Notable Phd  theses summary page of Faiz ul haque zeya

1.Albert Einstein 's phd thesis.

   " A new determination of molecular dimension". A note about it.

Albert Einstein's PhD thesis was titled "Eine neue Bestimmung der Moleküldimensionen", which translates to "A New Determination of Molecular Dimensions". He submitted it to the University of Zurich in 1905. The thesis focused on methods for calculating the size of molecules, particularly through the analysis of diffusion and viscosity, laying the groundwork for his later groundbreaking work in theoretical physics.

2.Kurt Godel 's phd thesis.

   " On the completeness of first order logic"

Kurt Gödel's PhD thesis, completed in 1929 at the University of Vienna, was titled:

"Über die Vollständigkeit des Logikkalküls", translated into English as "On the Completeness of the Calculus of Logic."

Summary of Gödel's PhD Thesis:

In his dissertation, Gödel proved the completeness theorem for first-order predicate logic, demonstrating that every logically valid statement can be derived (or formally proven) from the axioms using standard inference rules. Specifically, he showed that if a statement is logically true (valid in every interpretation or model), there must exist a formal proof for it.

Importance:

• Gödel’s Completeness Theorem provided a fundamental assurance: that first-order predicate logic is both sound and complete—any logically valid conclusion can, in principle, be proven within the system.
• Interestingly, Gödel’s later famous Incompleteness Theorems (1931) did not contradict his earlier Completeness Theorem. Instead, they showed fundamental limitations for arithmetic and more powerful formal systems, clarifying that completeness applies specifically to first-order predicate logic itself, not to arithmetic or higher-order logic systems.

Thus, Gödel's doctoral work established crucial foundations for mathematical logic, while his later incompleteness results highlighted subtle and profound limitations in stronger formal systems.

3. John Von Neumann 's phd thesis.

John von Neumann's PhD thesis was titled:

"Az általános halmazelmélet axiomatikus felépítése", translated into English as "The Axiomatic Foundations of General Set Theory."

He completed this dissertation in 1925 at the University of Budapest (now Eötvös Loránd University).

Summary of von Neumann's Thesis:

In his doctoral dissertation, von Neumann developed an axiomatic approach to set theory, presenting an alternative axiomatization that aimed to resolve logical contradictions present in earlier formulations (such as Russell's paradox). His axiomatic system helped clarify the foundations of mathematics and set theory, addressing issues related to self-reference and class membership.

Importance:

• Von Neumann’s thesis introduced concepts now fundamental to modern mathematics, particularly "classes", distinct from "sets", providing a foundation for distinguishing between collections that can be members of other sets and those too large to be members (proper classes).
• It laid groundwork crucial for later developments in logic, mathematics, and theoretical computer science.

This work positioned von Neumann among the early pioneers who rigorously formalized mathematics, paving the way for significant contributions he later made in numerous fields, including game theory, quantum mechanics, and computing.

4. Alan Mathison Turing 's  phd thesis

Alan Turing's PhD thesis was titled "Systems of Logic Based on Ordinals," submitted in 1938 at Princeton University under the supervision of Alonzo Church.

Summary of Turing's Thesis:

In this dissertation, Turing explored extensions of formal logic using ordinal numbers to address fundamental limitations in mathematical systems, specifically focusing on the relationship between logic and mathematics. Turing aimed to overcome Gödel’s incompleteness results by introducing the concept of ordinal logics, which are logical systems constructed using transfinite ordinals to systematically strengthen existing formal systems.

Key Contributions and Insights:

• Ordinal Logic:
  Turing proposed that by iteratively extending logical systems through increasingly powerful rules—indexed by ordinal numbers—it might be possible to systematically resolve certain undecidable statements.

• Limits of Mathematical Proof:
  Although ordinal logic did not solve Gödel’s incompleteness problem outright, it provided a framework for understanding how logical systems could evolve into ever-more powerful forms, explicitly recognizing the inherent limitations of formal methods.

• Influence on Computability and Complexity:
  This work deepened the understanding of the structure of logical systems, influencing subsequent research in computability theory and complexity, and providing insights relevant to theoretical computer science.

Impact and Legacy:

Turing’s thesis is considered a foundational work in logic, particularly in advancing the understanding of the relationships between logic, computation, and mathematical proof. It exemplifies Turing's innovative approach toward foundational problems, demonstrating his early insights into the nature of computation, logic, and complexity.

5. John Nash (1950, Princeton University)

Title: "Non-Cooperative Games"

• Significance: Nash introduced the concept of the "Nash Equilibrium," revolutionizing game theory. His thesis established a method for predicting outcomes in strategic interactions where players make independent, non-cooperative decisions, fundamentally influencing economics, politics, biology, and computer science. Nash won the Nobel Prize in Economics in 1994 for this groundbreaking work.

6. Paul Samuelson (1941, Harvard University)

Title: "Foundations of Economic Analysis"

• Significance: Samuelson’s thesis transformed economics by introducing rigorous mathematical methods into economic theory. It formalized economics as a precise scientific discipline, employing advanced mathematical tools to analyze economic behavior and equilibrium. His work laid the foundation for modern economic analysis, earning Samuelson

  Here are five notable PhD theses in Artificial Intelligence that significantly impacted the development of the field:

7. Marvin Minsky (1954, Princeton University)

• Title: "Theory of Neural-Analog Reinforcement Systems and Its Application to the Brain-Model Problem"

• Contribution: One of the earliest attempts to model human cognition using neural networks, laying groundwork for AI research and connectionist approaches.

8. John McCarthy (1951, Princeton University)

Title: "Projection Operators and Partial Differential Equations"

• Contribution: While McCarthy's thesis was mathematical, his later pioneering contributions, including coining "Artificial Intelligence," creating LISP programming language, and proposing logical approaches to AI, were fundamental to shaping the field.

9. Geoffrey Hinton (1978, University of Edinburgh)

Title: "Relaxation and its Role in Vision"

• Contribution: Hinton's thesis introduced foundational ideas for neural network learning and vision modeling. He later became a pioneer of deep learning, significantly shaping neural network research and modern AI.

10. Yann LeCun (1987, Université Pierre et Marie Curie, Paris)

Title: "Modèles connexionnistes de l'apprentissage" (Connectionist models of learning)

• Contribution: LeCun’s thesis introduced early convolutional neural networks (CNNs), demonstrating their capability in recognizing handwritten digits, laying groundwork for modern image recognition and deep learning applications.

11. Andrew Ng (2003, University of California, Berkeley)

Title: "Shaping and Policy Search in Reinforcement Learning"

• Contribution: Andrew Ng advanced reinforcement learning techniques, influencing robotic learning and autonomous decision-making. His work contributed significantly to machine learning applications and helped popularize deep learning.

• These theses represent pivotal contributions that shaped AI's evolution, significantly influencing neural networks, machine learning methods, deep learning, and computational cognition.

  the Nobel Prize in Economics in 1970.

These two dissertations dramatically reshaped economics, influencing theory, methodology, and practical policymaking for decades.