The role of the mathematician is to create concepts and...
Let me take one instance, the notion of truth, in order to illustrate what I mean. We all have in mind that something is either true or false. If we attend a debate on politics or another controversial topic, we are prone to say that this guy is right and that guy is wrong and that’s our way of making a judgement. Now, it turns out that probably we should be more advanced at the level of the formalisation of the idea of truth. In fact, there is a mathematical concept which has been created by A. Grothendieck which is the concept of topos and which has, thanks to contributions of F.W. Lawvere, a far more sophisticated notion of truth [read transcript of the video below about topos]. Technically the “truth values” form an object of the topos and this object classifies sub-objects exactly like the characteristic function (which takes values in the two point set “True, False”) of a subset does in the case of the topos of sets. Thus for this simplest topos something is true or false. But as soon as you take a slightly more involved topos, such as the topos of quivers, you get a much more refined notion of truth values and in the case of quivers it involves "making mistakes, corrections, checking" as fundamental parts of the structure. From this example, you witness that mathematics is a factory of concepts which are extremely rich, which are subtle and which of course are hard to grasp by the public in general due to their mathematical precise and involved formulation. This lack of grasp by the public holds at a certain time in the history of civilisation but I believe that in later years these concepts will become common. This sophisticated notion of truth has, by the way, nothing to do with probabilities. It’s a very beautiful and precise notion developed by a great genius of mathematics.to me, this is the role of mathematics: fabricate concepts and facilitate the process by which the public acquires them. That’s it.
Alain Connes mathematcian, interviewed by a theoretical physicist Jay Armas in Conversations on Quantum Gravity
Transcription of an extract in French:
Aucun commentaire:
Enregistrer un commentaire
Cher-ère lecteur-trice, le blogueur espère que ce billet vous a sinon interessé-e du moins interpellé-e donc, si le coeur vous en dit, osez partager avec les autres internautes comme moi vos commentaires éclairés !
Dear reader, the blogger hopes you have been interested by his post or have noticed something (ir)relevant, then if you are in the mood, do not hesitate to share with other internauts like me your enlightened opinion !