Tuesday 17 November 2015

The Riemann Hypothesis Remains Unproven

Dr Opeyemi Enoch claims to have proved
the Riemann Hypothesis.
There were stories going around today that one of the longest-standing problems in mathematics had been solved, namely the Riemann Hypothesis.

The Riemann Hypothesis relates to a mathematical function called the Zeta function, and in particular where the value of this function is zero. Proving the hypothesis would give mathematicians new insight into the distribution of the prime numbers.

A Nigerian academic named Dr Opeyemi Enoch was reported to have finally proved the 156 year old problem, which is one of the Clay Institute's outstanding millennium problems.

As this article on the Aperiodical website makes clear, Dr Enoch has a very varied academic background, including designing a prototype silo for peasant farmers and detecting people on an evil mission.

His "proof" was presented at a poorly-attended conference, which doesn't seem to have attracted the audiences or world attention that such a ground-breaking piece of work would warrant. But the BBC ran an interview with Dr Enoch, in which he was asked, among other things, what he would do with the one million dollar prize for solving the problem.

In an article on Radio 4's Today programme this morning (scroll to 2:50:44), however, Professor Marcus du Sautoy of Oxford University refuted the claims of the proof and managed to plug his book at the same time, of course.

The Clay Institute is clearly unconvinced about the proof, stating that the problem remains unsolved.

Tuesday 3 November 2015

Another Maths Question Goes Viral (this time from down under)

Another maths question has been popping up all over Twitter and other social media. This time the question comes from the Victorian Certificate of Education, an Australian maths exam.

Here it is:

While many were left puzzled, the question may appear easier if a simple straight line is drawn downwards dividing X into two equal parts, as shown below:

Now the angle marked is simply the external angle of a regular 12-sided shape. The formula for the external angle of any regular shape is:

where n is the number of sides, i.e. 12.


It was fairly easy when you know how! But like Hannah's sweets from the English Edexcel board, the trick is spotting how! Expect more of this type of question in years to come, as the exam boards try to separate out pupils who have just learnt the formulas from those who can spot when to use them!

And, of course, social media means we'll get to hear about all of them!

Nicky Morgan's Plans for Education

Nicky Morgan will announce her plans
for English schools today.
It seems that every education secretary wants to unveil their own big revolution for our education system, before schools, pupils and teachers have had time to adapt to the last seismic shifts.

Today it was Nicky Morgan's turn to announce a raft of measures that will bring profound changes to our schools.

The eye-catching suggestions are:

  • Primary school pupils in England could face formal tests at the age of seven;
  • A pool of "elite teachers" will be recruited to work in struggling schools in coastal towns;
  • A target will require 90% of pupils to take core academic subjects at GCSE.

Mrs Morgan maintains her changes will help "every young person get the best start in life". At present, she says, there are 20 local authorities where most pupils do not achieve five good GCSEs, including English and maths. For Labour, shadow education secretary Lucy Powell said that rather than raising standards, the government has caused a "chronic shortage" of teachers.

In her speech today, Mrs Morgan will announce details of the pre-election pledge to create a National Teaching Service. It will recruit a pool of 1,500 high-achieving teachers over five years who would be deployed to struggling schools. It will also give local "commissioners" the power to intervene in under-performing state schools in a variety of ways. These commissioners are already in post, created to oversee academies and free schools.

The plans also include the re-introduction of testing all pupils at the age of 7, which was previously scrapped. Critics point out that the UK's pupils are already the most examined in Europe and our schools are in danger of becoming "exam factories".

In secondary school, there is clarification of the last education secretary Michael Gove's target that all pupils will have to take traditional GCSE subjects, in what he named the English Baccalaureate. This requires pupils to take GCSEs in English, maths, history or geography, two sciences and a language.
There will now be a target of 90% of pupils, which will allow for just a small number of exemptions, such as for pupils with special needs. At present, only about 39% of pupils take these subjects.

Brian Lightman, leader of the ASCL head teachers' union, said it would be "immensely challenging" for schools to get enough staff for subjects such as modern languages to meet these new targets.

Are you a teacher, head teacher, parent or pupil? What are your thoughts on the big changes being announced today?

Monday 2 November 2015

George Boole born 2/11/1815

Today Google is celebrating the 200th anniversary of the birth of George Boole, with an animated logo.

So who was George Boole and why is his work relevant today?

George Boole -
picture credit Wikipedia

George Boole was a British mathematician and logician and was ahead of his time. Until his time, logic was a subject mainly applied to philosophy and natural language. Boole was the first to apply logic to mathematics in a systematic way. By doing this, his work paved the way for the digital revolution and "Boolean logic" was a precursor for the way computers perform their calculations.

Boolean logic treats variables as either on or off (true or false, or 1 or 0). In the 1930s, the American Claude Shannon applied Boolean logic to build the first electrical circuits.

Today Boolean logic underpins almost every computer program in some way. For example, if you search the web for a two-word term, such as "cheesy chips", the search engine's algorithms will apply an AND operation, and bring you web pages where the two words BOTH appear. You would not find it very useful if the results shown were pages where either "cheesy" OR "chips" were on the page.

Different parts of the Google logo light up when the x and y in the second g are shown. See if you can work out the rules.

As well as inventing this field of logic, George Boole published work on differential equations and probability theory. He died aged just 49 in 1864 and will be remembered as an important pioneer of the information age.