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A '''formal science''' is the academic study that is predominantly concerned with abstract [[formal systems]], for instance, [[logic]], [[mathematics]], and the theoretical branches of [[theoretical computer science|computer science]], [[information theory]], and [[statistics]].  

A '''formal science''' is the academic study that is predominantly concerned with abstract [[formal systems]], for instance, [[logic]], [[mathematics]], and the theoretical branches of [[theoretical computer science|computer science]], [[information theory]], and [[statistics]].  

It is arguable whether formal science is, besides [[natural science]] and [[social science]], the third branch of science and some of the disciplines of formal science like [[mathematics]] and [[statistics]] are often even referred as natural science. For instance, [[Carl Friedrich Gauss]] referred to mathematics as "the Queen of the Sciences".<ref>Waltershausen</ref> In some notable universities, e.g. [[Imperial College London]] and [[Tokyo University]], their [[Academic department|department]] of mathematics/statistics run under the [[faculty (university)|faculty]] of natural science/science.  

It is arguable whether formal science is, besides [[natural science]] and [[social science]], the third branch of science and some of the disciplines of formal science like [[mathematics]] and [[statistics]] are often even referred as natural science. For instance, [[Carl Friedrich Gauss]] referred to mathematics as "the Queen of the Sciences". In some notable universities, e.g. [[Imperial College London]] and [[Tokyo University]], their [[Academic department|department]] of mathematics/statistics run under the [[faculty (university)|faculty]] of natural science/science.  

The changing definition of the word 'science' maybe primarily induces such a confusion. In the original Latin ''Regina Scientiarum'', as well as in [[German language|German]] ''Königin der Wissenschaften'', the word corresponding to ''science'' means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to modern ''scientific method'' is of later date.

The changing definition of the word 'science' maybe primarily induces such a confusion. In the original Latin ''Regina Scientiarum'', as well as in [[German language|German]] ''Königin der Wissenschaften'', the word corresponding to ''science'' means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to modern ''scientific method'' is of later date.