Announcements

Nobel Prizes are the world’s most prestigious recognition of scientific breakthroughs, honoring discoveries that push the boundaries of knowledge and reshape entire fields. They bring into the public eye researchers whose work might otherwise remain known only within specialized circles.

For many, winning a Nobel Prize is a surreal experience. Laureates often describe a mix of joy, humility, reflection, and gratitude for the teams and collaborators whose contributions made the achievement possible. Behind every Nobel-winning idea lies years of careful, incremental work—a process that often goes unseen.

When Prof. Steven Weinberg won the Nobel Prize in Physics in October 1979, his wife Louise, a legal scholar, reminded him to keep doing the ordinary hard work of science, joking: “Now you have to write some unimportant papers.” True to form, Weinberg continued to push the boundaries of our understanding of the Universe, showing that curiosity and dedication extend far beyond the moment of recognition (Hofmann 2025: https://www.mdpi.com/2073-8994/17/6/840).

Discover the science behind the world’s most transformative ideas

Over the years, dozens of Nobel laureates have published their work with MDPI, entrusting our open access journals to disseminate their findings to a global audience. As of 2024, more than 40 laureates have contributed over 115 articles across 35 journals, ranging from pioneering research on microRNAs and mRNA therapeutics, to fundamental insights in theoretical physics, and advances in structural biology.

We regularly spotlight how Nobel Prize–winning research intersects with the contributions of our authors. This not only celebrates the achievements of the laureates, but also underscores the role of open access in ensuring that transformative science reaches the widest possible audience.

On this page, we invite you to explore selected works by Nobel laureates within the MDPI portfolio, and to join us in celebrating the global impact of their ideas.

The Nobel Prize in Physiology or Medicine 2025 has been awarded to Mary E. Brunkow, Fred Ramsdell, and Shimon Sakaguchi for for their discoveries concerning peripheral immune tolerance. MDPI sincerely invites you to explore research in a related field.

The Science Behind the Prize: 2025 Nobel Physiology or Medicine Roundtable
6 October 2025, 03:30 pm (CEST)
You are welcome to watch the recording here!

The Nobel Prize in Physics 2025 has been awarded to John Clarke, Michel H. Devoret and John M. Martinis for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit. MDPI sincerely invites you to explore research in a related field.

The Science Behind the Prize: 2025 Nobel Physics Roundtable
7 October 2025, 02:30 pm (CEST)
You are welcome to watch the recording here!

The Nobel Prize in Chemistry 2025 has been awarded to Susumu Kitagawa, Richard Robson and Omar M. Yaghi for the development of metal-organic frameworks. MDPI sincerely invites you to explore research in a related field.

As artificial intelligence (AI) systems increasingly shape critical decisions in finance, auditing, cybersecurity, and governance, the demand for interpretable, transparent, and data-authentic models continues to grow. In this context, Benford’s Law—a mathematical law that predicts the frequency distribution of leading digits in naturally occurring datasets—emerges as a valuable tool for anomaly detection, model validation, and forensic analysis.

This webinar explores the evolving role of Benford’s Law in the age of AI, emphasizing how it can be integrated into machine learning workflows as a statistical feature for identifying irregularities and improving model accountability. By embedding digit-based conformity tests into AI pipelines, analysts and developers can enhance the explainability of models and proactively detect data manipulation, bias, or fraud in large-scale systems.

One of the focuses of the session will be the statistical analysis of how Pareto and Weibull distributions, frequently used in economics, risk modeling, and reliability engineering, align with Benford’s expected digit frequencies. We will discuss both the theoretical underpinnings and present empirical evidence to evaluate the extent to which these distributions comply with Benford’s Law and what that means for AI systems trained on such data.

Participants will gain insights into cutting-edge applications, including hybrid AI models that combine traditional statistical methods with deep learning, as well as the use of Benford-based metrics in improving robustness, reducing false positives, and enhancing the interpretability of black-box models.

