Being a mathematician or philosopher was generally respected. Rulers sought out men of wisdom for instruction for them and their children and occasionally used them as advisors. They ran for-profit and state-controlled schools and libraries. Archimedes was venerated in Syracuse and so respected even by Romans that Marcellus ordered Archimedes to spared despite having wrought havoc with his assault of the city. Unfortunately, his orders were not carried out.

It differs by city-state and era. Philosophers and mathematicians were generally respected, but mainly for their practical applications of their thinking. We see the early philosophers being praised mainly for their ability to predict astronomical and meteorological phenomena (see for instance the writings on Thales and Anaximander).

Abstract philosophy and mathematics was seen as frivolous, for not being applicable to common life, and was not always perceived as favorably. Most notably in the execution of Socrates, one of the old charges is that he concerns himself with the heavens and the things beneath the earth. Plato notes that Socrates has the reputation of being a "busybody" for his inquiries. Later, Aristotle would flee Athens in fear of suffering a similar fate to Socrates.

So my answer would be that practical mathematics and philosophy was viewed very highly, while abstract mathematics and philosophy was seen as frivolous (at least in some locations in the ancient world).