Mathematics in the Age of AI and the 4 Generation University

Mathematics in the Age of AI and the 4th Generation
University Celebration of the π-Day 2025: ”Mathematics, Art, and Creativity” Khemis-Miliana University, March 11, 2025 Prof. Mohammed Hachama, hachamam@gmail.com National Higher School of Mathematics, Algerian Society of Industrial and Applied Mathematics, hachama.github.io/home

Outline What is Mathematics? The rise of Artificial Intelligence Recent
breakthrough mathematical applications The Fourth Generation University Conclusion Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 2/23

AI and Mathematics AI = Teach computers to ”think” like
humans Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 3/23

humans y = f (x, P), L = (ytrue − ypredicted )2. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 3/23

humans Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 3/23

humans Very complex optimization problem + data management! Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 3/23

What is Mathematics? What is Mathematics? • Study of numbers,
quantities, shapes, structures, and their relationships • Abstraction • Formal language + logical reasoning • Art + Science • Precise tools for understanding reality • Art and Creativity: Inspiring beauty and creativity • Simplicity, Elegance, Conciseness, Symmetry, Unexpected relationships, Infinity, Intrigue. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 5/23

What is Mathematics? Key goals of Mathematics • Understanding/Description •
comprehend patterns, structures, and relationships. • Application/Calculus • solve real-world problems in science, engineering, and finance. • Optimization • find the most efficient solutions. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 5/23

What is Mathematics? Key applications of Mathematics • Engineering •
Designing structures, machines, and systems • Finance • Managing investments, risk, and economic models • Cryptography • Securing communication and data • Physics • Modeling natural laws and physical phenomena • Artificial Intelligence • Powering machine learning and data-driven decision-making Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 5/23

Rise of Artificial Intelligence AI, the revolution! • AI =
Simulation of human intelligence processes by machines, especially computer systems. • Growth in recent years • Data availability. • Increased computing power. • Development of efficient mathematical models and algorithms, machine learning, and deep learning capabilities. . • Key applications: healthcare, finance, manufacturing, and autonomous systems. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 7/23

Mathematical Foundations of AI Mathematics for AI • Linear Algebra:
Vector spaces and matrix operations. • Calculus and Optimization: rate of change in learning algorithms. Training AI models via optimization. • Probability and Statistics: making predictions and decisions under uncertainty. Statistical learning. • Logic and Set Theory: Formal reasoning, symbolic AI. • Differential Equations: Modeling in physics-informed AI. Breakthrough Results led to the success of Deep Learning and models like ChatGPT. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 8/23

Mathematical Foundations of AI Mathematical Formulation y = f (x,
P), L = (ytrue − ypredicted )2. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 8/23

Mathematical Foundations of AI Theorem (Universal Approximation Theorem) For any
continuous function f : Rn → R defined on a compact subset K ⊂ Rn and for every ϵ > 0, there exists a feedforward neural network function N such that: ∀x ∈ K : |f (x) − N(x)|< ϵ. A NN with can approximate any continuous function. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 8/23

How Mathematics Revolutionized AI Attention and transformers • Traditional AI
models (RNNs and LSTMs): processed words sequentially, making them slow and inefficient. • In 2017: Google introduced the Transformer, which processes entire sentences at once. • Self-Attention Mechanism: Determines how words relate to each other. Advanced optimization algorithms (such as Adam) + Parallel Computation speed up processing dramatically and made deep learning scalable. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 9/23

How Mathematics Revolutionized AI The Age of Large Language Models
• GPT-4, ChatGPT, and BERT are all based on Transformers. • Chatbots and Assistants: ChatGPT, Google Bard, Alexa. • Translation: Google Translate uses Transformer-based BERT models. • Search Engines: Google Search ranks pages using BERT. • Medical AI: AI-powered diagnosis and research assistants. • Education and Research • Use of LLM • The role of universities in AI-driven transformation Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 9/23

Recent breakthrough applications Five Innovations 1. Protein Folding: Nobel Prize
in Chemistry 2024! 2. First Black Holes images 2019. 3. Cybersecurity: Quantum computers threatening cryptography. 4. Physics-Informed Neural Networks for Weather Forecasting 5. Diffusion Models: A Generative AI Revolution Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 11/23

Computational Biology Protein Folding: Nobel Prize in Chemistry 2024! •
AlphaFold: Maths + AI to predict 3d shapes of Proteins • Google DeepMind + European Bioinformatics Institute Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 12/23

