Pure math is not very useful. Pure mathematicians publish results among themselves and never really get used. Applied mathematicians and engineers make the world.
We hear such statements from time to time in academia. Typically one perceives something to be useful if one can ensure survival through it. It's true that not many can survive in pure mathematics because it is so damn tough. Here I should mention that typically abstractions higher than one's level of imagination are considered "pure" by him. Pure is rather a spectrum of higher abstractions. In fact the higher the abstraction the higher are the chances that the results can survive through odds or in other words stand the test of time. I encourage to read this article and this one to get a nice perspective on math.
Conferences are a good way to measure the progress and importance of a field. For e.g. conferences on aritificial intelligence kind of died but several of them are budding again. Hence participating in conferences is a big treasure to learn the dynamics of a field. If you can actively participate in conferences of a particular field it means you possibly can be fit in the survival sense in that field. You can always learn not only from active participation but also from passive participation. By passive participation I mean being mostly a spectator. Conferences' radiance can be measured in different dimensions like by rigor (typical pure math conferences), immediate impact (engineering conferences), deeper impact (theoretical conferences), commercial impact (industrial conferences). Even though you survive using one class of conferences it always helps to gain edge benefits by being aware of the dynamics of other classes.
After all people in academia struggle to survive primarily using science. It's important for one to have broader awareness if he wants to survive the real significant dynamics. The deeper or steeper one's understanding is the higher are the chances of his survival in times of crisis. Rationality is sufficient when things are smooth, rationality with rigor is necessary when sailing through rough waters.