Whether you are a researcher, auditor, data scientist, or AI practitioner, this webinar will offer a multidisciplinary perspective on how mathematical laws, statistical rigor, and artificial intelligence can work together to build more trustworthy and resilient systems.

Date: 29 September 2025
Time: 12:00 p.m. CEST | 06:00 a.m. EDT
Webinar ID: 865 9326 5734
Website: https://sciforum.net/event/Mathematics-20?subscribe

Register now for free!

After registering, you will receive a confirmation email outlining how to join this webinar. Registrations with academic institutional email addresses will be prioritized.

Unable to attend? Register anyway, and we will let you know when the recording is available to watch.

Webinar Chairs and Keynote Speakers:

• Prof. Dr. Vesna Rajić, Department for Statistics and Mathematics, Faculty of Economics and Business, University of Belgrade, Belgrade, Serbia;
• Dr. Dragan Azdejković, Department of Statistics and Mathematics, University of Belgrade, Faculty of Economics and Business, 11000 Belgrade, Serbia;
• Dr. Jelena Stanojević, Department of Statistics and Mathematics, University of Belgrade, Faculty of Economics and Business, 11000 Belgrade, Serbia;
• Prof. Dr. Tatjana Rakonjac-Antić, Department of Economic Policy and Development, University of Belgrade, Faculty of Economics and Business, Belgrade, Serbia;
• Dr. Dragana Radojičić, Department of Statistics and Mathematics, University of Belgrade, Faculty of Economics and Business, 11000 Belgrade, Serbia.

Relevant Special Issue:

“Statistics and Nonlinear Analysis: Simulation and Computation”
Guest Editor: Prof. Dr. Vesna Rajić
Deadline for manuscript submissions: 30 September 2025

We are pleased to announce the top 10 highly viewed papers in 2023 and 2024 from the “Mathematics and Computer Science” Section of Mathematics (ISSN: 2227-7390), carefully selected for their exceptional quality and relevance. We invite you to read these papers, which represent cutting-edge research combining mathematical reasoning and computing.

1. “A Mathematical Investigation of Hallucination and Creativity in GPT Models”
by Minhyeok Lee
Mathematics 2023, 11(10), 2320; https://doi.org/10.3390/math11102320
Full text available online: https://www.mdpi.com/2227-7390/11/10/2320

2. “It’s All in the Embedding! Fake News Detection Using Document Embeddings”
by Ciprian-Octavian Truică and Elena-Simona Apostol
Mathematics 2023, 11(3), 508; https://doi.org/10.3390/math11030508
Full text available online: https://www.mdpi.com/2227-7390/11/3/508

3. “Review of Quaternion-Based Color Image Processing Methods”
by Chaoyan Huang, Juncheng Li and Guangwei Gao
Mathematics 2023, 11(9), 2056; https://doi.org/10.3390/math11092056
Full text available online: https://www.mdpi.com/2227-7390/11/9/2056

4. “A Mathematical Interpretation of Autoregressive Generative Pre-Trained Transformer and Self-Supervised Learning”
by Minhyeok Lee
Mathematics 2023, 11(11), 2451; https://doi.org/10.3390/math11112451
Full text available online: https://www.mdpi.com/2227-7390/11/11/2451

5. “Review of GrabCut in Image Processing”
by Zhaobin Wang, Yongke Lv, Runliang Wu and Yaonan Zhang
Mathematics 2023, 11(8), 1965; https://doi.org/10.3390/math11081965
Full text available online: https://www.mdpi.com/2227-7390/11/8/1965

6. “Performance Analysis of Long Short-Term Memory Predictive Neural Networks on Time Series Data”
by Roland Bolboacă and Piroska Haller
Mathematics 2023, 11(6), 1432; https://doi.org/10.3390/math11061432
Full text available online: https://www.mdpi.com/2227-7390/11/6/1432

7. “On the Quality of Synthetic Generated Tabular Data”
by Erica Espinosa and Alvaro Figueira
Mathematics 2023, 11(15), 3278; https://doi.org/10.3390/math11153278
Full text available online: https://www.mdpi.com/2227-7390/11/15/3278

