Do We Create Mathematics or Do We Gradually Discover Theories Which Exist Somewhere Independently of Us?

[摘要] The headline question is a phrase from the article“Mathematics: Art and Science” by A. Borel, which is theEnglish translation of the text of his lecture delivered (inGerman) in Munich in 1981. I remembered about thisarticle in October 2016 when I saw the title “Discoveries,not inventions – Interview with Ernest B. Vinberg” of anarticle for publication in the EMS Newsletter, No. 102,December 2016 [2]. The very title clearly implies a definite answer to this question but it turns out that, in theinterview, the issue of whether mathematicians exploresomething that exists independently of them or something they have invented is not discussed.