[Math] Has anyone developed a ‘theoretical minimum’ for mathematics

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Lev Landau, a great theoretical physicist, wrote a series of books which he called the 'Theoretical Minimum' which contained everything he considered elementary for an aspiring theoretical physics researcher. Leonard Susskind, is apparently interested in continuing this tradition. In fact, there's an interesting discussion of Lev Landau's text on the physics stack-exchange.

My question is whether there have ever been significant attempts to do a similar thing in mathematics. If so, why don't these texts have the same
importance in the mathematical community?

Here's the list of the texts that had to be mastered:

  1. Mathematics I. Integration, ordinary differential equations, vector algebra and tensor analysis.
  2. Mechanics. Mechanics, Vol. 1, except §§ 27, 29, 30, 37, 51 (1988 russian edition)
  3. Field theory The Classical Theory of Fields, Vol. 2, except §§ 50, 54-57, 59-61, 68, 70, 74, 77, 97, 98, 102, 106, 108, 109, 115-119 (1973 russian edition)
  4. Mathematics II. The theory of functions of a complex variable, residues, solving equations by means of contour integrals (Laplace's method), the computation of the asymptotics of integrals, special functions (Legendre, Bessel, elliptic, hypergeometric, gamma function)
  5. Quantum Mechanics. Quantum Mechanics: Non-Relativistic Theory, Vol. 3, except §§ 29, 49, 51, 57, 77, 80, 84, 85, 87, 88, 90, 101, 104, 105, 106-110, 114, 138, 152 (1989 russian edition)
  6. Quantum electrodynamics. Relativistic Quantum Theory, Vol. 4, except §§ 9, 14-16, 31, 35, 38-41, 46-48, 51, 52, 55, 57, 66-70, 82, 84, 85, 87, 89 – 91, 95-97, 100, 101, 106-109, 112, 115-144 (1980 russian edition)
  7. Statistical Physics I. Statistical Physics, Vol. 5, except §§ 22, 30, 50, 60, 68, 70, 72, 79, 80, 84, 95, 99, 100, 125-127, 134-141, 150-153 , 155-160 (1976 russian edition)
  8. Mechanics of continua. Fluid Mechanics, Vol. 6, except §§ 11, 13, 14, 21, 23, 25-28, 30-32, 34-48, 53-59, 63, 67-78, 80, 83, 86-88, 90 , 91, 94-141 (1986 russian edition); Theory of Elasticity, Vol. 7, except §§ 8, 9, 11-21, 25, 27-30, 32-47 (1987 russian edition)
  9. Electrodynamics of Continuous Media. Electrodynamics of Continuous Media, Vol. 8, except §§ 1-5, 9, 15, 16, 18, ​​25, 28, 34, 35, 42-44, 56, 57, 61-64, 69, 74, 79-81 , 84, 91-112, 123, 126 (1982 russian edition)
  10. Statistical Physics II. Statistical Physics, Part 2. Vol. 9, only §§ 1-5, 7-18, 22-27, 29, 36-40, 43-48, 50, 55-61, 63-65, 69 (1978 russian edition)
  11. Physical Kinetics. Physical Kinetics. Vol. 10, only §§ 1-8, 11, 12, 14, 21, 22, 24, 27-30, 32-34, 41-44, 66-69, 75, 78-82, 86, 101.

Note: Landau's texts were necessary for an exam which aspiring researchers had to pass in order to do research in theoretical physics. However, only 43 people passed the exam between 1933 (when Landau first administered it) and 1961(Landau suffered a car accident).

Best Answer

In 1991, Vladimir I. Arnold compiled a list of 100 mathematical problems in a paper titled "A mathematical trivium". (You can view all 100 problems in that pdf.)

In that paper he says:

The compilation of model problems is a laborious job, but I think it must be done. As an attempt I give below a list of one hundred problems forming a mathematical minimum for a physics student. Model problems (unlike syllabuses) are not uniquely defined, and many will probably not agree with me. Nonetheless I assume that it is necessary to begin to determine mathematical standards by means of written examinations and model problems. It is to be hoped that in the future students will receive model problems for each course at the beginning of each semester, and oral examinations for which the students cram by heart will become a thing of the past.

Although the problems are aimed at physics students, most of the problems are purely mathematical.

I don't know how famous these problems are, but there is an entire subforum on the Art of Problem Solving (AoPS) Fourms dedicated to these problems.

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