Mathematics Collectives

Extraordinary mathematical ideas have historically been met with renewed interest and excitement. In the age of AI, a multitude of new ideas come from the machine; beautiful ideas are lost in the infinite sea of preprints; we feel great pressure to produce more and more new mathematics at the cost of ignoring the work of others. The snake will eat its own head and consume the human motivation to practice mathematics.

A collective provides space to rebuild this motivation. Since intellectual credit is shared, any individual member feels ownership of the work and motivation to engage in new progress. Joint commitment to a common research agenda ensures that the collective itself—at the very least—retains an interest in its own activities. Richer discussion, collaboration, and coordination are natural and central aspects of working in a group with shared goals.

The escalating competition in mathematics, greatly exacerbated by AI companies disregarding good academic practice, makes us less open in our science, in our asking of questions, and in our mathematical discourse. We aim to locally preserve an environment of open science. We believe that this is to the greater benefit of the community, to scientific progress, and for human understanding at large.

The immediate benefit of sharing of credit is a local reduction of competition. Moreover, a broad and ambitious shared research program centred on exploration and understanding is at much less risk from external stress.

When the individual pressure to produce a continuous output of new results is reduced, there is more space for the highly valuable but less externally rewarded aspects of the practice. For instance, members of a collective need not devote all of their time to proving new results, as the credit for new results is shared: this will provide more capacity for the reshaping, simplification, and communication of existing ideas to other experts, to the broader mathematical community, and to the general public.

There are differing views and principles on the usage of AI in the mathematical practice. We believe that the collective model of doing mathematics will be able to preserve the diversity of approaches to doing mathematics.

We cannot predict in what way careers in mathematics will continue to evolve. We do expect that being a junior researcher in a tightly-knit, well-aligned community is more exciting and educational than being a junior researcher working alone. Mentorship of new students can be shared in the collective and early-career risk can be managed more effectively with a larger support group. Moreover, we envisage that a collective can provide a basis for the evaluation of junior researchers on the grounds of their activities and work within the collective and the communication of mathematics more broadly.

A mathematical collective also provides a more flexible environment to develop transferrable skills. Work in a collective will plausibly involve a mix of interpersonal coordination combined with the freedom to pursue one’s own direction within a greater framework. These are core tenets of working in any larger group. There is moreover space for work beyond the traditional bounds of mathematics research, which gives junior researchers more space to pursue their own interests and direction.

We predict that mathematics in the future will be increasingly defined by the production of high-quality work, as the cost of production of low-value AI-generated writing rapidly diminishes. In fact, the value of quality already existed before AI: a few great individual publications are typically valued more than many average publications. However, for the majority of mathematicians, the dilemma is complicated: devoting time to only work on the most impactful of problems is incompatible with the consistent publication record required for a career in academia.

Within a collective, there is more capacity to focus on producing beautiful work. Even if the overall pressure to produce novel work continues to mount, individual members of the collective can choose to pursue higher risk but higher reward approaches to mathematics, or have the space to refine the best ideas.

We believe that the collective model for mathematical research has even greater potential to produce important results and robust understanding of mathematical phenomena. Larger collaborations also provide the opportunity for more points of view: members have less individual obligation to follow the standard approaches and can more safely pursue alternative ideas. Robust organizations are an indication of sustainability: the collective is a commitment to future interest in a given direction. Large groups and collaborations indicate substantial interest on given problems.

The research output of a collective also becomes more diverse. The collective as a whole can give more effort to broader communication of their research. There is moreover additional space for experimentation and application outside of mathematics, which can provide more direct public benefit of our work.