Female researchers in mathematics are underrepresented among their peers in most countries and on most career levels. The fact that the proportion of women decreases when their cohort moves to higher qualification levels and career stages is known as the “leaky pipeline” effect. This metaphor visualizes a researcher’s career path as a pipeline that starts at enrolment in a program at a university and ends at a (full) professorship; at each transition stage of the pipeline, the proportion of women decreases. These leaks may occur at the transition from a bachelor course to a master program, from a master program to a PhD program, or later.  The size of this effect and at what stages it is most notable depend on the mathematical field and the geographical region. Still, it undoubtedly exists and can be measured across many different disciplines and countries.

One possible contribution to counteracting this gender gap is to offer specific mentoring programs for women in math. The goal is to provide women in science with female mentors who can serve as their role models. To support and encourage them as well as help them build a professional network so that ultimately less female researchers drop out of the leaky pipeline.

While the literature on mentoring is vast and its practice is as widespread as varied, there are (to our knowledge) no practical guidelines and manuals for how to implement a mentoring program with said goal specifically for women in mathematics.

We aim at closing this gap by laying down principles for mentoring, giving best practice examples, providing checklists and templates for launching and administrating a mentoring program (emails, registration and evaluation forms, posters, etc.), describing in detail training for mentors (which is specifically targeted to women in mathematics), and providing free and open access materials for said training.

The practices we describe are for mentoring within an academic institution. They are based on the following principles and convictions:

1. A pyramid structure of mentors and mentees: the mentor should be only one or at most two career stages ahead of her mentee(s) so that the proximity in professional and likely personal situations enables them to empathize better with each other’s challenges.
2. Confidentiality between mentor and mentee goes both ways. It gives both parties the possibility to share personal experiences in a protected environment.
3. Respecting the individuality of the mentee is paramount. Rather than forcing solutions on her, the mentor should provide a cognitive framework that helps the mentee structure her thoughts and priorities.
4. Both parties need to recognize the limitations of the mentoring relationship. The mentor might help the mentee find resources or people that can provide a solution rather than provide a solution herself.
5. Regular meetings of mentor and mentee help to build trust. It is crucial to build the mentoring relationship before the mentee encounters serious problems or situations she needs her mentor.
6. Within the framework of confidentiality and trust, there is room for individual preferences. It is up to mentors and mentees to decide how they keep in touch and in what setting they meet.

The training for mentors takes about 2.5 to 3 hours. Its goals are to introduce the (future) mentors to the ground rules of mentoring, to familiarise them with arguments for and against mentoring for women in academia, to train them in active listening, and to enable them to react adequately to potentially difficult challenges in the mentoring relationship. Its core modules include:

1. Why mentoring for women in math: In this module, the participants reflect on the goals of the mentoring program, its necessity, and its desired impact. They learn to counter-arguments that discredit mentoring programs for women. The core part of this training module is a fishbowl discussion with the guiding question, “Are there enough women in math? Does one need to take action?”. The participants are split into two teams that must defend opposing opinions in the discussion (regardless of their actual opinions on that matter). They reflect on the outcome of the discussion.
2. Roleplay “mentor-mentee”: The goal of this module is to try out possible interactions in realistic situations that may arise in the context of mentoring and to reflect upon own beliefs, attitudes, and habits relevant to a mentoring partnership. Two participants act as mentor and mentee. The “mentee” plays a role assigned to her by a vignette, e.g. approaching the mentor with a certain problem, and the “mentor” reacts accordingly. One other participant and the trainer provide feedback on the interaction.
3. Preparing for the first meeting with the mentee: The goal of this module is to lower the psychological barrier of contacting the mentee and meeting with her as well as to reduce possible nervousness or tension. The participants work in pairs to prepare for the first meeting with their mentee(s) and imagine in detail what the first meeting should be like, guided by key questions. They also receive a list of relevant contact points for further help.

Some of the principles of mentoring that we describe – like confidentiality between mentor and mentee – are universal tenets of mentoring; others – like the pyramid structure of the mentoring – have been proven useful by experience for mentoring in math in different settings. However, other best practice recommendations should be regarded as mere rules of thumb and can be changed depending on the education system, the academic stage of mentors and mentees, and other factors. This is why we describe different options for all aspects and stages of mentoring programs – whether it be advertising the program, training the mentors, evaluating the program, or another facet of mentoring. Accordingly, all materials (copy templates, materials for the training, ideas for a list of contact points etc.) can be modified and adjusted to the local needs, extended or abridged, and translated. The handbook and the additional materials will be published under a Creative Commons license (allowing for re-use, modification, translation, and further sharing); they are available under https://mentoring.spp2026.de and also can be requested by emailing math.mentoring.handbook@gmail.com. Feedback, suggestions, and further additions are also welcome! We hope to have sowed a seed for a living handbook that will grow as more experience from mentoring women in mathematics will be incorporated!

The handbook is written by Carla Cederbaum, Sophia Jahns, and Anna Wienhard within the framework of the Priority Programme SPP 2026 Geometry at Infinity of the German Research Foundation (DFG). It is based on the experiences with the Math Ment♀ring Program at Tübingen University led by Carla Cederbaum and the UPSTREAM Mentoring network at Heidelberg University led by Anna Wienhard and Michael Winckler. A mentoring program based on this handbook will soon be integrated into the DFG-Priority Programme SPP 2026 Geometry at Infinity.

It contains materials and ideas developed by or in collaboration with May-Britt Becker, Benjamin Cooke, Ingrid Daubechies, Katrin Grass, Mareike Kaina, Maria Rupprecht, Anna Schilling, Lea Schmid, Sarah Schott, and Michael Winckler. Additional funding by Duke University, the Institutional Strategy of the University of Tübingen (DFG, ZUK 63) and by the Athene-Mentoring Programm, University of Tübingen, the HGS MathComp at IWR Heidelberg, the Excellence Cluster STRUCTURES, and the Research Station Geometry & Dynamics at Heidelberg University.

 

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