Session 3
On Saturday, February 1, 2020, HIS EVOLV3 introduced its third session, 'Unsolved Problems,' to 29 mathematically inclined students from Years 6 to 12.
They had the chance to delve into parts of Maths that they didn’t know existed; looking at some of the problems that have troubled mathematicians for decades, and in some cases, centuries. The students also explored the big picture of maths and had the chance to discuss mathematical futures and connect with Dr Sunny Modhara, who uses mathematics from his PhD every day to solve problems to help the UK’s railway system run smoothly.
This EVOLV3 session was correctly titled “Unsolved Problems: The hardest way to make a million dollars” and as the name suggests’ it gave students the opportunity to encounter Maths that was far more difficult and obscure than they had ever come across before as well as engaging them with completely new concept. The students responded very positively to this and worked collaboratively to overcome the challenges they faced.
High Tea Work Shop
High Tea Workshop: A Day of Creativity, Collaboration, and Culinary Excellence
This EVOLV3 session was correctly titled “Unsolved Problems: The hardest way to make a million dollars” and as the name suggests’ it gave students the opportunity to encounter Maths that was far more difficult and obscure than they had ever come across before as well as engaging them with completely new concept. The students responded very positively to this and worked collaboratively to overcome the challenges they faced.
In the year 2000 the Clay Mathematics Institute announced the seven most difficult and important unsolved problems in the field of Mathematics.
Each problem offers a prize of $1 million US dollars for a solution, a proof, or in some cases just “furthering our understanding of the problem”. These problems would form the basis of the session; they include:
The Riemann Hypothesis, formulated in the 1850s and renowned as one of the toughest problems going uses Complex Analysis to search for a pattern in the prime numbers, which if cracked would have extraordinary implications for the entire world of internet banking, cyber-security and the safety of the global financial system
The Hodge Conjecture, concerning the mathematical discipline of topology, put simply involves the relationship between algebra and geometry, except in higher dimensions (such as 4, 5, 6 dimensional ‘shapes’ and beyond)
The Navier-Stokes Equations from the field of fluid mechanics describe how fluids behave – very useful for keeping planes in the air, predicting changes in the Earth’s climate system and understanding how blood moves around the body. Mathematicians want to further our understanding of the solutions of some of the more complex cases of these equations
Unraveling the Tapestry of Mathematical Enigmas: Challenges Spanning Computer Science, Quantum Mechanics, and Elliptical Curves, with Only One Solved in Two Decades
The other problems are wide ranging, concerning computer science and the solvability of complex problems, quantum mechanics and the behaviour of particles at low energy levels and the relationships between elliptical curves and rational numbers. To say that these problems are difficult is an understatement. So far, two decades on, only one of the problems (the Poincaré Conjecture) has been solved.
The purpose of the session was not for students to learn maths, but to learn about some of the maths that goes on at the cutting edge of the discipline. When Andrew Wiles was 10 years old he discovered Fermat’s Last Theorem, a problem that had puzzled mathematicians for over 300 years. Nearly 30 years later, Wiles proved the theorem he had discovered as a 10-year-old, making an invaluable contribution to the field of Mathematics along the way. Plenty of the maths on offer in our Evolv3 session may be too obscure for young students now, but they may be able to look back to the start of their journey when they prove the Riemann Hypothesis in the year 2050!
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