Schmid College, Chapman University Courses

The Philosophical Significance of Gödel's Dialectica Translation

Explore Gödel's Dialectica paper and its impact on Hilbert's Program. Analyze the epistemological significance of Gödel's consistency proof for arithmetic and its implications for mathematical foundations.

• YouTube
• 1 hour 44 minutes
• On-Demand
• Free Video

Making AI Systems Trustworthy Through Intuitive Design and Human Interaction

Explore key technical approaches for building trustworthy AI systems, focusing on intuitiveness, interaction, explainability, and human domain knowledge integration for more reliable and transparent artificial intelligence.

• YouTube
• 1 hour 53 minutes
• On-Demand
• Free Video

Interestingness in Mathematics - Exploring AI's Role in Mathematical Discovery

Explore the concept of interestingness in mathematics and its implications for AI-driven mathematical discoveries. Gain insights into defining proxies for mathematical interest using formal proof archives.

• YouTube
• 1 hour 27 minutes
• On-Demand
• Free Video

A Possible Way to Read and Interpret Euclid's Elements

Explore a novel approach to reading Euclid's Elements, focusing on fundamental theorems in Books I and II as a guide to understanding Euclidean geometry and its philosophical implications.

• YouTube
• 2 hours 3 minutes
• On-Demand
• Free Video

The Gödel Translation: History and New Directions

Explore the Gödel translation's history, its impact on intuitionistic and modal logic, and future research directions in this advanced mathematical seminar.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Frege's Definition of Real Numbers is Consistent

Explore Frege's consistent definition of real numbers as ratios of magnitudes. Uncover how slight modifications to his original work could have preserved this groundbreaking mathematical concept.

• YouTube
• 1 hour 50 minutes
• On-Demand
• Free Video

Geometric Inequalities Between Intrinsic and Extrinsic Curvature Invariants

Explore geometric inequalities between intrinsic and extrinsic curvature invariants in Riemannian manifolds, focusing on Nash's Theorem and recent developments in the field.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Formalization of Infinity Category Theory

Explore ∞-category theory's formalization, unifying mathematics, computer science, and physics. Learn synthetic reasoning and the Yoneda Lemma in this advanced mathematical seminar.

• YouTube
• 1 hour 51 minutes
• On-Demand
• Free Video

From Mathematical Object to Philosophy of Culture - Lecture 8

Explore mathematical objects and their cultural significance with Prof. Salanskis. Delve into philosophy of science, culture, and etho-analysis in this thought-provoking seminar series.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

From Mathematical Object to Philosophy of Culture - April 26, 2024

Explore mathematical objects and their relation to philosophy of culture with Prof. Salanskis. Examine truth, presentation, and multiplicity in mathematics, and delve into the intersection of science and cultural philosophy.

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

From Mathematical Object to Philosophy of Culture - April 19, 2024

Explore mathematical objects, their philosophical interpretations, and the role of philosophy of science in cultural analysis with Professor Jean-Michel Salanskis.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

Revised GCH or Would Cantor Have Understood - A Contemporary Perspective on the Continuum Hypothesis

Explore the Continuum Hypothesis and its philosophical implications in set theory. Examine contemporary perspectives on Cantor's famous postulate and its generalized form.

• YouTube
• 1 hour 39 minutes
• On-Demand
• Free Video

Remarks about Cantor's Theorem

Explore Cantor's Theorem and its implications for infinite cardinalities. Examine the historical context, compare proofs, and discover applications to paradoxical mathematical situations.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

From Mathematical Object to Philosophy of Culture - April 12, 2024

Explore mathematical objects, their philosophical interpretations, and the role of philosophy of science in cultural analysis with Professor Salanskis.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

Topology in 1930s America - A Tale of Two Camps

Explore the rivalry between point-set and combinatorial topology camps in 1930s America, examining their approaches, key figures, and impact on the mathematical research community.

• YouTube
• 1 hour 54 minutes
• On-Demand
• Free Video