The IMA’s Gold Open Access online journal Transactions of Mathematics and its Applications: A Journal of the IMA (shortened to Transactions) is published by Oxford University Press (OUP). This year, 2026, marks the 10th anniversary of the launch of Transactions and the publication of its 10th volume. As the editors‑in‑chief, we wanted to take this opportunity to present a ‘warts‑n‑all’ assessment of the journal, to describe some of the papers published in Transactions over the years, and to encourage readers of Mathematics Today to consider submitting forthcoming articles to celebrate its anniversary.
The Philosophy Behind Transactions
Transactions was launched in 2016 as the brainchild of Professor Arieh Iserles FIMA, strongly supported by the IMA Council. Arieh noted that while pure mathematics has several journals whose publications can make a career (such as Annals of Mathematics and Inventiones), there was no equivalent broad, high‑impact home for applied mathematics.
Although many excellent journals exist in applied mathematics—some with long and distinguished histories—they tend to be discipline‑specific. Numerical analysts may never see important results in fluid mechanics, and vice versa.
Transactions was created to fill that gap: a journal aimed at publishing excellent articles spanning the full breadth of applied mathematics, reflecting the diversity and richness of the IMA community. Articles may be of any length and are published on a rolling basis. The Article Processing Charge is modest and covered under the Jisc–OUP Read and Publish agreement, making it widely accessible.
In its first decade, Transactions has published 28 papers with 478 citations and 56,000 views. While many excellent papers have appeared, the journal has not yet consistently attracted the volume of high‑quality submissions needed to fully achieve its ambition.
However, we remain committed to the original vision and encourage all IMA members to submit their very best work during this milestone anniversary year.
Some Success Stories
Below are examples illustrating the breadth, depth, and quality of work published in Transactions. These are a small selection chosen for expediency, not preference.
Likely oscillatory motions of stochastic hyperelastic solids (2019)
In this paper, Mihai et al. addressed how uncertainties in material properties (such as shear modulus) propagate into uncertainties in the behaviour of solids. For example, the probability distribution of the displacement of a point in a vibrating elastic bar can be predicted over time.
The paper introduced a novel approach merging ideas from solid mechanics, applied probability, and analysis, offering methods expected to extend to a wide variety of physical modelling challenges.
Learning stochastic closures using ensemble Kalman inversion (2021)
This highly influential paper tackled the challenge of matching reduced‑order stochastic models to real data. In many multiscale systems—atmospheric science, climate dynamics, molecular dynamics—full‑resolution simulation is computationally prohibitive.
The paper showed how to overcome incompatibilities between SDE models and real data at short timescales by deriving sufficient statistics and using ensemble Kalman inversion to learn model parameters.
This work has drawn significant attention from applied mathematicians, statisticians, climate scientists and experimentalists.
Error estimates for DeepONets (2022)
Scientific machine learning has exploded in recent years, and DeepONets are a major framework for learning operators between infinite‑dimensional spaces. However, rigorous error bounds were lacking.
Lanthaler et al. provided the first optimal approximation and generalisation error estimates for DeepONets and showed that the method can break the curse of dimensionality in important classes of PDE problems.
This is the most‑cited paper in Transactions, with over 10,000 views and 160 citations.
Modelling organoid growth with TDA (2024)
Topological Data Analysis (TDA) has become increasingly important in understanding geometric and structural changes in complex systems. Marsh et al. introduced a TDA‑based method for quantifying temporal shape changes using imaging data from mouse small‑intestine organoids.
Despite the specialised application, the techniques have broad potential in fluid dynamics, medical imaging, and image processing.
The Future
Applied mathematics is vibrant, expanding, and deeply impactful. Members of the IMA are at the forefront of many of these advances. Transactions offers a Gold Open Access platform to showcase your highest‑quality work and ensure it is accessible to the entire global community.
Help us make the journal’s 10th anniversary year truly special—send us your best articles!
More details on submitting an article or contacting the editors
References
- Mihai, L.A., Fitt, D., Woolley, T.E. & Goriely, A. (2019). Likely oscillatory motions of stochastic hyperelastic solids.
https://doi.org/10.1093/imatrm/tnz003 - Schneider, T., Stuart, A.M. & Wu, J.-L. (2021). Learning stochastic closures using ensemble Kalman inversion.
https://doi.org/10.1093/imatrm/tnab003 - Lanthaler, S., Mishra, S. & Karniadakis, G.E. (2022). Error estimates for DeepONets: a deep learning framework in infinite dimensions.
https://doi.org/10.1093/imatrm/tnac001 - Marsh, L., Zhou, F.Y., Qin, X., Lu, X., Byrne, H.M. & Harrington, H.A. (2024). Detecting temporal shape changes with the Euler characteristic transform.
https://doi.org/10.1093/imatrm/tnae002
