Proofs and Prompts

Notes from the common room

Axioms v.1.0.

Jarek Kędra, Professor at University of Aberdeen

As many of you, I feel lost in the new world. I am gaining experience and face questions I find hard to answer and choices I find hard to make. For this reason, I wanted to create a very minimal set of axioms which I can quickly apply when I am not sure. Also, I wanted them to be helpful in discussions about the new shape of mathematical research and education. They are not original very likely obvious to many of you, and they go back to Thurston, at least. I wrote them mainly for my personal use. Here is version 1.0.

AXIOMS v.1.0

  1. Mathematics is done to deepen human understanding.
  2. Mathematics advances only through human understanding.
  3. Independent human mathematical thought must be preserved.

Received 4 October 2026.

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4 responses to “Axioms v.1.0.”

  1. anonymous Avatar
    anonymous

    Perhaps I can add: Research requires being interested in what one is working on. Authors who are so disinterested that they have better things to do than writing their own papers are, very probably, those who should stop “making preprints” entirely.

    Reply
  2. Björn Ivarsson Avatar
    Björn Ivarsson

    I also feel that these axioms are important when talking to people outside the field. Also to other mathematicians of course.

    Reply
  3. anon Avatar
    anon

    One problem the mathematical community faces is that “Mathematics is done to deepen human understanding” might our goal, but it is not how society looks at it, at least in the United States, and is not how we have presented the case for funding for mathematics in the past to the government. Society thinks, and we have often said, that Mathematics is done for the sake of applications, and Mathematicians are worth funding because mathematics helps other sciences and they train scientists from all fields to think mathematically. Tao’s often criticized example of cancer research is case in point: The government doesn’t care if a cancer cure involve “understanding” or not. Much of science has stopped caring about “understanding” already ten years ago, when machine learning started to be popular. So I don’t think that this argument is very helpful for the broader discussions with society that are going on – and the fact that we might come off badly in those discussions just increases the peril for young people.

    Reply
  4. a Avatar
    a

    I would remove Axioms 1 and 3 (if it is to be a minimal set).

    Reply

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  1. I would remove Axioms 1 and 3 (if it is to be a minimal set).

  2. One problem the mathematical community faces is that “Mathematics is done to deepen human understanding” might our goal, but it...

  3. I also feel that these axioms are important when talking to people outside the field. Also to other mathematicians of...

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