Is it permissible to create a website to publish wise sayings and useful quotes, transmitted from Muslim and non-Muslim philosophers and scholars, in various fields such as life, will, friends, and optimism?

There is no harm in transmitting beneficial and useful speech from a Muslim or a non-Muslim. This is supported by the Prophet's (peace be upon him) statement regarding the poetry of Umayya ibn Abi al-Salt and his recitation of a verse by Tarafa. As for the hadith, "Wisdom is the lost property of the believer," it is weak, but its meaning is sound, supported by the general texts; which is that a useful word that does not contradict the Sharia can be benefited from, regardless of its speaker. Nevertheless, one should not extensively concern oneself with the sayings of non-Muslims, lest they contain anything that contradicts the Sharia or leads to the glorification of their false speakers. It is better to suffice with the Quran, Sunnah, and the sayings of the imams and righteous people.