appeal of the outrageous

We should perhaps also add to this list of criteria the response from the famous mathematician John Conway to the question of what makes a great conjecture: “It should be outrageous.” An appealing conjecture is also somewhat ridiculous or fantastic, with unforeseen range and consequences. Ideally it combines components from distant domains that haven’t met before in a single statement, like the surprising ingredients of a signature dish.

Robbert Dijkgraaf - The Subtle Art of the Mathematical Conjecture

We are used to click-bait new with outrageous titles that incite your curiosity. This may look like a one-off ugly phenomenon, but it is not. As consumers of information, we display the same behavior everywhere. This is forcing even scientists to produce counter-intuitive papers with outrageous titles so that they can attract the attention of the press. (No wonder why most published research is false!)

Generally speaking, people do not immediately recognize the importance of an emerging matter. Even in mathematics, you need to induce a shock to spur activity and convince others join you in the exploration of a new idea.

In 1872, Karl Weierstrass astounded the mathematical world by giving an example of a function that is continuous at every point but whose derivative does not exist anywhere. Such a function defied geometric intuition about curves and tangent lines, and consequently spurred much deeper investigations into the concepts of real analysis.

Robert G. Bartle &‎ Donald R. Sherbert - Introduction to Real Analysis (Page 163)

Similar to the above example, differential topology became a subject on its own and attracted a lot of attention only after John Milnor shocked the world by showing that 7 dimensional sphere admits exactly 28 different oriented diffeomorphism classes of differentiable structures. (Why 28, right? It actually marks the beginning of one of the most amazing number sequences in mathematics.)