On the current debate about AI replacing Mathematicians (take 2)
by Oded Goldreich
Given the dramatic increase in the damage that AI-tools are causing the mathematical community, I find it necessary to sharpen the points I made in my prior posting on this subject [Aug'25]. Before doing so, I wish to note that these opinions are aligned with my older brief short opinions on the imporatnt of good expositions and on progress in Math (following W. Thurston).
I am also happy to endorse the public statement about the severe misalignment of current AI practices with Mathematics.
Let me start with the principles, then comment on their alignment with a better human society, and only later comment on their chance of survival in today's sour state of affairs.
The principles
As stated in my prior post, my main point is that theoretical research is not aimed at specific achievements but rather at general understanding. The specific achievements are an indication of general understanding; they also advance the general understanding and may have external (technological) utilities, but the goal remains human understanding. If a machine (or an extraterrestrial entity) obtains an achievement, this (by itself) does not promote or help human understanding. Humans are not a mean for generating achievements (i.e., obtaining results), but are rather the end of these achievements (i.e., their improved understanding is the goal).
In other words, providing an answer to any specific question, without gaining an understanding of why this is the answer, leaves humans in ignorance (and bewilderedness) in front of the world. Actually, the world itself may be viewed as a machine that provides answers to questions (alas not always the questions chosen by humans). (This is somewhat analogous to JS Borges's stories about the ``ultimate map'' and about The Lottery in Babylon.)
The desire to understand the world (including our modeling of aspects of the world) is an existential need. Let me stress that while this desire is located in individuals, it is actually a desire to participate in a communal project that is aimed at understanding the world. This project yields technological benefits and is often motivated by seeking such benefits, but it does not reduce to these benefits.
When I talked about understanding Math, I meant Math as a communal project, starting with individual learning, continuing to research (i.e., going beyond the communal knowledge), and culminating in sharing the obtained understanding with the research community at large and enriching it. (Indeed, learning and researching are related in their nature, and I distinguish them by whether or not they transcend the knowledge of the community. Likewise, I use the term ``teaching'' in the sense of advancing the understanding of others, typically to a level below the one reached by the community (but sometimes even to that level), and therefore I objected to the view that the value of understanding reduces to the value of teaching.)
These principles are well aligned with a (humane) society that places humans' well-being at the focus of its attention, where the term well-being refers to the state of almost all individuals rather than to the state of the upper strand of society. Such a society views humans as its ends, not as means for some other end. In particular, the question is how to organize economy such that this goal is met, rather than how do individuals serve the economy. Let me stress that I am not talking about an ideal society, but rather about a society that is more committed to this view than the current society. For example, I'd claim that the ``western society'' of the ``golden decades'' (i.e., 1945-70) was far more aligned with this view than the ``western society'' that emerged in the last decades (say, since the mid 1990s).
On survival in today's society
Nevertheless, any society need a cadre of humans that understand Mathematics (and analogous cadres for any discipline of knowledge). Hence, even today's inhumane society will maintain such a cadre. It may be that in future struggles about funding theoretically oriented research this point will have to be pushed to the front stage (replacing the current ``popular star'' of technological benefits). I believe that this line-of-argument will find willing ears, to say the least.
But let us put things in perspective. Theoretical research is not the only aspect of human life that is threatened by today's inhumane society and the recent ``AI revolution'' taking place in it. For a couple of decades now, the deterioration of living conditions for much of the population, acute uncertainty about the future, lack of hope, and the fear of various dangers have darken the sky above humanity. The current AI revolution adds a very significant facet to this gloomy picture. This reality has hit those who have time to think about it (i.e., the upper strands of society) most strongly, and it is manifested in deep emotional problems that many enlightened young people have. Things are only getting worse (with the AI revolution), but the source of evil is actually in the society.
There is hope that the AI revolution will force the current society to reconsider its nature (and maybe even re-orient itself); at the very least, it will have to take action w.r.t the AI revolution, which is indeed in contradiction to its proclaimed `neo-liberal' ideology. (This is not unrelated to what Mathematics and other theoretical disciplines will have to do -- see next.)
Back to Math
I believe that the AI revolution will force theoretical research communities to reconsider their nature and re-orient themselves more directly at the centrality of understanding in their endeavor. The notion of understanding is hard to define, let alone evaluate, and this led theoretical research communities to use research achievements (i.e., results) as a proxy for understanding. This convenience had bad side effects, which are related to the neglect of understanding and conceptual aspects, unless the latter are coupled by new (striking) results (*). It seems that this convenience may disappear, and so the focus will have to be on human understanding (per se) and on interaction within a relevant research community.
*) I have written about these side effects a lot in the past; see my essays page.
A final comment
Needless to say, the AI-revolution could have been a good thing (if it were really aimed at reducing the hardships of the life of most humans (esp., of those who have it worse) and increasing the broad social welfare (*)), but this is unlikely to happen in a society that is NOT structured in a humanistic manner.
*) I always objected the view that social welfare is some average; one should look at the lowest (say third) tier/strand of society. The welfare of a society should be defined at the welfare of its less fortunate members.
Acknowledgements
I am grateful to Salil Vadhan for discussions regarding the topic.[Sept 2026]
Back to Essays and Opinions of Oded Goldreich.