It is essentially a communications problem. Brian Conrad summed it up:
For every subject I have ever understood in mathematics, there are instructive basic examples and concise arguments to illustrate what is the point to generally educated mathematicians. There is no reason that IUT should be any different, especially for the audience that was present at Oxford. Let me illustrate this with a short story. During one of the tea breaks I was chatting with a postdoc who works in analysis, and I mentioned sheaf theory as an example of a notion which may initially look like pointless abstract nonsense but actually allows for very efficient consideration of useful ideas which are rather cumbersome (or impossible) to contemplate in more concrete terms. Since that postdoc knew nothing about what can be done with sheaf theory, I told him about the use of sheaf cohomology to systematize and analyze the deRham theorem and topological obstructions to construction problems in complex analysis; within 20 minutes he understood the point and wanted to learn more. Nobody expects to grasp the main points of IUT within 20 minutes, but if someone says they understand a theory and does not provide instructive visibly relevant examples and concise arguments that clearly illustrate what is the point then they are not trying hard enough. Many are willing to work hard to understand what must be very deep and powerful ideas, but they need a clearer sense of the landscape before beginning their journey.
For every subject I have ever understood in mathematics, there are instructive basic examples and concise arguments to illustrate what is the point to generally educated mathematicians. There is no reason that IUT should be any different, especially for the audience that was present at Oxford. Let me illustrate this with a short story. During one of the tea breaks I was chatting with a postdoc who works in analysis, and I mentioned sheaf theory as an example of a notion which may initially look like pointless abstract nonsense but actually allows for very efficient consideration of useful ideas which are rather cumbersome (or impossible) to contemplate in more concrete terms. Since that postdoc knew nothing about what can be done with sheaf theory, I told him about the use of sheaf cohomology to systematize and analyze the deRham theorem and topological obstructions to construction problems in complex analysis; within 20 minutes he understood the point and wanted to learn more. Nobody expects to grasp the main points of IUT within 20 minutes, but if someone says they understand a theory and does not provide instructive visibly relevant examples and concise arguments that clearly illustrate what is the point then they are not trying hard enough. Many are willing to work hard to understand what must be very deep and powerful ideas, but they need a clearer sense of the landscape before beginning their journey.
http://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-works...