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Occupations related to mathematics.

A mathematician is a person whose primary area of study and research is the field of mathematics.


  • Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium... cavendi sunt, ne consortio daemoniorum irretiant.
    • Translation: Therefore, a good Christian should beware that mathematicians, and any others who prophesy impiously... may be entangled in the companionship of demons.
    • St. Augustine, De Genesi ad Litteram
    • Augustine uses "mathematicians" in this context to refer mainly to astrologers and occultists using numerology.
  • A mathematician is a machine for turning coffee into theorems.
  • I united the majority of well-informed persons into a club, which we called by the name of the Junto, and the object of which was to improve our understandings. ... The first members of our club were...
    Thomas Godfrey, a self-taught mathematician, and afterwards inventor of what is now called Hadley's dial; but he had little knowledge out of his own line, and was insupportable in company, always requiring, like the majority of mathematicians that have fallen in my way, an unusual precision in everything that is said, continually contradicting, or making trifling distinctions—a sure way of defeating all the ends of conversation. He very soon left us.
  • Avec toute l’algèbre du monde on n’est souvent qu’un sot lorsqu’on ne sait pas autre chose. Peut-être dans dix ans la société tirera-t-elle de l’avantage des courbes que des songe-creux d’algébristes auront carrées laborieusement. J’en félicite d’avance la postérité; mais, à vous parler vrai, je ne vois dans tous ces calculs qu’une scientifique extravagance. Tout ce qui n’est ni utile ni agréable ne vaut rien. Quant aux choses utiles, elles sont toutes trouvées; et, pour les agréables, j’espère que le bon goût n’y admettra point d’algèbre.
    • [A] man with all the algebra in the world is often only an ass when he knows nothing else. Perhaps in ten years society may derive advantage from the curves which these visionary algebraists will have laboriously squared. I congratulate posterity beforehand. But to tell you the truth I see nothing but a scientific extravagance in all these calculations. That which is neither useful nor agreeable is worthless. And as for useful things, they have all been discovered; and to those which are agreeable, I hope that good taste will not admit algebra among them.
    • Letters of Voltaire and Frederick the Great (New York: Brentano's, 1927), trans. Richard Aldington, letter 93 from Frederick to Voltaire (1749-05-16)
  • Die Mathematiker sind eine Art Franzosen; redet man zu ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anders.
    • Translation: Mathematicians are [like] a sort of Frenchmen; if you talk to them, they translate it into their own language, and then it is immediately something quite different.
    • Johann Wolfgang von Goethe, Maximen und Reflexionen, 2006 (Helmut Koopmann, ed.) ISBN 3423343788
  • The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another.
    • Gösta Mittag-Leffler
    • Quoted in N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
  • Mathematicians seem to have no difficulty in creating new concepts faster than the old ones become well understood.
    • Edward Norton Lorenz (1991) "A scientist by choice". Speech by acceptance of the Kyoto Prize in 1991.
  • I have hardly ever known a mathematician who was capable of reasoning.
    • Plato, from Benjamin Jowett's interpretive vernacular translation (1871) of Plato's Republic, Book VII, 531-e. Plato actually has Socrates say that few mathematicians are dialecticians (διαλεκτικοί) (Jowett, Plato's Republic: The Greek Text, Vol. I "Text", 1894), by which he refers to step by step reasoning based on mutual agreement, (G. M. A. Grube, Plato's Republic (1974), Book VII, note 13). It is an accurate observation on the primitive mathematics of his day.
  • Aristotle, so far as I know, was the first man to proclaim explicitly that man is a rational animal. His reason for this view was one which does not now seem very impressive; it was, that some people can do sums.
    • Bertrand Russell, "An Outline of Intellectual Rubbish", in Unpopular Essays (1950), p. 71
  • Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs Aristotle to keep her mouth open while he counted.
    • Bertrand Russell, "An Outline of Intellectual Rubbish", Unpopular Essays (1950).
  • These experiences are not 'religious' in the ordinary sense. They are natural, and can be studied naturally. They are not 'ineffable' in the sense the sense of incommunicable by language. Maslow also came to believe that they are far commoner than one might expect, that many people tend to suppress them, to ignore them, and certain people seem actually afraid of them, as if they were somehow feminine, illogical, dangerous. 'One sees such attitudes more often in engineers, in mathematicians, in analytic philosophers, in book keepers and accountants, and generally in obsessional people'.
    The peak experience tends to be a kind of bubbling-over of delight, a moment of pure happiness. 'For instance, a young mother scurrying around her kitchen and getting breakfast for her husband and young children. The sun was streaming in, the children clean and nicely dressed, were chattering as they ate. The husband was casually playing with the children: but as she looked at them she was suddenly so overwhelmed with their beauty and her great love for them, and her feeling of good fortune, that she went into a peak experience . . .

See also

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AbelAnaxagorasArchimedesAristarchus of SamosAverroesArnoldBanachCantorCartanChernCohenDescartesDiophantusErdősEuclidEulerFourierGaussGödelGrassmannGrothendieckHamiltonHilbertHypatiaLagrangeLaplaceLeibnizMilnorNewtonvon NeumannNoetherPenrosePerelmanPoincaréPólyaPythagorasRiemannRussellSchwartzSerreTaoTarskiThalesTuringWeilWeylWilesWitten


123360eπFibonacci numbersIrrational numberNegative numberNumberPrime numberQuaternion


AbstractionAlgorithmsAxiomatic systemCompletenessDeductive reasoningDifferential equationDimensionEllipseElliptic curveExponential growthInfinityIntegrationGeodesicInductionProofPartial differential equationPrinciple of least actionPrisoner's dilemmaProbabilityRandomnessTheoremTopological spaceWave equation


Euler's identityFermat's Last Theorem

Pure math

Abstract algebraAlgebraAnalysisAlgebraic geometry (Sheaf theory) • Algebraic topologyArithmeticCalculusCategory theoryCombinatoricsCommutative algebraComplex analysisDifferential calculusDifferential geometryDifferential topologyErgodic theoryFoundations of mathematicsFunctional analysisGame theoryGeometryGlobal analysisGraph theoryGroup theoryHarmonic analysisHomological algebraInvariant theoryLogicNon-Euclidean geometryNonstandard analysisNumber theoryNumerical analysisOperations researchRepresentation theoryRing theorySet theorySheaf theoryStatisticsSymplectic geometryTopology

Applied math

Computational fluid dynamicsEconometricsFluid mechanicsMathematical physicsScience

History of math

Ancient Greek mathematicsEuclid's ElementsHistory of algebraHistory of calculusHistory of logarithmsIndian mathematicsPrincipia Mathematica


Mathematics and mysticismMathematics educationMathematics, from the points of view of the Mathematician and of the PhysicistPhilosophy of mathematicsUnification in science and mathematics