The teaching of mathematics in universities "may not be fit for purpose", not least because it tends "to focus on content without a clear idea of what can be done with it".
This is among the conclusions of a report that says universities risk leaving graduates ill-equipped to apply their mathematical training in the "real world".
The analysis, which expands on an HE Mathematics Curriculum Summit run by the Maths, Stats and OR Network and the Institute of Mathematics and its Applications earlier this year, calls for "a more flexible approach to meet employer needs".
The summit at the University of Birmingham brought together heads of mathematics or their representatives from 26 universities offering maths degrees. The resulting report, published last week, spells out both challenges and possible solutions.
One discussion group focused on the knowledge and attributes that maths students must possess to be allowed to graduate.
There was "considerable consensus" about the core areas and essential graduate attributes such as problem-solving, flexibility, enthusiasm for the subject - and the ability to communicate mathematics.
The last of these came under scrutiny in another discussion group.
Participants acknowledged that some maths students had "low social ability" and chose the subject "specifically to get away from having to present through long-form written and oral communication". However, they also thought that universities should address these deficits.
Institutions offering maths degrees had "a duty and a necessity to meet students' career aspirations", which, the report says, includes developing graduate skills in presenting and other forms of communication. The report recommends that students be required to gain such skills and that universities help them to do so by, for example, providing maths support centres that encourage students to "work collectively".
Even more contentious was the issue of students learning to handle new problems, which is vital because in many areas of employment, graduates "will be tackling unfamiliar problems", the analysis notes.
Both modularisation and the rote learning encouraged by current assessment methods could add to students' unease in novel situations.
More useful would be for lecturers to act as role models in "trying to solve unfamiliar problems, particularly 'dirty' problems with substantial risk of failure".
The report calls for "a coordinated voice" and less anxiety about the demands of the Quality Assurance Agency, arguing that "if we are clear enough about what we want to do with our students, the QAA will be happy for us to do what we like".
It also cautions academics not to project their own ambitions - namely a career as a mathematician - on their undergraduate students and to design each curriculum to meet the "aspirations of those people who will study that curriculum".
More specific recommendations include "the development of a bank of industry-based problems" and further reflection on the difference between rigorous proof and ways of approaching unfamiliar real-life scenarios that might yield useful answers.