In the next month, Ieyasu returned to Edo Castle and Adams began a new routine. Every other day, at eight o’clock, he left home by horse and at nine o’clock began to teach Ieyasu every branch of western knowledge that he knew. Ieyasu was particularly interested in mathematics. First of all, Adams taught him arithmetic using the Arabic numerals. Ieyasu was impressed at how the correct answer was reached without an abacus. He also learnt the Roman numbers and then practiced arithmetic, even to three or four figures. When he found a correct answer, his joy was like that of a child. In turn, Adams was impressed at the Japanese abacus, a rectangular box formed with wood and crammed with wooden beads on bars. Calculations were done by flipping the beads. Adams was told that the abacus was introduced from China in the fourteenth century and he realized that Japanese culture had reached quite an advanced level.

However, their lessons were often disturbed by Ieyasu's close retainers, who needed decisions on various matters. Several retainers signalled Adams to leave the room, but Ieyasu ignored them and allowed Adams to stay and listen. In this way, Adams learnt who the Shogun's regular visitors were and who were his most important retainers.

Ieyasu's first priority was to deal with his government, the economy and negotiations with the Toyotomi family. He had support from his close Fudai, the highest-ranking retainers, Lord Honda, Lord Matsudaira, Lord Andō and others. The second was to deal with the temples and shrines, where philosophy, literature and other subjects were being taught. The third was to deal with finance and commerce, with support from Suminokura, Chaya Shirojirō and other merchants. The fourth was to familiarize himself with international affairs and obtain Western knowledge so he could deal with diplomacy, trade and Christianity in Japan; which is why Adams quickly became one of his closest advisers.

At first, Adams felt honoured to be accepted into a position of privilege that he would never have gained in his own country. However, he noticed that Ieyasu's other close retainers began to show some kind of jealousy towards him.