8. “C-KAN: A New Approach for Integrating Convolutional Layers with Kolmogorov–Arnold Networks for Time-Series Forecasting”
by Ioannis E. Livieris
Mathematics 2024, 12(19), 3022; https://doi.org/10.3390/math12193022
Full text available online: https://www.mdpi.com/2227-7390/12/19/3022

9. “Quantum Computing in Telecommunication—A Survey”
by Frank Phillipson
Mathematics 2023, 11(15), 3423; https://doi.org/10.3390/math11153423
Full text available online: https://www.mdpi.com/2227-7390/11/15/3423

10. “A Depth-Progressive Initialization Strategy for Quantum Approximate Optimization Algorithm”
by Xinwei Lee, Ningyi Xie, Dongsheng Cai, Yoshiyuki Saito and Nobuyoshi Asai
Mathematics 2023, 11(9), 2176; https://doi.org/10.3390/math11092176
Full text available online: https://www.mdpi.com/2227-7390/11/9/2176

We would like to invite you to attend the 1st International Conference on Modern Mathematical Physics, organized by MDPI’s Modern Mathematical Physics (ISSN: 3024-5034), Symmetry (ISSN: 2073-8994, IF: 2.2) and Mathematics (ISSN: 2227-7390, IF: 2.2 ). This event will take place from 30 October to 3 November 2026 in Hangzhou, China.

Honorary Chair:

• Prof. Dr. Changpu Sun, China Academy of Engineering Physics, Beijing, China.

Executive Chairs:

• Prof. Dr. Haiqing Lin, Zhejiang University, Hangzhou, China;
• Prof. Dr. Xiwen Guan, University of Chinese Academy of Sciences, Wuhan, China;
• Prof. Dr. Murray Batchelor, Australian National University, Canberra, Australia.

The topics of interest:

S1. Quantum Field Theory, String & Brane Theory, and Gravitation;
S2. Condensed Matter Physics and Statistical Physics;
S3. Quantum Information and Quantum metrology;
S4. Atomic, Molecular, and Optical Physics;
S5. Nonlinear Dynamics and Computational Physics.

Important dates:

Deadline for abstract submission: 10 July 2026;
Notification of acceptance: 10 August 2026;
Deadline for Early Bird Registration: 25 August 2026;
Deadline for Covering Author Registration: 31 August 2026.

Guide for Authors:

To submit your abstract, please click on the following link:  https://sciforum.net/user/submission/create/1507.

To register for this event, please visit the following website: https://sciforum.net/event/ICMMP2026?section=#registration.

For details regarding abstract submission, poster submission, and publication opportunities, please refer to the “Instructions for Authors” Section: https://sciforum.net/event/ICMMP2026?section=#instructions.

For any enquiries regarding this event, please contact icmmp2026@mdpi.com.

We look forward to seeing you at the 1st International Conference on Modern Mathematical Physics.

MDPI will be attending the 2025 INFORMS Annual Meeting, which will be held from 26 to 29 October 2025 in Atlanta, GA, USA. 

The Institute for Operations Research and the Management Sciences (INFORMS) is the premier global association for professionals in operations research, analytics, and management science. With a vibrant community of 12,000+ members across more than 50 countries, INFORMS advances the science and practice of decision-making through world-class research, industry-leading journals, and influential conferences. Since its founding in 1995, INFORMS has been a catalyst for innovation, connecting experts across sectors to tackle real-world challenges with analytical insight.

The following open access journals will be represented at this conference:

• Systems;
• BDCC;
• Stats;
• Axioms;
• Logistics;
• ASI;
• Telecom;
• Network;
• World;
• Knowledge;
• Platforms;
• Data;
• Forecasting;
• Information;
• Mathematics.

Subjects:

• Social Sciences & Psychology;
• Business & Economics.

If you are planning to attend this event, please feel free to visit our booth (#418) and speak to our representatives. We look forward to meeting you in person and will assist you with any queries that you may have. 

