The nature versus nurture debate has left many people divided on various topics, and the study of mathematics is no exception. Although some people may prioritise only one factor of the two, I believe that both of them play equally important roles in the development of mathematical skills.
On the one hand, I can understand people claiming that an inborn talent is what is required to be good at mathematics. Some people have what we call a ‘mathematical thinking’: they do not limit the study of this subject to plain theory, but actively utilise mathematical knowledge in practice to solve real-life problems. This helps them conceptualise mathematics as a useful tool to understand the surrounding world rather than a boring academic discipline that will not benefit in the later life. This attitude to mathematics is what differentiates gifted people from the rest and helps them develop a much more thorough understanding of the subject.
On the other hand, those emphasising the role of a techer also voice some sound reasoning. A teacher is a highly-skilled professional whose very job is to bring the best out of a student regardless of their initial skill-set. These people have many years of experience working with all sorts of different students and thus can find an individual approach to cater for a student’s personal needs and capabilities. With a good teacher present, even the most struggling student may make far strides in the learning process once they grasp the fundamental principles of the subject. All is needed is discipline and determination, and a teacher is exactly the one to bring these to the learning process.
In my opinion, however, neither of the factors is more important that the other, and it is their intricate interplay that helps a person to succeed in mathematics. Without a good mentor, a mathematical prodigy may not be developing their talent in an efficient way or may not even realise that they have a talent in mathematics to begin with. At the same time, however good a teacher is and however much experience they have, they will still find it much easier to teach a student who is already good at mathematics. In individual scenarios, having a natural aptitude to mathematics may prove more important than having a good teacher, but this may also work the other way.
In conclusion, I strongly believe that neither pure talent nor the quality of teaching can ensure a good understanding of mathematics single-handedly. In reality, both these factors are equally important, even if in separate cases, one prevails over the other.