Areas of Expertise
- Number Theory
- Primality Testing Algorithms
- Prime Factorization of Large Numbers
- Factorization of Mersenne Primes and Fermat Numbers
- Polynomial Identities
- Formal Differentiation in Number Theory
- Fibonacci Numbers and Lucas Numbers
- Diophantine Equations
- Mathematics Education and Pedagogy
- Cinematic Approaches to Online Math Lectures
Education
- PhD in Mathematics
University of Warwick, England
Funded by the Engineering and Physical Sciences Research Council (UK) and the Marie Curie Fellowship.
Research Focus: Applications of Andrew Wiles' Proof of Fermat’s Last Theorem in Number Theory.
Biography
Dr. Moustafa Ibrahim is deeply interested in developing new methods for the factorization and primality testing of Mersenne primes and Fermat numbers. Recently, he introduced the orbit notion to both the Fibonacci sequence and Mersenne primes, a concept he presented in a contributed talk at the International Conference of Fibonacci Numbers in Los Angeles, California, in July 2024.
Dr. Ibrahim holds a PhD in Mathematics from the University of Warwick, England, funded by the Engineering and Physical Sciences Research Council (UK) and the Marie Curie Fellowship. His doctoral research focused on certain applications of Andrew Wiles' proof of Fermat’s Last Theorem, exploring new ways to apply this groundbreaking result in number theory.
Dr. Ibrahim’s academic journey has earned him recognition, including his inclusion in the official Number Theory Genealogy published by the University of Warwick, which traces his academic lineage back to prominent figures like Marin Mersenne and Isaac Newton. This honor reflects his deep connection to the long history of mathematical research.
In his over six years of experience as an Assistant Professor, Dr. Ibrahim has taught and coordinated a variety of courses, including Calculus I, II, III, Statistics and Probability, Group Theory, Number Theory, Commutative Algebra, Linear Algebra, and more.
After completing his PhD, Dr. Ibrahim participated in the European Research Project GTEM on number theory, a collaborative effort with a £2.3 million budget. During this time, he developed a new classical approach to formal differentiation, which he applied to the study of Fibonacci and Lucas numbers. His discovery of the Fibonacci-Lucas expansion and his parametric solutions to a quintic Diophantine equation were published in The Ramanujan Journal in a paper titled “A New Approach to Polynomial Identities.” He was also the first Egyptian to publish in this prestigious journal by Springer.
Dr. Ibrahim's commitment to research has been supported by several grants, including a full grant from the Isaac Newton Institute at the University of Cambridge and a grant from the Pacific Institute of Canada in Vancouver. He has also given invited lectures at institutions such as the Graduate Research Center of New York (CUNY) and the University of Illinois, sharing his insights into number theory with a broader academic community.
In addition to his research, Dr. Ibrahim has contributed significantly to education, serving as a math supervisor for first-year students and as a tutor for the Algebraic Number Theory course at the University of Warwick. His research interests continue to focus on number theory, particularly in areas such as primality testing algorithms, prime factorization of large numbers, factorizations of Mersenne and Fermat numbers, and the development of new polynomial identities. He remains deeply engaged in advancing techniques for factoring polynomials in multiple variables and exploring the 3x+1 conjecture.
Most recently, Dr. Ibrahim delivered a talk on Mersenne primes and number theory at Louisiana State University, at a conference supported by the National Security Agency (NSA). He has also demonstrated his dedication to educational innovation by developing a cinematic approach to delivering online math lectures, which he presented at the American University of Bahrain. This approach seeks to enhance student engagement and improve the overall learning experience in digital environments.
Achievements
- Marie Curie Fellowship
Awarded for doctoral research in Mathematics at the University of Warwick, England.
- Engineering and Physical Sciences Research Council (EPSRC) Grant
Received funding for PhD research under this prestigious UK council.
- First Egyptian to Publish in The Ramanujan Journal by Springer
Recognition for pioneering research in polynomial identities and number theory.
Affiliations
- University of Warwick, England
PhD in Mathematics, Department of Mathematics
- European Research Project GTEM on Number Theory
Researcher on a £2.3 million project focused on number theory
- Louisiana State University
Speaker at a conference supported by the National Security Agency (NSA)
- American University of Bahrain
Speaker and presenter on educational innovation
- Graduate Research Center of New York (CUNY)
Invited lecture
- University of Illinois
Invited lecture
- Isaac Newton Institute, University of Cambridge
Recipient of a full grant for research and Junior Member
- Pacific Institute of Canada, Vancouver
Recipient of a research grant
Grants & Contracts Awarded
- Marie Curie Fellowship
Awarded for doctoral research in Mathematics at the University of Warwick, England.
- Engineering and Physical Sciences Research Council (EPSRC) Grant
Received funding for PhD research under this prestigious UK council.
- Full Grant from the Isaac Newton Institute, University of Cambridge
Awarded for research work at the Isaac Newton Institute.
- Grant from the Pacific Institute of Canada, Vancouver
Awarded for research work in Vancouver.
Publications & Presentations
- Moustafa Ibrahim. (2024). ""Generalizing the Eight Levels Theorem: A Journey to Mersenne Prime Discoveries and New Polynomial Classes.""
Arab Journal of Basic and Applied Sciences 31:1, pages 32-52.
- Ibrahim, M. (2023). ""On the Eight Levels Theorem and Applications Towards Lucas-Lehmer Primality Test for Mersenne Primes, I.""
Arab Journal of Basic and Applied Sciences, 30(1), 267–284. https://doi.org/10.1080/25765299.2023.2204672.
- ""A New Approach to Polynomial Identities.""
Published in The Ramanujan Journal, Springer. This paper introduced the Fibonacci-Lucas expansion and new parametric solutions to a quintic Diophantine equation.
- Contributed talk: ""Orbit Notion and Applications to Fibonacci Numbers and Mersenne Primes.""
Presented at the International Conference of Fibonacci Numbers, Los Angeles, California, July 2024.
- Presentation on ""Mersenne Primes and Number Theory.""
Delivered at Louisiana State University, at a conference supported by the National Security Agency (NSA).
- ""Cinematic Approach for Online Math Lectures.""
Presented at the American University of Bahrain, focusing on educational innovation for online learning environments.
- Invited Lectures at the Graduate Research Center of New York (CUNY) and the University of Illinois.
Delivered talks on various topics in number theory.