We are pleased to announce the top 10 highly viewed papers in 2023 and 2024 from the “Operations Research and Fuzzy Decision Making” Section of Mathematics (ISSN: 2227-7390), carefully selected for their exceptional quality and relevance. These papers, which we welcome you to read, represent cutting-edge research in the theory and application of operations research and decision making.

1. “When Fairness Meets Consistency in AHP Pairwise Comparisons”
by Zorica Dodevska, Sandro Radovanović, Andrija Petrović and Boris Delibašić
Mathematics 2023, 11(3), 604; https://doi.org/10.3390/math11030604
Full text available online: https://www.mdpi.com/2227-7390/11/3/604

2. “Assessing Strategies to Overcome Barriers for Drone Usage in Last-Mile Logistics: A Novel Hybrid Fuzzy MCDM Model”
by Snežana Tadić, Mladen Krstić and Ljubica Radovanović
Mathematics 2024, 12(3), 367; https://doi.org/10.3390/math12030367
Full text available online: https://www.mdpi.com/2227-7390/12/3/367

3. “Review of Stochastic Dynamic Vehicle Routing in the Evolving Urban Logistics Environment”
by Nikola Mardešić, Tomislav Erdelić, Tonči Carić and Marko Đurasević
Mathematics 2024, 12(1), 28; https://doi.org/10.3390/math12010028
Full text available online: https://www.mdpi.com/2227-7390/12/1/28

4. “Comparative Sensitivity Analysis of Some Fuzzy AHP Methods”
by Irina Vinogradova-Zinkevič
Mathematics 2023, 11(24), 4984; https://doi.org/10.3390/math11244984
Full text available online: https://www.mdpi.com/2227-7390/11/24/4984

5. “An Enhanced Simulation-Based Multi-Objective Optimization Approach with Knowledge Discovery for Reconfigurable Manufacturing Systems”
by Carlos Alberto Barrera-Diaz, Amir Nourmohammadi, Henrik Smedberg, Tehseen Aslam and Amos H. C. Ng
Mathematics 2023, 11(6), 1527; https://doi.org/10.3390/math11061527
Full text available online: https://www.mdpi.com/2227-7390/11/6/1527

6. “Decision Making in Fuzzy Rough Set Theory”
by Fernando Chacón-Gómez, M. Eugenia Cornejo and Jesús Medina
Mathematics 2023, 11(19), 4187; https://doi.org/10.3390/math11194187
Full text available online: https://www.mdpi.com/2227-7390/11/19/4187

7. “Bilevel Optimal Sizing and Operation Method of Fuel Cell/Battery Hybrid All-Electric Shipboard Microgrid”
by Hao Jin and Xinhang Yang
Mathematics 2023, 11(12), 2728; https://doi.org/10.3390/math11122728
Full text available online: https://www.mdpi.com/2227-7390/11/12/2728

8. “Integrating Fuzzy MCDM Methods and ARDL Approach for Circular Economy Strategy Analysis in Romania”
by Camelia Delcea, Ionuț Nica, Irina Georgescu, Nora Chiriță and Cristian Ciurea
Mathematics 2024, 12(19), 2997; https://doi.org/10.3390/math12192997
Full text available online: https://www.mdpi.com/2227-7390/12/19/2997

9. “Stochastic Configuration Based Fuzzy Inference System with Interpretable Fuzzy Rules and Intelligence Search Process”
by Wei Zhou, Hongxing Li and Menghong Bao
Mathematics 2023, 11(3), 614; https://doi.org/10.3390/math11030614
Full text available online: https://www.mdpi.com/2227-7390/11/3/614

10. “A Fuzzy Multi-Criteria Evaluation System for Share Price Prediction: A Tesla Case Study”
by Simona Hašková, Petr Šuleř and Róbert Kuchár
Mathematics 2023, 11(13), 3033; https://doi.org/10.3390/math11133033
Full text available online: https://www.mdpi.com/2227-7390/11/13/3033

Welcome to our webinar series on Quantum Mechanics and Open Access, organized in recognition of the International Year of Quantum Science and Technology (IYQ 2025).

