How many primes can you name? In March this year mathematician Robert Langlands won the Abel Prize for research showing how concepts from different branches of mathematics all share links to prime numbers. To analyse these numbers mathematicians have to sift through numbers using mathematical filters, eliminating all non-primes. This search has its origins in antiquity; Euclid wrote in 300 BC that “a prime number is that which is measured by the unit alone”, and it was he who proved that the number of primes is infinite. However, it was probably Eratosthenes who first developed the sifting process, which filters out all multiples of 2, 3, 5, and 7—the first 4 primes.
A notable figure in the early history of the study of primes is John Pell, whose urge to categorise and collect useful numbers led him to identify and publish the primes up to 100,000 in the early 1700s. A century later, others had found the primes up to 1 million. As more and more primes were found, the process was made easier by the invention of sliders and stencils to quickly eliminate multiples. However, it was Carl Friedrich Gauss who decided to actually analyse prime numbers, looking for interesting patterns. He found, for example, that the higher he counted, the fewer prime numbers there were. More recently it has been found that, with the exception of 2 and 5, all prime numbers end in 1,3,7, or 9.
Langlands’ research, which has been described as “revolutionary”, is founded on the work of previous mathematicians, in particular Gauss. In the late 18th century he formulated a law of reciprocity whereby certain types of primes share defining characteristics; for example, primes that are the sum of two squares also leave a remainder of 1 when divided by 4. Langlands built on this by proposing that prime numbers encoded in higher-degree equations than simply squares might be in a reciprocal relationship with the branch of mathematics known as harmonic analysis, which is often used in physics.
Applicants for Mathematics may wish to read Langland’s research and look into the contemporary questions in the study of prime numbers. Students wishing to study Physics could familiarise themselves with harmonic analysis and learn about how prime numbers are relevant to physics.
- What’s the Most Important Part of Your Application? An application to Oxford or Cambridge involves various different elements,... Read more >
- Pooling: Fast Facts You may have heard people talk about “pooling”, or maybe... Read more >
- MLAT mini mock paper & answers The MLAT or Modern Languages Test is required by Oxford... Read more >
- History of Art Reading List History of Art at Oxford and Cambridge allows you to... Read more >
- How is the BMAT marked? The BioMedical Admissions Test (BMAT) is marked significantly differently from... Read more >
- Download a Medicine Personal Statement 2 “Further work experience has highlighted some of the demands and challenges... Read more >
- Your free E-book… “So You Want To Go To Oxbridge? Tell me about a banana…” If you are applying to Oxford or Cambridge, there are... Read more >
- UCAS: A How To Guide The process of applying to university through UCAS can seem... Read more >
- LNAT overview If you’re applying for Law at Oxford you will need to sit... Read more >
- Biological Sciences & Medicine: answer like a pro What kind of questions can you expect in an Oxford... Read more >
- Funding Your Oxbridge Degree Many people are under the impression that it is more... Read more >
- Stats report: our annual survey Every year, we survey hundreds of applicants who applied the... Read more >
- Taking a Gap Year There are a number of advantages to taking a gap... Read more >
- Your Open Day Guide Open Days can be an extremely useful way of finding... Read more >
- PPE: answer like a pro If you’re applying for Politics, Philosophy and Economics (PPE) or... Read more >
- Law: answer like a pro Law is a notoriously competitive subject; this, along with the... Read more >
- Bursaries Both Oxford and Cambridge are committed to the principle that... Read more >
- Oxford and Cambridge Access Schemes Oxford and Cambridge aim to offer places to the best... Read more >
- Download a History & English Personal Statement “Evidently reading is a major passion and Graham Greene has... Read more >
- The Differences Between Similar Courses At Oxford and Cambridge For some applicants, deciding between applying to Oxford or Cambridge... Read more >
- Personal statement: our tips in the Independent Here are 3 quick tips every hopeful should consider before... Read more >
- Cambridge Language Test mini mock paper & answers Many Cambridge colleges require applicants for Modern Languages to sit... Read more >
- Interactive Interview Exercise Manual ‘What should I expect at my Oxbridge interview?’ ‘How will... Read more >
- Oxford and Cambridge International Grade Requirements If you’re applying to Cambridge or Oxford but you’ve not... Read more >