The British-Lebanese mathematician Sir Michael Atiyah spoke at the Heidelberg Laureate Forum on 24th September. In a 45 minute talk he claimed to have found a “simple proof” to the Riemann hypothesis, a problem that has remained unsolved since 1859. Correct proof to support the hypothesis, labelled by the Clay Mathematics Institute as one of the seven “Millenium Prize Problems”, could have huge implications for the majority of modern day cryptography, including cryptocurrencies like Bitcoin.
The hypothesis concerns prime numbers and the ability to find the number of primes smaller than any given integer, N. The hypothesis relies on the Riemann zeta function and its return of zero. It is known that zero is returned when a negative integer is used in the function, these are known as trivial zeros. This is also the case with any complex number whose real part is ½, known as non-trivial zeros. The non-trivial zeros have varying imaginary units but consistent ½ values, allowing for their calculation.
However, the continuing problem is the lack of proof that complex numbers with a ½ real value are the only form of non-trivial zeros. Until now this has been assumed to be true and has provided the basis for modern cryptography. This is due to the property of prime numbers where calculating the product of two primes is simple but finding the two primes used when the only information given is the result is very difficult. This allows for one-way functions that cannot be easily inversed by those that are not the intended recipient.
But proof of the hypothesis may lead to a connection being observed between prime numbers and this could be exploited to counteract contemporary forms of coding. This could lead to hash algorithms being easily hacked and bitcoin being mined at an exponentially faster rate.
Atiyah’s claim of proof is currently met with scepticism but if correct his work could have an enormous impact. Computer Science and Mathematics applicants can develop their understanding of the Riemann hypothesis and its underpinning of cryptography and its other applications.
- The Most Competitive Subjects At Oxbridge (And How To Choose Wisely) Oxford and Cambridge are two of the best universities in the... Read more >
- Oxbridge: the global impact Concerning UK university admissions, UCAS have released some interesting stats.... Read more >
- Personal Statement Solution: Brainstorm Sheet Writing your personal statement may just be the grimmest part... Read more >
- Stats report: our annual survey Every year, we survey hundreds of applicants who applied the... Read more >
- LNAT ‘So you want to go to Oxbridge’ Answers If you have been reading our book ‘So you want... Read more >
- Your Open Day Guide Open Days can be an extremely useful way of finding... Read more >
- Download an Economics Personal Statement 2 “Beyond this essential interest in the subject, I find that... Read more >
- BMAT mini mock paper & answers With over 90% of applicants now preparing for the admissions... Read more >
- Music Reading List Applying for Music at Cambridge or Oxford requires a range... Read more >
- PPE: answer like a pro If you’re applying for Politics, Philosophy and Economics (PPE) or... Read more >
- The Architecture of an Education: what are colleges all about? Explaining the difference between Oxford and Cambridge colleges and the... Read more >
- Economics & Logic Puzzle: ticket touts We asked top Economics blogger Resham Kotecha to challenge us... Read more >
- Choosing a course From Arch and Anth to Veterinary Medicine, the range of... Read more >
- Pooling: Fast Facts You may have heard people talk about “pooling”, or maybe... Read more >
- Personal Statement Action Plan: Section 1 of 2 The UCAS personal statement will be a key part of... Read more >
- February’s Top News Stories Read more about some of the biggest news stories to... Read more >
- Mathematics Reading List Studying Mathematics at university requires a different approach to studying... Read more >
- Download a Philosophy Personal Statement “Philosophy of the mind is my particular interest, especially the... Read more >
- Taking a Gap Year There are a number of advantages to taking a gap... Read more >
- What’s the Most Important Part of Your Application? An application to Oxford or Cambridge involves various different elements,... Read more >
- The Great Collection of Past Oxbridge Interview Questions The great thing about an Oxbridge interview is that it... Read more >
- The Differences Between Similar Courses At Oxford and Cambridge For some applicants, deciding between applying to Oxford or Cambridge... Read more >
- TSA overview A huge range of subjects at both Oxford and Cambridge... Read more >
- Science Puzzle: experimenting with mice… We asked our Medicine graduate Jennifer to tell us a... Read more >