This year marks a historic milestone—the centenary of the birth of quantum mechanics, a field that has transformed our understanding of the universe and continues to drive innovation across physics, chemistry, computing, and beyond. It is both a moment of reflection on a century of extraordinary breakthroughs and an opportunity to envision the next hundred years of discovery.

Our theme, “Quantum Mechanics and Open Access”, highlights not only the profound scientific achievements of the past but also the vital role that open knowledge plays in shaping the future of research. Open access ensures that discoveries are shared, collaborations are strengthened, and progress in quantum science remains a truly global endeavor.

We are delighted to bring together a distinguished group of speakers, researchers, and practitioners who will share their insights on how open access is transforming the way we communicate, collaborate, and innovate in quantum science.

Thank you for joining us on this exciting journey of science, openness, and collaboration. We look forward to engaging discussions and to collectively imagining the quantum future together.

Date: 25 September at 9:00 a.m. CEST | 3:00 p.m. CST Asia
Webinar ID: 862 8077 3592

Register now for free

After registering, you will receive a confirmation email containing information on how to join the webinar. Registrations with academic and institutional email addresses will be prioritized.

Unable to attend? Register anyway, and we will let you know when the recording is available to watch.

Webinar Keynote Speakers:

• Ivan Arraut, Institute for Data Engineering and Sciences, University of Saint Joseph, Macau;
• Florin Felix Nichita, Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania;
• Dr. Joao Pacheco Bicudo Cabral de Mello, Universidade Cruzeiro do Sul, São Paulo, Brazil.

Prof. Dr. Apala Majumdar is an applied mathematician specializing in the mathematical modelling and analysis of nematic liquid crystals and partially ordered materials, with applications in industry and technology. Her research bridges mathematical modelling, applied analysis, and theoretical physics, focusing on four key themes: (i) the analysis of continuum theories for liquid crystals and soft materials; (ii) multiscale theories that focus on the relationship between microscopic and macroscopic continuum approaches; (iii) non-equilibrium phenomena, e.g., switching processes and transition pathways between metastable states; and (iv) modelling of soft-matter-based applications in industry and technology, with emphasis on geometry- and energy-driven pattern formation. With a strongly interdisciplinary approach, she collaborates with mathematicians (pure, applied, numerical, and industrial), physicists, chemists, and industry partners. Her global network includes researchers in Luxembourg, Austria, Germany, the Czech Republic, China, India, and Mexico, supported by multiple active externally funded projects. Before joining the University of Strathclyde, Professor Majumdar held positions at the Universities of Bristol, Oxford, and Bath. At Bath, she served as Director of the Centre for Nonlinear Mechanics (2018–2019), fostering interdisciplinary applied mathematics, and led a Bath–Chile–Mexico research network that organized multiple international workshops. She is also a Visiting Professor at IIT Bombay in India. Her leadership extends to advisory roles, including membership in the Programme Committee of the International Centre for Mathematical Sciences (Edinburgh), the London Mathematical Society Research Committee, the Glasgow Mathematical Journal Trust, and sectional committees of the Royal Society of Edinburgh. Committed to interdisciplinary applied mathematics, she welcomes inquiries about collaborations, PhD, and postdoctoral opportunities.

The following is a short interview with Prof. Dr. Apala Majumdar:

