Paradox Festival

In this presentation of Berry's Paradox, we take a more general approach towards how we see and solve such paradoxes. We see how, these kinds of self-referential paradoxes arise in certain language domains only, and the reason behind them doing so.

Presented by Hridam Majumder and Sirjan Hansda

The Cramer-Euler paradox is a mathematical paradox found within the realm of differential geometry. It presents a situation where the number of intersections between two curves of higher order in the plane can exceed the number of arbitrary points typically required to define one of those curves.
This paradox arises due to a misunderstanding or misapplication of two fundamental theorems: Bézout's theorem and Cramer's theorem. By properly considering the constraints and conditions involved, the paradox can be resolved, and the expected number of intersections between curves can be determined accurately.

Presented by Varivashya Poladi, Anishka Vaitla and Sannidhi V. Hebbar

Gödel's theorem of incompleteness revolutionized our understanding of the foundation of mathematics, shook its limits of concreteness, and shattered the dreams of complete and consistent proof.
So, what is it? Was it a bunch of hefty equations, axioms, theorems, and bulky Greek symbols compiled into one blob of mathematical tragedy? No.
In fact, its simplicity is a derision of the fragility of mathematics.
1 Line. 4 words. At the core of what broke mathematics.
“This statement is False.”

Presented by Anushka Dassi and Pinakin Choudhary

Addiction to gambling is a paradoxical dance between fleeting wins and inevitable losses. In this presentation, we'll delve into this perplexing phenomenon, exploring why gamblers always feel the urge to play "just one more" despite the odds stacking against them. We'll also reveal how a touch of math can transform seemingly unfavorable situations, shedding light on not only gambling but also real-world scenarios like investments.

Presented by Sahil Chaudhary and Mrigank Pawagi

Prepare to have your perception of language and logic turned on its head as you join us on a mind-twisting journey into the fascinating realm of the Grelling Nelson Paradox. In this thought-provoking video, we explore a paradoxical conundrum that delves into the intricate relationship between words, meaning, and self-reference. Have you ever come across words that describe themselves? Words like "autological" and "heterological" that either apply to themselves or don't? In this video, we'll unravel the complexities as we dive into philosophical and linguistic foundations.

Presented by Naman Mishra and Indrayudh Das

The Banach Tarski Paradox was proposed by Stefan Banach and Alfred Tarski, is all about creating two identical objects from one (without cheating!) by using math! It’s all about creating “something from nothing”. Believe it or not, it can help you create a Sun using a pea, knife, and a lot of math.
The paradox questions, “Can a ball be decomposed into a finite number of point sets and reassembled into two balls identical to the original?”, and even proves it in affirmation. The proof involves concepts of bijections, set theory, and free groups.
It's powerful enough to give a reason to discard the axiom of Choice, a foundation of modern math!
This paradox is a forceful illustration of the counter-intuitive nature of sets and how things don't remain valid in the domain of infinity.

Presented by Armaan Khetarpaul

In this thought-provoking video, we explore the mind-boggling world of a shape with infinite surface area but finite volume. Join us on an intellectual journey as we delve into the enigmatic paradox known as Gabriel's Horn. Imagine a trumpet-shaped object, also referred to as the Devil's Horn, with a finite length but an infinitely expanding curve. How can this be? How can a shape have an infinite surface area, yet contain a finite amount of space? Join us as we unravel the mathematical intricacies and philosophical implications.

Presented by Sanidhya Kaushik, Arnav Bhatt and Ayush Raina

We give you a special lemon (possibly larger and any object you could think of) and chop it into pieces in a weird way, only to group them into two parts which we move around and magically obtain two lemons back at the chopping board.

Presented by Maitreya Bhaduri and Ishaq Hamza

Prepare to be captivated as you join us to explore the enigmatic world of the Unexpected Hanging Paradox. In this thought-provoking video, we embark on a journey into the depths of logic and unravel the mysteries of a paradoxical situation that challenges our understanding of truth and anticipation. Picture a prisoner on death row, facing an execution that will surprise even the keenest of minds. How can a seemingly certain outcome turn into an unexpected twist? In this video, we'll unravel the complexities of as we explore its philosophical and logical foundations.

Presented by R.K. Shishir and Aditya Gupta