TL;DR -- GenAI is everywhere for the good and the bad. Which is which? There are many themes like this that need attention. One thing to address is how humans and mathematics go together. Along that line, we have to address the history and philosophy of mathematics, in general. But, then, those aspects of the discipline dealing with computing and GenAI (and AGI), in particular, require special attention.
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We have been trying to avoid use of GenAI, in general, while a few issues get worked out. That is not a "luddite" approach as we have studied several of these and definite knowledge about how things went awry. As a reminder, here are some of our posts: ChatGpt; Bard, later Gemini; GenAI.
Of late, Google has a summary in Chrome which is from Gemini's take on the matter at hand. This applies to any search.
Example, we looked for material related to "humanizing mathematics" which is now a growing topic due to the emergence on the landscape of GenAI. This comment was for a search on "humanist mathematics".
Humanist mathematics is a way of teaching and studying mathematics that emphasizes the human aspects of the subject. It can include using history, imagery, and technology to help students understand mathematical concepts.
Now, why mathematics? Are we picking on it? Well, it's about time that someone does. And, this is merely a small start.
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Before getting in that, let's look at a couple of things related to the Humanist's view.
- HumanizingMathematics and its Philosophy (book review) - "The Humanist view is contrasted with Platonism and Formalism. Platonism is the position that mathematical objects and truths exist independently of individuals, and the obligation of mathematicians is to discover these truths. Formalism regards mathematics as the study of formal deductive systems, and athematical truth is just provability in the system." This is a simple summary of positions; there are more which we will be getting into as the discussion continues.
- Journal of Humanistic Mathematics - Editorial from the lastest issue: "We feel strongly about the human nature of mathematics; there is a reason “humanistic” is in the title of this Journal after all! So it is quite appropriate that several articles in this issue remind us that mathematics has always flourished as a human endeavour and it is perhaps the reduction to sterile algorithms that has stripped it of interest for many students. So we are actually trying to rehumanize mathematics, to bring back that spark that leads to students looking upon their math journey in a more positive light.
Again, a major motivation is the GenAI appearance which represents a particular type of applied mathematics be used for make an argument for computer superiority. People react to that various ways which brings in psychology. But, science needs to weigh in as well. Our posts of the Nobel activity this past summer suggest another type of motivation. The subject is not simple, by any means.
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Frankly, to do this right, we will go back to Kant's time and look at two of his works: Prolegomena; Logic. We started with the first one in 2022, after ChatGpt and its peers were out long enough for us to know something of substance. Actually, back in the late 2010s, I started to use AIn't. In 2023, Larry Walker of the former Sperry Knowledge Systems Center used "no critter" in response to something that I had written.
Since that time, we now see lots of mathematical analysis coming forward. Our task is to bring these notions to public view, including the C-Suite where the mentality seems to be buying into the hype prematurely. But, that's another topic or two.
We intend to be regular in posting material. As well, we would like to hear from others on their views with respect to GenAI as well as examples of how they have put it to use or have done studies in order to determine the ins and outs.
Remarks: Modified: 02/28/2025
02/28/2025 --
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