There is nothing scientific about my ranking system; I am featuring the equations that seem to have permeated the mainstream.
In terms of fame, there are three big equations, derived from Einstein, Pythagoras, and Newton. We are all exposed to these regularly through mainstream media and/or through secondary education. While Schrödinger’s Equation is not that well-known by the layperson, most of us have heard of the associated Schrödinger’s cat thought experiment which helps to explain the principles of quantum mechanics.
This equation has even made it onto T-shirts as some kind of nerdy fashion statement, so most people are aware of it, even if they don’t know what it means. Proposed by Albert Einstein, perhaps the most famous scientist in history, it’s no surprise this E = mc² is the most well-known, but one of the least understandable to the layman. The answer? In short, Einstein showed that a small amount of mass can create a heck of a lot of energy – as in the amount you find in in stars – and it paved the way to the nuclear age.
We all did this at school so it’s one’s pretty famous and is attributed to the ancient Greek mathematician Pythagoras. It states that for any triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem forms the basis of Euclidean geometry which is used in architecture and navigation.
Formulated by Sir Isaac Newton, and popularised by the scientist’s apple falling on head Eureka moment, this equation describes the relationship between force (F), mass (m), and acceleration (a). The first states that an object’s motion will not change unless acted upon by a force (Inertia). The second law states that the force exerted by an object is equal to its mass times its acceleration (Force). And the third is that when two moving objects they exert equal and opposite forces on each other (Action and Reaction).
Erwin Schrödinger’s Equation describes how the quantum state of a physical system evolves over time, incorporating the wave-particle duality of matter, which refers to the fact that matter at one moment acts like a wave and yet at another moment acts like matter. This equation has been popularised by the famously related Schrödinger’s Cat thought experiment which was designed to simplify quantum mechanics and which is now referenced in many science fiction works.
If you are interested in studying Maths as a subject, Oxford Open Learning offer you the chance to do so at a variety of levels, listed below. You can also Contact Us here.
To mark British Science Week, from the 8th to the 17th of March, let’s shine a light on some of the greatest contemporary British minds in Science, Technology, Engineering and Maths (or STEM, for short).
Sue Black is a Professor of Computer Science at Durham University. An outspoken and active social media campaigner, Sue led a campaign to save Bletchley Park and is one of the most influential women in tech. An advocate for equality, diversity, and inclusion, particularly for women in computing, she founded BSCWomen, an online network for women in tech, and #techmums, a social enterprise which empowers mothers and their families through technology. In the 2016 New Year Honours, Sue received an OBE for services to technology.
Timothy Berners-Lee is a computer scientist and software engineer who is most famous for inventing Hypertext Transfer Protocol, or HTTP, and the World Wide Web. He also created the first internet browser, the HTML language, and the URL system, and in 1991 was named one of the 100 Most Important People of the 20th Century by Time Magazine. In 2004, Timothy was knighted by Queen Elizabeth II for his pioneering work, and he now works as Professor of Computer Science at the University of Oxford. He is also a professor emeritus at the renowned Massachusetts Institute of Technology (Often referred to as MIT).
Maggie Aderin-Pocock is a space scientist, educator, and communicator. Throughout her career, she has worked on some of the most prestigious projects at some of the UK’s top universities and is currently an honorary research associate within the Department of Physics and Astronomy at University College London and Chancellor at the University of Leicester. She is also a presenter of the TV show The Sky at Night and does much outreach work to engage young people in science. Her academic work now focuses on building instruments and equipment to aid the fight against climate change. Maggie received an MBE for services to science education in 2009 – an honour that was upgraded to OBE in this year’s New Year Honours.
Donald Palmer is an Associate Professor of Immunology at the Royal Veterinary College where his current research interests focus on the ageing of the immune system. After completing his PhD at King’s College London, he took post-doctoral fellowship positions at Cancer Research UK and Imperial College where he carried out research on lymphocyte development. Donald is also a co-founder of the Reach Society – an initiative to inspire, encourage and motivate young people, particularly young Black men and boys, to achieve their full potential.
Roma Agrawal is a structural engineer who is most known for her work on The Shard in London. Born in Mumbai, she completed her undergraduate degree in physics at the University of Oxford and gained an MSc in structural engineering from Imperial College London. She has gained several awards for her work, including the Institute of Structural Engineers’ Structural Engineer of the Year’ award in 2011 and, more recently, the Royal Academy of Engineering’s ‘Rooke Award for Public Promotion of Engineering’. She is an active public speaker and advocate for diversity and inclusion within STEM.
Saiful Islam is Professor of Materials Modelling at the University of Oxford. He gained a chemistry degree and PhD from University College London and his research interests focus on gaining a deeper understanding of the processes that exist within energy materials, particularly batteries. As well as numerous academic awards and honours, Saiful holds a Guinness World Record for the highest voltage lemon battery (usually a low powered, simple battery used for the purposes of education).
To learn about more successful British scientists, visit the Inspiring Scientists website.
