Future of mathematics

The examples and perspective in this article may not represent a full view of the subject. Please improve this article and discuss the issue on the talk page. (April 2021)

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The progression of both the nature of mathematics and individual mathematical problems into the future is a widely debated topic; many past predictions about modern mathematics have been misplaced or completely false, so there is reason to believe that many predictions today will follow a similar path. However, the subject still carries an important weight and has been written about by many notable mathematicians. Typically, they are motivated by a desire to set a research agenda to direct efforts to specific problems, or a wish to clarify, update and extrapolate the way that subdisciplines relate to the general discipline of mathematics and its possibilities. Examples of agendas pushing for progress in specific areas in the future, historical and recent, include Felix Klein's Erlangen program, Hilbert's problems, Langlands program, and the Millennium Prize Problems. In the Mathematics Subject Classification section 01Axx History of mathematics and mathematicians, subsection 01A67 is titled Future prospectives.

The accuracy of predictions about mathematics has varied widely and has proceeded very closely to that of technology.^[1] As such, it is important to keep in mind that many of the predictions by researchers below may be misguided or turn out to be untrue.