In the field of Statistical research, Mathematicians or Theoreticians come in two very distinct flavors:
Connectionist: Mathematicians who invent and connect novel algorithms based on new fundamental ideas that address real data modeling problems.
Confirmatist: Mathematicians who prove why an existing algorithm works under certain sets of assumptions/conditions (post-mortem report).
Albeit, the theoreticians of the first kind (few examples: Karl Pearson, Jerzy Neyman, Harold Hotelling, Charles Stein, Emanuel Parzen, Clive Granger) are much more rare than the second one. The current culture has failed to distinguish between these two types (which are very different in their style and motivation) and has put excessive importance on the second culture – this has created an imbalance and often gives a wrong impression of what “Theory” means. We need to discover new theoretical tools that not only prove why the already invented algorithms work (confirmatory check) but also provide the insights into how to invent and connect novel algorithms for effective data analysis – 21st-century statistics.