Starting a field of mathematics is like taking an expedition across a vast ocean. The founders of the expedition decide where their boat will be going and they embark towards their destination. They have some idea of what they will find (if and) when they get there and they hope to find things they did not expect there as well.
However, the ocean may be large enough that the initial crew is not there to arrive at their destination. The crew of the ship then must convince the second generation that the boat is heading in an interesting and fruitful direction and assure them of the bounties that lay ahead so that they may maintain the course of the ship. If the ocean is vast enough, the second generation may have to convince the third , and so the third the fourth, and so on.
It may happen that, by the tenth generation, the crew does not know where the boat is going. They even do not know where the boat originally departed. They are happy maintaining the ship and aspire to become the best sailors possible.
The ship begins to sail around in circles amongst the endless sea that encompasses their vision. They never arrive and the ship is lost en route.
Each Mathematician, whom is not just a sailor but a true adventurer, must know both from where their boat took sail and to where their boat is due to arrive. Their duty is to keep the ship on track and to have a crew left with them to enjoy the plunder.
