The article referenced in this column can be found here. I recommend reading this before following on.
The term “proof” in the article actually seems quite daunting. Some 500 pages of writing just to prove that the ABC Conjecture is true is too hard to fathom. A proof in Real Analysis is already so difficult to read that I couldn’t imagine finishing even the first page of Mochizuki’s proof!
Tackling research questions such as the ABC Conjecture may not have any direct application to the real world, but it certainly provides value to Fermat’s Last Theorem or Catalan’s Conjecture according to the article. Fermat’s Last Theorem has some use in Physics i.e. Supersymmetry Breakings and Fermat’s Last Theorem. Though the ABC Conjecture may not have any direct applications, it can indirectly support another theorem which does have direct applications.
Additionally, the thought processes of number theorists shine in written proofs, showing a way of thinking which may influence a peer/reader to be more logical and clear within the realms of mathematics, or even outside the realms of mathematics, sharpening the skill of reasoning which has brought us such a long way in the history of humanity.
Let me know your thoughts on this article, do you think there is value in researchers undertaking research questions such as the ABC Conjecture?