1. Could you summarize the key mathematical breakthroughs or contributions that led to this award? What excites you most about your current research?
My research focuses on the mathematics of material science, with a focus on the mathematics of liquid crystals. Liquid crystals are classic examples of partially ordered materials. They are more ordered than liquids but less ordered than solids. They have anisotropic, or direction-dependent, physical, optical, and rheological properties. They are also very soft materials and have become the working material of choice for a variety of electro-optic devices, including the display industry. Today, their applications are expanding into healthcare technologies, engineering, biology, smart materials, and energy applications.
The mathematics of liquid crystals is rich because it intersects many different branches of mathematics. At the heart of it are continuum mechanics, nonlinear partial differential equations, calculus of variations, applied analysis, functional analysis, topology, geometry, and scientific computation. It sits at the interface of pure and applied mathematics and is intrinsically interdisciplinary.
In terms of breakthroughs, my collaborators and I were among the first people to develop rigorous mathematical foundations for continuum theories for liquid crystals; in particular, the Landau-de Gennes theory for nematic liquid crystals. We developed benchmark mathematical analytic tools for this theory and rigorously analyzed this theory for physically relevant scenarios. I have also worked on multiscale theories that bridge microscopic and macroscopic models, have worked extensively on multistable liquid crystal systems used in real-life applications, and on mathematical models for new types of materials such as bent-core and ferronematic liquid crystals. More recently, I have also been working on machine learning for liquid crystal applications. It is not one single breakthrough but a sequence of interconnected results that together reveal the big picture for liquid crystals and soft matter.
What excites me most about my current research is the tremendous potential of the field. It brings together mathematics in its abstract and applied forms and connects directly to physics, chemistry, biology, and industry. I am excited by the possibility of using mathematics to design material systems to perform specific functions in an automated and programmed way. I also value the interdisciplinary and global nature of the work, with collaborators in Asia, Europe, Africa, and the Americas, and the inclusiveness of the research community. While doing fundamental research, we are also making a positive impact on society and education, and I find that rewarding.

2. Your work bridges mathematical modeling, applied analysis, and theoretical physics. How do interdisciplinary perspectives shape your approach to problems?
Interdisciplinarity is crucial for liquid crystal research and for applied research in general. Out of about 80 peer-reviewed papers that I have published, 20 are with non-mathematicians. I have worked with theoretical physicists, experimentalists, chemists, geoscientists, and with industry, including Hewlett-Packard and Merck.
Practical collaborators give us problems wherein we can apply mathematical methods and test our theories. These problems provide an excellent test bed to see if the theories are viable and realistic. Interdisciplinarity also motivates the development of new mathematical tools. It creates a two-way feedback loop; mathematics is applied to real problems to explain physical reality, and real-life problems guide the creation of new mathematical theories and tools.
For example, with Prof. Jan Lagerwall’s experimental group in Luxembourg, we have published several papers on liquid crystal shells, which can be used for authentication and security purposes. We combined experiments and mathematical modelling to explain experimental observations and refine our models. With colleagues at IIT Delhi in India, we developed theories for bent-core liquid crystals that model their physical experiments. These collaborations show how interdisciplinarity shapes my approach to problems.

3. What inspired you to pursue mathematics, and were there pivotal moments or mentors who guided your path? As the winner of this award, is there something you want to express or someone you wish to thank most?
Mathematics is the language of the physical sciences and engineering, but it is also abstract with symmetry, patterns, and fundamental concepts. It has deep connections with philosophy. It is logical and often deterministic, with yes or no answers. It is inclusive and can be practiced with few constraints.
I was naturally good at mathematics and found it interesting. As a child, I attended schools in India and multiple schools across the United Kingdom, with broadly supportive teachers. At the University of Bristol, I studied for my undergraduate degree and benefited from good lecturers and a strong syllabus. My most important mentorship came during my PhD, with supervisors Professor Jonathan Robbins, Dr. Maxim Zyskin, and Dr. Chris Newton. Later, at Oxford, I worked in two groups, led by Professor Sir John Ockendon and Professor Sir John Ball, who shaped my career in different ways. I have also had excellent colleagues in my workplace.
My biggest thanks and tremendous gratitude go to my parents, Dr. Swadhin Kumar Majumdar and Mrs. Atreyi Majumdar, who are medical doctors and university academics, and my extended family. They believe in me, my values, and in education and have always supported me as a person.

4. From your perspective, what are the biggest challenges women researchers face in your field? Do you have any advice for aspiring young women researchers looking to make a meaningful impact in their respective fields?
Women researchers face a glass ceiling effect, stereotyping, and workload issues. Dedicated time for research is difficult to secure, and women often have caring responsibilities. There are also issues with visibility, diversity of networks, opportunities for collaboration, and career progression. Work is being done to improve visibility, such as through awards and interviews, but systemic issues remain.
My advice to aspiring young researchers is that if there is a will, there will be a way. People find their way without needing to plan every step. It is also important not to fear failure, because failure often leads to success.

