-mathematicians-theorybuilders-problemsolvers-timothy-gowers

mathematicians-themselves-set-up-standards-generality-elegance-in-their-exposition-which-are-bar-to-understand-kenneth-e-boulding

john-wheeler-rejuvenated-general-relativity-he-made-it-experimental-subject-took-it-away-from-mathematicians-freeman-dyson

mathematicians-may-flatter-themselves-that-they-possess-new-ideas-which-mere-human-language-is-as-yet-unable-to-express

because-mathematicians-frequently-make-use-time-they-ought-to-have-distinct-idea-meaning-that-word-otherwise-they-are-quacks-isaac-barrow

mathematicians-are-bit-like-laconic-vermonter-who-when-asked-if-hes-lived-in-state-his-whole-life-replies-not-yet-john-allen-paulos

mathematicians-boast-their-exacting-achievements-but-in-reality-they-are-absorbed-in-mental-acrobatics-contribute-nothing-to-society-ogyu-sorai

the-greatest-mathematicians-as-archimedes-newton-gauss-always-united-theory-applications-in-equal-measure

a-surprising-proportion-mathematicians-are-accomplished-musicians-is-it-because-music-mathematics-share-patterns-that-are-beautiful-martin-gardner

for-other-great-mathematicians-philosophers-he-used-epithets-magnus-clarus-clarissimus-for-newton-alone-he-kept-prefix-summus-ww-rouse-ball

mathematicians-didnt-invent-infinity-until-1877-so-they-thought-it-was-impossible-that-africans-could-be-using-fractal-geometry

all-mathematicians-share-sense-amazement-over-infinite-depth-mysterious-beauty-usefulness-mathematics-martin-gardner

mathematicians-tend-to-prefer-worstcase-analysis-kind-paranoia-that-is-especially-understandable-if-you-live-in-israel-noga-alon

mathematics-is-world-created-by-mind-men-mathematicians-are-people-who-devote-their-lives-to-what-seems-to-me-wonderful-kind-play-constance-reid

the-danger-already-exists-that-mathematicians-have-made-a-covenant-with-the-devil-to-darken-the-spirit-and-confine-man-in-the-bonds-of-hell

first-rate-mathematicians-choose-first-rate-people-but-second-rate-mathematicians-choose-third-rate-people