Terence Tao

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Terence Tao in 2006

Terence "Terry" Chi-Shen Tao (simplified Chinese: 陶哲轩; traditional Chinese: 陶哲軒; pinyin: Táo Zhéxuān) (born 17 July 1975, Adelaide), is a Chinese Australian mathematician.



Solving Mathematical Problems (2nd ed., 2006)

  • Understand the problem. What kind of problem is it? There are three main types of problems:
    ‘Show that ...’ or ‘Evaluate ...’ questions, in which a certain statement has to be proved true, or a certain expression has to be worked out;
    ‘Find a...’ or ‘Find all...’ questions, which requires one to find something (or everything) that satisfies certain requirements;
    ‘Is there a ...’ questions, which either require you to prove a statement or provide a counterexample (and thus is one of the previous two types of problem).
    • Ch. 1 : Strategies in problem solving

What Is Inquiry-Based Learning? (2017)

  • The objective in mathematics is not to obtain the highest ranking, the highest score, or the highest number of prizes and awards; instead, it is to increase understanding of mathematics (both for yourself, and for your colleagues and students), and to contribute to its development and applications. [1]

On requests for career advice

  • Relying on intelligence alone to pull things off at the last minute may work for a while, but generally speaking at the graduate level or higher it doesn't. One needs to do a serious amount of reading and writing, and not just thinking, in order to get anywhere serious in mathematics. [2]
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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

  1. Dana C. Ernst, Angie Hodge, Stan Yoshinobu (2017). "What Is Inquiry-Based Learning?" (pdf). Notices of the AMS 64 (6): 570-574. Retrieved on 2018.
  2. http://www.math.ucla.edu/~tao/advice.html