To learn all of mathematics from scratch to doctor level, one needs to have a strong foundation of the basics. Here is a graphic representation of the topics to learn from a very basic level to doctor level:At the very basic level, one needs to learn about numbers, basic arithmetic operations like addition, subtraction, multiplication, and division. After mastering these basics, one needs to learn about fractions, decimals, and percentages. Once these are understood, one needs to study algebra which includes equations, polynomials, and functions.After algebra, geometry needs to be studied which includes concepts like lines, angles, triangles, circles, and 3D shapes like cubes, spheres, and cones. Trigonometry, calculus, and differential equations are also important topics that should be studied at an intermediate level.Finally, at the doctor level, one needs to study advanced topics such as group theory, topology, number theory, and real analysis. Learning all of these topics will give one a comprehensive understanding of mathematics.