In the realms of art and craftsmanship commitment plays a central role. In these domains the link between the person and the product produced is out of question. In order to achieve mastery the artist as well as the craftsman has to commit him- or herself as much as possible to his or her work. There seems to be a similar link between a mathematician and … and what? A problem? A field of research? A mathematical landscape? A technique? Nevertheless the similarity between a mathematician and an artist concerning the commitment of both is striking.
Another area where commitment plays a central role is sports. A good analogy to mathematics might be the area of the so-called ‘mental sports’ like Chess or Go. In these sports which depend less on special physical capabilities like extreme height in basketball or like certain proportions of the body in athletics or swimming, the level of commitment plays a central role with respect to the achievements.
The level of commitment may also partially explain why the highest achievements are made at an early age and mostly by male mathematicians. This is very similar in chess. At an early age there are most often no additional commitments to family and children or to professional or societal issues which might reduce the level of commitment to mathematical research. Women in most contemporary societies (and in relevant previous ages) have been driven to commit themselves to a very big extend to family issues of which motherhood is of course the part which is most difficult to neglect. And women have been prepared for these ‘standard’ commitments already from an early age which is also important with respect of achieving extraordinary results either in mathematics, in the arts or in the domain of mental games.
Why is it important to mention commitment? Because it should not only be restricted to high-level research on the frontiers of ‘dead mathematics’. There should be credits for commitment to other valuable part of mathematics like expository presentation, teaching, applications, philosophy, history, de-specialising activities (outreach), etc. The point is that for all these activities the best results would be achieved when there is a high-level commitment at an early age and this is not possible and not allowed or better, not appreciated nowadays. Without any reason the listed activities are considered to be on a lower level and hence not to need such an intensive commitment as research does. This leads to feedback-effects which result in a predominantly lower level of all the above listed activities. A potential change in this respect would automatically lead to new requirements to mathematicians doing high-level research. Namely to present it in a manner that would keep the other mathematicians up-to-date – those who have committed themselves to some of the other above mentioned and then considered equally important activities but also to those doing research in other fields of mathematics. This would lead to something we might call the ‘unity’ of ‘living mathematics’ which clearly does not exist today. By the way, I consider the speculations about the ‘unity’ of ‘dead mathematics’ to be as unimportant to the daily work of a mathematician as this is the case with the speculations about the status of existence of numbers (the last point has been stated by T. Gowers already in 1999 at his talk at the ‘Visions in Mathematics’ conference).
In his major treatise ‘Personal Knowledge’ which is one of the main inspirational sources of this encyclopaedia, Michael Polanyi has devoted a main chapter to the issues of commitment. The above text can serve only as a first vague attempt to point at some aspects of ‘living mathematics’ where the notion of commitment should be useful in approaching some philosophical questions.