After I heard someone ask about what a mathematician does, I myself wonder what it means to do mathematics if all what one can answer is that mathematicians do mathematics. Solving problems have been considered by some as the main activity of a mathematician, which might then be the answer to the question. But, could reading and writing about mathematics or crafting a new theory be considered as serious mathematical activities or mere extracurricular activities? It seems mathematicians and mathematics students are expected to always solve problems. Many mathematicians I know or hear about have always been busy with solving problems; some of the named theorems, such as HeineBorel Theorem or Brouwer FixedPoint Theorem, could have been problems on which Heine, Borel, and Brouwer spent a long time to solve. Also, many papers published in journals are solutions to problems, which makes me think that mathematical research is synonymous to solving problems. I also have the impression that solving problems is seen by some as the “right” way to do mathematics by the emphasis put on such activity. But, if someone writes an expository paper about a mathematical topic, could that also be seen as doing mathematics? Could this enterprise be counted among a mathematician’s achievements? For students being trained in mathematics, should there also be an emphasis on reading and writing about mathematics, which is not necessarily reading and writing proofs? Furthermore, when a mathematician comes up with a theory after years of work, could he be seen as having wasted his time while he could have solved many problems in the time he took him to complete his work? If one thinks it indeed is a waste of time, would one also see problems arising from this theory as unmathematical since their source is not mathematical enough? What if this theory has been inspired by a problem, would that qualify it as a genuine mathematical activity? Because of this apparent ambiguity about what constitutes the “right” mathematical activity, what would students of mathematics need to focus on for their training? Do they need to focus more on solving problems, which necessarily could involve the other activities since understanding a problem might demand some preliminary reading about its origin and motivation and solving it might push one to write about it for a wider audience and inspire one to come up with a new theory in the process of solving the problem? So, what would it mean to do mathematics? Besides the activities aforementioned, would there be other activities considered as doing mathematics? Please, share your comments.

The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society
Subscribe to Blog via Email

Recent Posts
Recent Comments
 Michael M. Ross on Legendre’s Conjecture
 Alan Caldwell on Odd Perfect Numbers: Do They Exist?
 Jonathan Rodriguez on How to Deal with “I Hate Math”
 Jon Pritzker on Is there a difference between “Education” and “Learning”?
 Spectre on The Problem Of Brocard
Archives
 January 2021
 November 2020
 July 2020
 June 2020
 May 2020
 March 2020
 February 2020
 January 2020
 December 2019
 November 2019
 October 2019
 September 2019
 August 2019
 November 2018
 September 2018
 June 2018
 May 2018
 March 2018
 February 2018
 January 2018
 December 2017
 November 2017
 October 2017
 September 2017
 August 2017
 July 2017
 June 2017
 April 2017
 March 2017
 February 2017
 January 2017
 December 2016
 November 2016
 October 2016
 September 2016
 August 2016
 July 2016
 June 2016
 May 2016
 April 2016
 March 2016
 February 2016
 January 2016
 December 2015
 November 2015
 October 2015
 September 2015
 July 2015
 June 2015
 May 2015
 April 2015
 March 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
 September 2011
 August 2011
 July 2011
 June 2011
 May 2011
 April 2011
 March 2011
 February 2011
 January 2011
 December 2010
 November 2010
 October 2010
 September 2010
 August 2010
 July 2010
 June 2010
 May 2010
 April 2010
 March 2010
 February 2010
 January 2010
 December 2009
 November 2009
 October 2009
 September 2009
 August 2009
 July 2009
 June 2009
 May 2009
 April 2009
 March 2009
 February 2009
Categories
 Advice
 Algebra
 Algebraic Geometry
 AMS
 Analysis
 Announcement
 Arts & Math
 Biology
 Book Reviews
 Conferences
 Crossword Puzzles
 Diversity
 Ecology
 Editorial Statement
 General
 Grad School
 Grad student life
 Interview
 Interviews
 JMM
 Jobs
 Linear Algebra
 MAM
 Math
 Math Education
 Math Games
 Math History
 Math in Pop Culture
 Math Teaching
 Mathematicians
 Mathematics in Society
 Mathematics Online
 News
 Number Theory
 Publishing
 puzzles
 Social Justice
 Starting Grad Schol
 Statistics
 staying organized
 Teaching
 Technology & Math
 Topology
 Uncategorized
 Voting Theory

Comments Guidelines
The AMS encourages your comments, and hopes you will join the discussions. We review comments before they're posted, and those that are offensive, abusive, offtopic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.
Meta