« Notations, proof practices and the circulation of mathematical objects. The example of groups (1800-1860) »

Résumé En

How exactly do mathematical objects circulate from the work of one mathematician to another? The meaning of any mathematical text belongs to its reader: they can understand it differently from its author, they can use the ideas and concepts for a different purpose, and they can even choose different notations and symbolism to write down the mathematical objects it involves. But doing so, they slightly change its original meaning. This paper is an attempt to show how far an object that would be said to remain “the same” by mathematicians working with it can be noted, symbolized and used in very different ways, and finally be associated with very different mathematical practices of proofs. For that purpose, I will take the example of groups from the beginning of the 19th century to the 1860s. This study of the “groups in the making” will thus emphasize the diversity of approaches that mathematicians can follow when they are working with what we would be said to be one mathematical object.