5. What distinctive strengths do women mathematicians bring to academic research, and what strategies would you recommend for leveraging these advantages in career development?
Women mathematicians often demonstrate attention to detail, patience, resilience, teamwork, and the ability to understand alternative points of view. These qualities are crucial for mathematics, where progress depends on detail, focus, and repeatedly revisiting problems. Such qualities help challenge perspectives and contribute to strong research.
To leverage these strengths, young women should seek opportunities, ask questions, and build connections. They should not be self-conscious about mistakes. By making their qualities and strengths more visible, they can progress in their careers and contribute to higher-quality mathematics.

6. Finally, which research topics do you think will be of particular interest to the research community in the coming years?
In the coming years, there will be many applications of artificial intelligence and machine learning to material science. Applied mathematics can play a role by providing rigorous analysis and frameworks for these methods, which are often treated as black boxes. Mathematics can help ensure that machine learning is accurate, efficient, robust, and validated.
This integration has the potential to support the design of smart materials, which connects directly to my area of research. If successful, it will be a crucial development in materials science, the physical sciences, and engineering.

We are pleased to announce the top 10 highly viewed papers in 2023 and 2024 from the “Applied Mathematics” Section of Mathematics (ISSN: 2227-7390), carefully selected for their exceptional quality and relevance. These papers, which we welcome you to read, represent cutting-edge research in areas of applied mathematics.

1. “A Survey on Active Learning: State-of-the-Art, Practical Challenges and Research Directions”
by Alaa Tharwat and Wolfram Schenck
Mathematics 2023, 11(4), 820; https://doi.org/10.3390/math11040820
Full text available online: https://www.mdpi.com/2227-7390/11/4/820

2. “The General Fractional Integrals and Derivatives on a Finite Interval”
by Mohammed Al-Refai and Yuri Luchko
Mathematics 2023, 11(4), 1031; https://doi.org/10.3390/math11041031
Full text available online: https://www.mdpi.com/2227-7390/11/4/1031

3. “Improved Beluga Whale Optimization for Solving the Simulation Optimization Problems with Stochastic Constraints”
by Shih-Cheng Horng and Shieh-Shing Lin
Mathematics 2023, 11(8), 1854; https://doi.org/10.3390/math11081854
Full text available online:  https://www.mdpi.com/2227-7390/11/8/1854

4. “Reducing Uncertainty and Increasing Confidence in Unsupervised Learning”
by Nicholas Christakis and Dimitris Drikakis
Mathematics 2023, 11(14), 3063; https://doi.org/10.3390/math11143063
Full text available online:  https://www.mdpi.com/2227-7390/11/14/3063

5. “Chaos Meets Cryptography: Developing an S-Box Design with the Rössler Attractor”
by Erendira Corona-Bermúdez, Juan Carlos Chimal-Eguía, Uriel Corona-Bermúdez and Mario Eduardo Rivero-Ángeles
Mathematics 2023, 11(22), 4575; https://doi.org/10.3390/math11224575
Full text available online:  https://www.mdpi.com/2227-7390/11/22/4575

6. “Approximation of Bivariate Functions by Generalized Wendland Radial Basis Functions”
by Abdelouahed Kouibia, Pedro González, Miguel Pasadas, Bassim Mustafa, Hossain Oulad Yakhlef and Loubna Omri
Mathematics 2024, 12(16), 2597; https://doi.org/10.3390/math12162597
Full text available online:  https://www.mdpi.com/2227-7390/12/16/2597

7. “Numerical Reconstruction of Time-Dependent Boundary Conditions to 2D Heat Equation on Disjoint Rectangles at Integral Observations”
by Miglena N. Koleva and Lubin G. Vulkov
Mathematics 2024, 12(10), 1499; https://doi.org/10.3390/math12101499
Full text available online: https://www.mdpi.com/2227-7390/12/10/1499