Computational Biology Protein Folding: From 2D sequences to 3D structures
• Proteins are fundamental biological molecules. • The function of a protein depends on its 3D shape. • AlphaFold = predicts protein 3D structures from amino-acid sequences using advanced mathematical models. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 12/23

Computational Biology Mathematics in Protein Folding • Graph Theory: Representing
protein structures. • Neural Networks: Predicting amino acid interactions. • Optimization: Finding the lowest-energy conformation. • Before AlphaFold: • Determining a single protein structure took years. • Required expensive laboratory experiments. • After AlphaFold: • Can predict millions of protein structures in minutes. • Accuracy comparable to lab experiments. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 12/23

Computational Biology Revolutionizing Biotechnology and Medicine • Drug Discovery (COVID-19,
cancer treatments). • Understanding Genetic Diseases (Alzheimer’s, Parkinson’s). • Synthetic Biology (designing new proteins). • Open database of 200M+ structures (vs. 180k experimentally solved pre-2020). Changing medicine, biotech, and chemistry forever! Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 12/23

Mathematics and Black Holes First Image of a Black Hole!
• Black holes are invisible, but we can observe their shadow by collecting radio signals. • 2019: This was possible due to mathematics, physics, and AI! Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 13/23

Mathematics and Black Holes Black hole imaging = A mathematical
problem! • 2019: First image of M87, 55 million light-years away. • 2022: Second image of Sagittarius A, the black hole at the center of our Milky Way (27,000 light-years away). • The imaging process • General Relativity: Einstein’s equations describe black holes. • Fourier Transform: Converts telescope signals into an image. • Inverse Problem Solving: Reconstructs missing data. • Machine Learning: Enhances image clarity. Mathematics continues to push the frontiers of space exploration! Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 13/23

Mathematics for Cybersecurity Cryptography • Secure banking, military, financial, internet
communications, WhatsApp encryption, Bitcoin, ... • Without cryptography, digital transactions wouldn’t be safe. • RSA and ECC encryption rely on number theory • Factorizing of a number into two prime numbers is hard: N = 15, Factors: 3 × 5 • For a 617-digit number, ”classical” computers take billions of years to factorize. • → RSA works (relies on hard mathematical problems)! Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 14/23

Mathematics for Cybersecurity The Quantum Threat to Cryptography • Quantum
computers can break RSA using Shor’s Algorithm. • Quantum computers use the Quantum Fourier Transform: |x⟩ → 1 √ N N−1 k=0 e2πixk/N|k⟩ • The world (Governments and industries) is now racing toward post-quantum cryptography. Mathematics is shaping the future of digital security! Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 14/23

Physics-Informed Neural Networks (PINNs) The Challenge of Weather Forecasting •
Weather forecasting relies on solving Partial Differential Equations (PDEs) that describe atmospheric dynamics. ∂u ∂t + u ∂u ∂x = − 1 ρ ∂p ∂x + ν ∂2u ∂x2 (1) ∂T ∂t + u ∂T ∂x = κ ∂2T ∂x2 (2) • Traditional Numerical Weather Prediction (NWP) models • High computational resources. • Long simulation times. • Large amounts of observational data. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 15/23

Physics-Informed Neural Networks (PINNs) Physics-Informed Neural Networks (PINNs) • Traditional
neural networks rely only on data. • PINNs incorporate physical laws (PDEs) into the learning process → predictions remain physically consistent even in regions with limited data. • Mathematical Formulation: a combined loss function: L(θ) = Ldata (θ) + λLPDE (θ) • PINNs learn the solution of PDEs directly from sparse or noisy data. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 15/23

Physics-Informed Neural Networks (PINNs) How PINNs Improve Weather Forecasting •
Faster Predictions (in seconds instead of hours). • Real-time decision-making: agriculture, transportation, and energy. • Less Data Dependency: Can predict in regions with sparse measurements. • Personalized Weather Forecasting: AI-driven hyper-local predictions for cities and industries. • Energy Efficient: Uses a fraction of computational resources. Revolutionizing numerical modeling in other scientific fields. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 15/23

Physics-Informed Neural Networks (PINNs) Recent Applications of PINNs in Weather
Prediction • FourCastNet (2023): global weather forecasting. • generates a week long forecast in less than 2 seconds • 1000x Faster than traditional numerical models Faster and more reliable hurricane warnings, saving lives and reducing economic damage. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 15/23

