Math exists. We explore it.
We do not invent math. We invent ways of understanding and communicating it. We choose which parts of it to study, and we develop an adequate language for that that suits us, humans. But we explore an objectively existing domain. Empirical fact: our abstract exploration bears fruits also in the physical world. This fact is often used as a retrospect justification, but it is rarely our initial motivation. A common metaphor for math exploration is landscape charting.
Geography exists.
Past cartographers sailed the seas. There was an heroic aspect to their profession. There was an artistic aspect to map drawing. Could they envision satellites and computerized general information systems? Their profession is less romantic now, but our maps are better.
Can we envision how math will be explored in years to come? I believe that we will ever be stunned by its inner beauty and astonished by its interplay with the physical world. This interplay will remain fruitful and relevant to society, perhaps more than ever before, and so also the math community. Yes, we are facing a challenge and we should publicly discuss how to adjust. However, we better stop ranting about progress, rather openly embrace it. We should celebrate new opportunities to better fulfil our mission.
Received 21 August 2026.
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