Is it permissible to seek knowledge and pursue it with worldly intentions, such as love of money, desire for advancement and distinction, and gaining people's respect, while also being able to add the intention of seeking knowledge for the sake of Allah the Almighty?

If the knowledge is worldly, like mathematics and physics, there is no impediment to seeking it for the benefit of oneself. However, if it is religious knowledge, it has two objectives: a primary one and a secondary one. The primary objective is to act upon it, and the secondary objective is what results from it, such as honor, influence, esteem, beauty, wealth, and pleasure. This secondary objective either serves the primary objective or it does not. If it serves it, then intending it is correct; otherwise, it is not, as the Prophet, peace and blessings be upon him, said: "Whoever learns knowledge by which the face of Allah is sought, but he does not learn it except to attain a worldly gain, he will not find the scent of Paradise on the Day of Resurrection."