Diffusion Models: A Generative AI Revolution Generative AI: A Landscape
Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 16/23

• Generative Adversarial Networks (GANs) • Generating realistic images but with some artifacts. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 16/23

• Variational Autoencoders (VAEs) • Tend to produce blurry images. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 16/23

• Variational Autoencoders (VAEs) • Tend to produce blurry images. The need for a robust and high-quality generative model. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 16/23

Diffusion Models: A Generative AI Revolution The Innovation: Diffusion Models
• Formulate image generation as a reverse diffusion process. • Forward SDE: dxt = − 1 2 β(t)xtdt + β(t)dWt • Reverse SDE (learned via score matching): dxt = − 1 2 β(t)xt − β(t)sθ (xt, t) dt + β(t)d ˜ Wt • Generate Data for the ANN. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 16/23

Diffusion Models: A Generative AI Revolution Advantages of Diffusion Models
• High-quality image generation • avoidance of GANs and VAEs artifacts • Text-to-image synthesis. • Training Data: 10x fewer samples than GANs. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 16/23

Diffusion Models: A Generative AI Revolution Faculty of Science and
Technology of Khemis-Miliana Univ. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 16/23

University four generations Evolution of University Generations • First Generation:
Medieval universities focused on teaching established knowledge. • Second Generation: integrating research alongside teaching. • Third Generation: Entrepreneurial universities integrating innovation and market needs. • Fourth Generation: actively shape their socio-economic environments, emphasizing co-creation and sustainable development. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 18/23

University 4.0 Human revolutions • Agricultural Revolution (10,000 BCE): Transition
of humans from a nomadic hunter-gatherer lifestyle to a more settled lifestyle based on agriculture and animal husbandry. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 19/23

University 4.0 Human revolutions Mathematics in the Age of AI
and the 4th Generation University M. Hachama (hachamam@gmail.com) 19/23

University 4.0 University 4.0/Industry 4.0 Mathematics in the Age of
AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 19/23

Fourth Generation University (4GU) Key Characteristics of 4GU 1. Digital
Transformation and Smart Campuses 2. Innovation and Entrepreneurship-driven, and societal Impact 3. Internationalization, global Networks and sustainable development Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 20/23

Fourth Generation University (4GU) 1. Digital Transformation and Smart Campuses
• Digitalization, AI, Big Data, IoT, and Blockchain. • Blended and personalized learning: AI, virtual labs, and online platforms. • Problem-based learning across multiple disciplines. • Automated university services for student experience improvement. • Smart campuses with digital infrastructure. • Management Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 20/23

Fourth Generation University (4GU) 2. Innovation and Entrepreneurship • Encourages
technology transfer and startups. • Universities act as incubators and accelerators. • Universities as solution hubs for global issues. • Community-driven research and social engagement. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 20/23

Fourth Generation University (4GU) 3. Internat., global Networks and sustainable
development • Global collaboration with top universities, research centers, and industries. • Exchange programs and dual degrees to promote international student mobility. • Multilingual education and cross-border learning platforms. • Participation in international research projects on global challenges. • Commitment to the UN Sustainable Development Goals. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 20/23

Mathematics in the 4GU Mathematics: The Backbone of Innovation •
Shifts in curriculum • Incorporation of AI into mathematics courses. • Emphasis on computational thinking and problem-solving skills. • New teaching methods • Use of AI for personalized learning experiences. • Integration of virtual environments for collaborative projects. • Modeling, Simulation, VR and AR. • Interdisciplinary Applications • Supporting advancements in science, engineering, economics, and beyond. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 21/23

Conclusion and perspectives • Mathematics remains the backbone of Science
and Technology advancements, especially in AI and Data Sciences. • Universities must integrate mathematical rigor with AI applications. • Future research should balance theoretical and applied approaches. • Anticipate further integration of mathematics and AI in educational practices. • Collaborative research opportunities between educational institutions and tech companies. Mathematics in the Age of AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 23/23

Conclusion and perspectives Thank you! Mathematics in the Age of
AI and the 4th Generation University M. Hachama (hachamam@gmail.com) 23/23

Mathematics in the Age of AI and the 4 Generati...

Mathematics in the Age of AI and the 4 Generation University

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