Mathematics in the age of AI

Xinzhe Li ·

I used AI to help verify some of the historical references and lightly edit my original text.

I feel that the public's attitude toward AI's impact on mathematics today is somewhat like the appeasement Britain and France practiced when Nazi Germany annexed the Sudetenland. I don't know whether people were still enjoying the beaches of France at the time, believing that Germany would have no effect on their lives. Japan did not stop after establishing the puppet state of Manchukuo. Fortunately, Chiang Kai-shek saw this coming and began training the army in preparation for a full-scale war of resistance against Japan. Even so, there wasn't enough time to finish preparing before full-scale war broke out. Incidentally, two German military advisers were helping with the training: von Seeckt and von Falkenhausen (yes, two vons). I seem to remember one of them also saving Jews in Europe. Anyway, never mind. AI may not give humanity any more time than Japan gave China.

I also want to say something about doing mathematics in the age of AI. AI is only beginning to affect us, and we are living through a time of change. I think of Sakamoto Ryoma, who was studying swordsmanship in Edo when the Black Ships arrived. In the NHK historical drama Ryomaden, the sight of those enormous ships makes him feel that swordsmanship has become useless. Yet he eventually returns to his training. As the drama presents it, swordsmanship cannot hold off Western armies, but it can push a person into a state of self-forgetfulness and shape someone capable of adapting to a new age. In many cases, swordsmanship in the Edo period was like mathematics in this respect: its value lay in cultivating the mind as well as in practical uses. Of course, an analogy cannot settle every question. A more practical consideration is that choosing to do something else may not be any wiser.

Sources and historical notes
  1. The Munich Agreement of September 1938 allowed Germany to annex the Sudetenland. The United States Holocaust Memorial Museum gives the sequence of the agreement and occupation.
  2. On China's preparations, see Su Sheng-hsiung's Re-visiting Chiang Kai-shek's Strategy for the Battle of Shanghai and Pao-Jen Fu's The German military mission in Nanking, 1928-1938. Military reform also faced civil war and financial constraints.
  3. A documented rescue involving Falkenhausen concerned 96 Belgian hostages in 1944, following an appeal by Qian Xiuling. That account does not identify them as Jewish. Falkenhausen also bore responsibility for anti-Jewish persecution and deportations, as discussed in the House of the Wannsee Conference's historical account.
  4. The Ryomaden scenes are in episode 5, 黒船と剣, and episode 6, 松陰はどこだ？. The discussion of training is paraphrased from the drama, with dialogue recorded in a contemporary viewer's notes; it is not presented as Ryoma's documented historical words.
  5. The All Japan Kendo Federation's history of kendo discusses the development of swordsmanship as a form of personal and mental cultivation during the Edo period.