Singularities at Home, Unofficial Observations
A story about Albert Einstein deals with his desire for a working place in a remote lighthouse for himself and his ideas. The following remarks are devoted to aspects of communication in mathematical sciences with the outside world, sometimes under unusua
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A story about Albert Einstein deals with his desire for a working place in a remote lighthouse for himself and his ideas. The following remarks are devoted to aspects of communication in mathematical sciences with the outside world, sometimes under unusual circumstances. Various considerations are developed from the viewpoint “singularities alone at home”. Singularities belong to the challenges in geometry and mathematical analysis and they may be rather “small” like the tip of a pencil and fit into a home office though applications to the real world are not necessarily situated in the hermitage of a researcher. We do not solve this contradiction here but recall remarkable episodes around personalities in singular situations, not only from the present exceptional crisis but also from the past.
1 Introduction The “home office” as a hideaway, evoked by an aggressive wave of infection, has certainly a different intention than the above-mentioned idea of being undisturbed Mathematics Subject Classification (2000): 00A99 Keywords Exponential development, Singular evolution, Research communication, Academic episodes D.-C. Chang Department of Mathematics and Statistics, Georgetown University, Washington, DC, USA Graduate Institute of Business Administration, College of Management, Fu Jen Catholic University, New Taipei City, Taiwan, China e-mail: [email protected] B.-W. Schulze (*) Institute of Mathematics, University of Potsdam, Potsdam, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 A. Wonders (ed.) Math in the Time of Corona, Mathematics Online First Collections, https://doi.org/10.1007/16618_2020_9
D.-C. Chang and B.-W. Schulze
somewhere. There is hope that the results of systematic research in the medical sciences, often induced by new ideas and combined with hard practical work, will be easing the situation in the end. Just as optimism and positive thinking have vitalizing effects on one’s general health, the scientific progress is being stimulated by a relaxed and humorous approach throughout all spaces of time, see also the setting of the novel [16]. In order to explain some effects it is helpful to remember that Euler’s exponential function should be taken seriously—not only in economy— when some quantity is growing or decaying. Clearly, optimism is more justified in the present situation when we may observe exponential decay of infection. However, if we are consuming too much from a resource, for instance, the earth (mixed up with a piece of cheese), we disappear after a while (not the cheese), because we do not experience the inevitable end. In other words, exponential effects can be pleasant or unpleasant and we should not ignore mathematical rules in favor of wishful thinking. Here we present a few impressions or opinions in connection with activities around mathematics and other arts.
2 Remarkable Personalities The practical consequences of systematic scientific research may be so serious that we are inclined to believe the most visi
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