8. “Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations”
by Peng Zhi, Yuching Wu, Cheng Qi, Tao Zhu, Xiao Wu and Hongyu Wu
Mathematics 2023, 11(12), 2723; https://doi.org/10.3390/math11122723
Full text available online: https://www.mdpi.com/2227-7390/11/12/2723

9. “Highly Accurate and Efficient Time Integration Methods with Unconditional Stability and Flexible Numerical Dissipation”
by Yi Ji and Yufeng Xing
Mathematics 2023, 11(3), 593; https://doi.org/10.3390/math11030593
Full text available online: https://www.mdpi.com/2227-7390/11/3/593

10. “Going Next after “A Guide to Special Functions in Fractional Calculus”: A Discussion Survey”
by Virginia Kiryakova and Jordanka Paneva-Konovska
Mathematics 2024, 12(2), 319; https://doi.org/10.3390/math12020319
Full text available online: https://www.mdpi.com/2227-7390/12/2/319

Name: Dr. Christian Budde
Affiliation: University of the Free State, South Africa
Research Interests: evolution equations; operator semigroups; functional analysis

Mathematics (ISSN: 2227-7390) is thrilled to share an interview with one of our 2025 Exceptional Reviewers, Dr. Christian Budde, who is a Senior Lecturer in the Department of Mathematics and Applied Mathematics at the University of the Free State in South Africa.

The following is a short interview with Dr. Christian Budde:

1. Could you introduce your current research direction and provide an update on your progress?
My research lies at the intersection of functional analysis and partial differential equations, with a particular focus on evolution equations, operator semigroups, and applications to large network dynamics. Recently, I have also been developing interdisciplinary projects, reflecting my broader interest in the applicability of mathematics beyond traditional boundaries. At present, much of my work is devoted to advancing the theoretical understanding of evolution equations in complex structures, while also building bridges to applied contexts where these tools can provide real insights.

2. Can you please share with us your sentiments upon winning the award?
I am deeply honored to be selected as an “Exceptional Reviewer”. Peer review is a cornerstone of academic life and an essential element in ensuring the rigor and integrity of our discipline. To have my efforts in this regard acknowledged is both humbling and motivating. It reaffirms for me that the time and care invested in the review process—often invisible to the wider community—are meaningful contributions to the advancement of mathematics.

3. Could you share some insights into your approach to reviewing manuscripts? How do you balance thoroughness with efficiency?
My approach to reviewing is guided by two principles: fairness and clarity. I try to place myself in the position of both the author and the reader. From the author’s perspective, constructive feedback is essential, not only to highlight areas that need improvement but also to recognize the strengths of the work. From the reader’s perspective, I ask whether the manuscript contributes something substantial, is clearly presented, and will be accessible to its intended audience. Balancing thoroughness with efficiency comes down to structured reading: I first develop a broad understanding of the manuscript’s main results and contributions and then proceed carefully through the technical details. This ensures that my review remains both comprehensive and timely.

4. What are the key factors and aspects that you consider most when reviewing a manuscript?
I pay particular attention to mathematical rigor, originality, and clarity of exposition. Rigorous arguments are the foundation of our discipline, and it is crucial that every step withstands scrutiny. Originality is equally important—whether in developing new theory, offering fresh perspectives, or providing applications that open new avenues for exploration. Finally, clarity ensures that these contributions can be appreciated and built upon by the community. A well-written paper not only communicates ideas but also invites collaboration and further research.

5. Based on your experience, which research topics do you think are of particular interest to the research community in the coming years?
I believe that research at the interface of pure and applied mathematics will continue to gain momentum. Topics such as the analysis of large networks, the mathematical modeling of complex systems, and the interplay between abstract operator theory and data-driven applications are areas of growing interest. Additionally, interdisciplinary approaches—where mathematics informs and is informed by other fields—will play an increasingly vital role. For me, this reflects one of the most exciting aspects of mathematics: its ability to provide both deep theoretical insights and powerful tools for understanding the world around us.