024 025 It is evident that quantum computing poses a threat to cybersecurity. Quantum computers are advancing exponentially and in a few decades, quantum computers that are able to run Shor’s Algorithm will be a thing of reality. Robust and secure transitions to safer options like the QSC will take a lot of time to plan and implement. Proactive efforts in developing quantum-resistant cryptography and secure communication protocols are essential to mitigate potential threats and ensure the security of sensitive information in the quantum era. How to tie your laces Alex Barnes I’m sure – or I would hope – anyone reading this article is comfortable in their ability to tie their shoelaces. After pulling yourself up against the weight of the morning, tidying your hair from its scruffy state, wrenching your jumper over your torso, tidying your hair again, and forcing your already late homework into your schoolbag, tying your own shoelaces should hold the minimum of your worries on a school morning. But, however unbelievable, the very nature of this task holds great significance in the workings of chemotherapy, the development of new materials and upholds decades of the history of mathematics. This is Knot Theory. An Introduction to Knot Theory A brief History In the late 1800s, most scientists believed in the theory of ether, a mysterious substance thought to entangle all matter. Lord Kelvin proposed that every element should take a unique and singular form based on how the element knotted up the surrounding ether, beginning the study of mathematical knots all over the world. He declared that atoms must be made of ‘vortex rings of ether’. However, this theory was quickly disproven by the atomic revolution, and mathematicians were left with what seemed like a completely useless branch of topology. Nevertheless, Knot Theory is finally starting to appear in modern science, and uses of it are being developed in areas such as materials science and chemotherapy. What is a mathematical Knot? A knot is a simple closed curve in a 3-dimensional space. When studying knots, mathematicians found them difficult to tease and manipulate without falling apart. To address this problem, both ends of the rope were attached, allowing free altercation of knots without them fundamentally changing. The simplest of all knots is called the Unknot, which in its reduced form, has zero crossings – and therefore is the only ‘0-crossing knot’. This knot was discovered by Peter Guthrie Tait, alongside one 3-crossing knot (Trefoil), one 4-crossing knot (Figure-8), two 5-crossing knots, three 6-crossing knots and seven 7-crossing knots. How to &e your laces – By Alex Barnes I’m sure – or I would hope – anyone reading this ar6cle is comfortable in their ability to 6e their shoelaces. A<er pulling yourself up against the weight of the morning, 6dying your hair from its scruffy state, wrenchin your jumper over your torso, 6dying your hair again, and forcing your already late homework into your schoolbag, tying your own shoelaces should hold the minimum of your worries on a school morning. But, however unbelievable, the very nature of this task holds great significance in the workings of chemotherapy the development of new materials and upholds decades of the history of mathema6cs. This is Knot Theory. An Introduc+on to Knot Theory A brief History In th late 1800s, most scien6sts believed in the theory of ether, a mysterious substance thought to entangle all maIer. Lord Kelvin proposed that every element should take a unique and singular form based on how the element knoIed up the surrounding ether, beginning the study of mathema6cal knots all over the w rld. He decl red that atoms must be made of ‘vortex rings of ether’. However, this theory was quickly disproven by the atomic revolu6on, and mathema6cians were le< with what seemed lik a completely useless branch of topology. Nevertheless, Knot Theory is finally star6ng to appear in modern science, and uses of it are being developed in areas such as materials science and chemotherapy. What is a mathema1cal Knot? A knot is a simple closed curve in a 3-dimensional space. When studying knots, mathem 6ci ns found them difficult to tease and manipulate without falling apart. To address this problem, both ends of the rope were aIached, allowing free alterca6on of knots without them fundamentally changing. The simplest of all knots is called the Unknot, which in its reduced form, has zero crossings – and therefore is the only ‘0-crossing knot’. This knot was discovered by Peter Guthrie Tait, alongside one 3-crossing knot (Trefoil), one 4-crossing knot (Figure-8), two 5-crossing knots, three 6-crossing knots and seven 7-crossing knots. A Link is what we call a collec6on of knots intertwined with each other, but not actually connected end-to-end. The simplest link is two unknots that don’t cross, called the Unlink. A collec6on of two knots is called a Hopf Link, and three knots are known as the Borromean Rings. Working with Knots The central problem of Knot Theory, known as the ‘Knot equivalence problem’, is determining whether two knots can be rearranged to be iden6cal, and hence concluding that they are the same knot. How to &e your laces – By Alex Bar es I’m sure – or I would hope – anyone reading thi ar6cle i comfortable their ability to 6e their shoelaces. A<er pulling yourself up against the weight of the morning, 6dying your hair from its scruffy state, wrenchi your jumper over your tors , 6dying your hair again, and forcing your already late homework int your schoolbag, tying your own shoelaces should hold the minimum of your worries on a school morning. But, however unbelievable, the very nature of this task holds great significance in the workings of chemotherapy, the development of new materials and upholds decades of the history of mathema6cs. This is Knot Theory. An Introduc+on to K ot Theory A brief History In the late 1800s, most scien6sts believed in the theory of ether, a mysterious substance thought to entangle all maIer. Lord Kelvin proposed that every element should take a unique and singular form based on how the element knoIed up the surrounding ether, beginning the study of mathema6cal knots all over the world. He declared that atoms must be made of ‘vortex rings of ether’. How ver, this theory was q ickly disproven by the atomic revolu6on, and mathema6cians were le< with what seeme like a completely useless branch of topology. Nevertheless, Knot Theory is finally star6ng to appear in modern science, and uses f it are being developed in areas such as materials science and ch motherapy. What is a mathema1cal Knot? A knot is a simple closed curve in a 3-dimensional space. When studying knots, mathema6cians found them difficult to tease and manipulate without falling apart. To address this problem, both ends of the rope were aIached, allowing free alterca6on of knots without them fundamentally changing. The simplest of all knots is called the Unknot, which in its reduced form, has zero crossings – and therefore is the only ‘0-crossing knot’. This knot was discovered by Peter Guthrie Tait, alongside one 3-crossing knot (Trefoil), one 4-crossing knot (Figure-8), two 5-crossing knots, three 6-crossing knots and seven 7-crossing knots. A Link is what we call a collec6on of knots intertwined with each other, but not actually connected end-to-end. The simplest link is two unknots that don’t cross, called the Unlink. A collec6on of two knots is called a Hopf Link, and three knots are known as the Borromean Rings. Working with Knots The central problem of Knot Theory, known as the ‘Knot equivalence
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