Introduction
The Foundations of Mathematics Group is a research collective dedicated to investigating the logical, axiomatic, and structural underpinnings of mathematical reasoning. By bridging abstract theoretical inquiry with modern computational paradigms, the group explores core areas including mathematical logic, set theory, proof theory, model theory, and category theory. A central focus of its work involves applying foundational principles to computer-assisted theorem proving and automated deduction systems. Through collaborative research, seminars, and interdisciplinary partnerships across pure mathematics, theoretical computer science, and philosophy, the group strives to refine the rigorous frameworks that govern both human mathematical practice and automated discovery.
Core Focus Areas
Mathematical Logic & Set Theory:
Exploring axiomatic systems, the structure of the mathematical universe, and independence results.
Proof Theory & Type Theory:
Analyzing the nature of formal deduction, constructive logic, and the structural equivalence between proofs and algorithms (Curry-Howard isomorphism).
Model Theory & Category Theory:
Investigating the relationships between formal languages, abstract structures, and universal semantics across mathematical fields.
Formalization & Automated Reasoning:
Applying foundational theory to computer-assisted theorem proving (e.g., Lean, Coq, Isabelle) and automated deduction.
.... and many more
"Mathematics is an activity of the human mind, completely independent of language and the physical world."
L. E. J. Brouwer
Mathematician & Philosopher;
Founder of Mathematical Intuitionism
What Are We Doing?
Theoretical Research & Logical Inquiry
- Independence & Forcing Techniques
- Model-Theoretic Classification
- Constructive & Intuitionistic Foundations
- Descriptive Set Theory
- Proof-Theoretic Ordinals & Consistency Strengths
- Univalent Foundations & Homotopy Type Theory (HoTT)
- Reverse Mathematics
- Logical Frameworks for Non-Well-Founded Structures
Computational Implementation& Formalization
- Formal Library Engineering
- Interactive Proof Assistant Design
- Metamath & Code Translation
- Extracting Programs from Proofs
- AI-Guided Automated Theorem Proving
- Formal Verification of Hardware and Cryptography
Academic & Interdisciplinary Operations
- Mentorship & Talent Pipeline Development
- Philosophical & Foundational Symposia
- Curriculum & Educational Outreach
- Interdisciplinary Industry Partnerships
- Grant Management & Collaborative Initiatives
- Academic Publishing & Editing
.... and many more
Related Publications
Collaborators
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VISION
The Foundations of Mathematics Group envisions a future where the boundary between theoretical logic and modern computational paradigms disappears, unlocking fundamentally new ways to discover, structure, and verify mathematical truth. By advancing the logical, axiomatic, and structural underpinnings of abstract thought—from classical set theory to Homotopy Type Theory—the group aims to establish an unshakeable, universal foundation for human knowledge. Ultimately, the group strives to pioneer a world where machine-verifiable mathematics and automated reasoning work seamlessly alongside human intuition, securing digital knowledge bases for generations to come and expanding our understanding of what can be formally known and computed.
"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."
Bertrand Russell
Logician, Philosopher, and Logician & Philosopher;
Co-author of Principia Mathematica
Related Programs
Venue: IIT Bhubaneswar, Odisha, India
Date: 26 September, 2026
An interdisciplinary symposium exploring special focus onexploring the hidden structures within number theory and their manifestations in the natural and cognitive worlds.
recent event
Symposium on
Foundations of Mathematics & Spirituality
Theme: Set Theory, Infinity and Beyond
Date: September 6, 2025
Venue: NIT Patna, Bihar, India
Distinguished Speakers:
- Prof. Henk Barendregt, Radboud University, Netherlands
- Prof. Pradip K. Jain, NIT Patna, India
- Prof. Manohar Lal Kaushik, IGNOU New Delhi, India
- Prof. Om Prakash, IIT Patna, India
- Prof. Sandeep Kumar, IIT (BHU) Varanasi, India and many more…
visionary
Dr. TD Singh, Founding Director, Bhaktivedanta Institute
Dr. T. D. Singh, as a visionary thinker and scientist, had a vision that the foundations of quantum physics can contribute a lot to deepening our understanding of reality and building bridges between science and spirituality. In pursuit of this vision, Dr. T. D. Singh interacted with dozens of brilliant Quantum Minds, including Prof. Roger Penrose, Prof. Karl Pribram, and many other eminent scholars, fostering a global conversation on the deeper implications of quantum science.
