go, excel
邁 centers on moving forward with purpose: going ahead, advancing, or excelling by pushing beyond ordinary limits.
邁 combines the movement radical 辶 with 萬, which likely contributes the sound and may suggest a large number or distance, together conveying the idea of going far or excelling.
The movement radical 辶 wraps around 萬 (ten thousand). Imagine striding forward ten thousand steps, going far and excelling with each step.
For マイ, picture a mighty (マイ) traveler striding ten thousand miles: mighty -> マイ, and the traveler excels at going the distance.
pushing forward (undaunted); pushing on (toward a goal); striving (for)
noble; lofty; high-minded
dash and go; pushing forward
heroic; courageous
highly gifted
push boldly forward
wise and great
intrepidity; indomitableness
excellence; superiority; preeminence