What happens to "knots" in 4D Space? Mathematics professor in Sydney revealed a mind-bending answer

Mathematicians say knots cannot exist in four-dimensional space. (Image: Canva)

• Knots cannot exist in four-dimensional space, say mathematicians.
• In 4D, any knot can be untied without cutting the rope.
• Knot theory aids in visualizing higher-dimensional knots.

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Knots are everywhere in everyday life. From shoelaces and headphones to ropes used in climbing or sailing. But what would happen if a rope existed in four-dimensional space instead of the three dimensions we live in?

According to mathematicians, the answer is surprising. The true knots would not exist at all in four dimensions. The extra dimension would allow any knot to be undone easily. The idea comes from a field of mathematics called Knot Theory, which studies how loops and strings can twist and entangle in space.

Who Is Behind This Study?

Zsuzsanna Dancso is an Associate Professor of Mathematics at the University of Sydney. She works in quantum topology, a field studying knots and their properties in three- and four-dimensional spaces. Her research explores how knots behave mathematically and how they connect with quantum algebra and theoretical physics.

Existence of 3D Knots

In the three-dimensional world, a rope can loop around itself and become trapped. Once the strands cross and tighten, the rope cannot move through itself to escape the knot. This restriction is what allows knots to exist in the first place.

Mathematicians study these tangled loops by imagining a closed piece of string, essentially a circle that can twist and turn in space. If that loop becomes entangled in a way that cannot be undone without cutting it, it forms a mathematical knot.

What Is Knot Theory?

Knot Theory is a branch of mathematics that studies how loops and strings can be twisted and tangled in space.

Unlike everyday knots, the ends are joined to form a closed loop, and mathematicians analyse how these loops can be arranged without cutting them.

What Changes in Four-Dimensional Space?

Things become very different in a universe with four spatial dimensions. In such a space, a rope would gain an extra direction in which it could move.

This additional freedom means a strand of rope could simply move into the fourth dimension, pass around another strand and return.

From three-dimensional perspective, it would look as though the rope had passed straight through itself. Because of this, any knot tied in a rope could always be untangled without cutting it.

How Do Scientists See a 4-Dimensional Knot?

Scientists rely on mathematical models and projections to understand objects in four dimensions. Just as a 3D object can cast a 2D shadow, a 4D knot can be represented as a 3D projection, helping mathematicians visualise its structure.

So, Is a 4D Knot Possible or Not?

In pure mathematics, knots can exist in four dimensions. In fact, some knots that are impossible to untangle in 3D can be smoothly undone in 4D space.

While humans cannot physically see the fourth dimension, mathematics allows scientists to describe and study such structures.