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\begin{document}

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\section*{development and current state of mathematics}

\hypertarget{the_development_and_current_state_of_mathematics}{}\section*{{The development and current state of mathematics}}\label{the_development_and_current_state_of_mathematics}

\noindent\hyperlink{on_the_relation_between_conjectural_and_proved_mathematics_styles}{On the relation between conjectural and proved mathematics styles}\dotfill \pageref*{on_the_relation_between_conjectural_and_proved_mathematics_styles} \linebreak
\noindent\hyperlink{some_other_issue}{Some other issue}\dotfill \pageref*{some_other_issue} \linebreak


This is not part of [[philosophy]] in a narrow sense, but the opinions on what is good [[mathematics]], how mathematics could develop better, and how it should be stimulated to develop, as well as overviews of the current state of mathematics and its important points, is an important part of reflection, but also of the practical action of a mathematician.

\hypertarget{on_the_relation_between_conjectural_and_proved_mathematics_styles}{}\subsection*{{On the relation between conjectural and proved mathematics styles}}\label{on_the_relation_between_conjectural_and_proved_mathematics_styles}

This is a topic of a well-known discussion series in 1990s.

\begin{itemize}%
\item Arthur Jaffe, Frank Quinn, \emph{``Theoretical mathematics'': Toward a cultural synthesis of mathematics and theoretical physics} , Bull. Amer. Math. Soc. (N.S.) \textbf{29} (1993), no. 1, 1--13; \href{http://www.ams.org/mathscinet-getitem?mr=1202292}{MR94h:00007},\href{http://arxiv.org/abs/math.HO/9307227}{math.HO/9307227}, \href{http://dx.doi.org/10.1090/S0273-0979-1993-00413-0}{doi}


\item [[Michael Atiyah]], [[Armand Borel]], G. J. Chaitin, Daniel Friedan, James Glimm, Jeremy J. Gray, Morris W. Hirsch, [[Saunders MacLane]], Benoit B. Mandelbrot, David Ruelle, [[Albert Schwarz]], Karen Uhlenbeck, Ren\'e{} Thom, [[Edward Witten]], Christopher Zeeman, \emph{Responses to ``Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics'', by A. Jaffe and F. Quinn}, Bull. Am. Math. Soc. \textbf{30}:178-207, 1994, \href{http://arxiv.org/abs/math/9404229}{math.HO/9404229}


\item [[Michael Atiyah]], \emph{Reflections on geometry and physics}, Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), 1--6, Int. Press, Cambridge, MA, 1995.


\item [[William P. Thurston]], \emph{On proof and progress in mathematics}, Bull. Amer. Math. Soc. (N.S.) \textbf{30} (1994), no. 2, 161--177, \href{http://www.ams.org/mathscinet-getitem?mr=1249357}{MR94m:00006}, \href{http://dx.doi.org/10.1090/S0273-0979-1994-00502-6}{doi}, \href{http://arxiv.org/abs/math/9307227}{arxiv/math.HO}


\item David Corfield at el. \emph{Wittgenstein and Thurston on understanding}, \href{http://golem.ph.utexas.edu/category/2006/10/wittgenstein_and_thurston_on_u.html}{nCafe}



\end{itemize}
Somewhat later and with different scope, but related to this series, is also a long article

\begin{itemize}%
\item Frank Quinn, \emph{Contributions to a science of contemporary mathematics}, \href{http://www.math.vt.edu/people/quinn/history_nature/nature0.pdf}{pdf}

\end{itemize}
\hypertarget{some_other_issue}{}\subsection*{{Some other issue}}\label{some_other_issue}

\begin{itemize}%
\item The [[big picture]] in [[mathematics]].

\end{itemize}
[[!redirects opinions on the development of mathematics]] [[!redirects opinions on development of mathematics]] [[!redirects development of mathematics]] [[!redirects development and current state of mathematics]]



\end{document}