If you are interested in studying a Science or Maths, Oxford Open Learning offers the opportunity to do so at a variety of levels, listed below. You can also find advice via our Contact Us page here.
Fast Track Human Biology IGCSE
Perfectionism is not, in and of itself, a negative trait. Perfectionists are often conscientious high achievers; our greatest weakness is also our greatest strength. But those trying to be constantly perfect can find that every task feels like an unconquerable burden and every essay a path to failure, however unlikely our friends and family might find our doom-laden predictions. Here are three thoughts to use to beat the unrealistic idealism that may currently be beating you.
What is perfect, anyway? Maybe you could decide. Perhaps perfection could simply mean sitting down at your messy desk, ignoring the clothes on the floor, and spending 10 minutes planning the first half of your essay. In this deeply imperfect and challenging world, if you were to be reasonable with yourself, your definition of perfect should, and could, be different. Redefine perfection: make it doable and make it your own.
A to-do list is a depressing sight, if, at every item, we are telling ourselves that we ‘have to’ or ‘must’ do this or that. But turn ‘have to’ into ‘get to’ and suddenly life seems more joyful. Perhaps it is an irritating piece of advice, an unwelcome call to simply have more gratitude, but studying is essentially an overwhelmingly positive thing. You are learning and growing, and you have access to great materials and educated teachers; you are lucky. And so, even if it feels at first like you are lying to yourself, tell yourself, next time you inspect your to-do list: “I get to plan my essay today”.
We will do it, but we are waiting for the perfect time when we are in the mood. Because we know we can do it well, and not just well but REALLY well. And so that is the aim. This isn’t laziness, for the fear is real: we cannot bear to submit anything less than our best; we cannot tolerate failure; and we want to be proud of what we have achieved. We have visualised (or we think we have) the perfect essay or assignment. But the truth is that you have a deadline. Perhaps you could achieve perfection if you had eternity to complete it. But you don’t. Most tasks have a timeline, whether it is 6 years to complete a part-time PhD, or one night to finish an essay. And the test is not what you can achieve, but what you can achieve in the time you have to complete it. The definition of perfect might simply be this: finished.
The world of cryptography is a fascinating realm, where secret codes and hidden messages hold the key to unlocking mysteries and securing information. Cryptography has played a vital role in human communication and security throughout history. Let’s delve into its intriguing evolution and explore its impact on our world.
The origins of cryptography can be traced back thousands of years to ancient civilisations such as those of Egypt and Mesopotamia. In those times, simple substitution ciphers and hieroglyphic codes were used to transmit messages securely. One of the most well-known examples is the Caesar cipher (illustrated above), named after the Roman Emperor, who employed a shift-based substitution cipher to protect military communications.
During the Renaissance, cryptography became more sophisticated, with the emergence of polyalphabetic ciphers (a cipher that uses multiple substitution alphabets) and the introduction of frequency analysis. Italian polymath Leon Battista Alberti invented the Alberti cipher disk, a mechanical device that allowed for the encryption and decryption of messages. These advancements marked a significant shift in complexity and paved the way for future developments.
The 20th century witnessed remarkable breakthroughs in the field. During World War II, the Enigma machine, a complex encryption device used by the German military, presented a formidable challenge to Allied code-breakers. However, the efforts of code-breaking teams such as Britain’s Bletchley Park, led by Alan Turing, ultimately cracked the Enigma code, providing crucial intelligence and contributing to the Allied victory.
The advent of computers brought forth new possibilities in cryptography. In the 1970s, the Data Encryption Standard (DES) was developed as a widely used encryption algorithm. However, as computing power increased, DES became vulnerable to brute-force attacks. This led to the development of more robust encryption algorithms, such as the Advanced Encryption Standard (AES), which remains a cornerstone of modern cryptography. The rise of the internet and digital communication presented new challenges and opportunities for cryptography.
Secure communication protocols like SSL (Secure Sockets Layer) and TLS (Transport Layer Security) became essential for safeguarding online transactions and protecting sensitive data. Public-key cryptography, introduced by Whitfield Diffie and Martin Hellman in the 1970s, revolutionised secure communication by using asymmetric key pairs.
Cryptography continues to evolve rapidly in the digital age. Blockchain technology, used in cryptocurrencies like Bitcoin, relies heavily on cryptographic principles to secure transactions and maintain the integrity of the distributed ledger. Zero-knowledge proofs and homomorphic encryption are among the cutting-edge cryptographic techniques being explored to enhance privacy and security in an increasingly interconnected world.
The fascinating world of cryptography combines mathematics, computer science, and the pursuit of secrecy. From ancient times to the present day, cryptography has shaped the flow of information, safeguarded secrets, and enabled secure communication. As we embrace an era of increasing digitisation, the importance of cryptography in protecting privacy, securing data, and ensuring trust cannot be overstated.
Whatever subject you are studying or qualification you are studying for, contact with your teacher or tutor – even when remote – is an invaluable part of that process. They are usually the subject experts, have a full understanding of the assessment process and have, more often than not, supported many other students who felt exactly the same as you do now about their learning. Whether you are confident in your subject knowledge and looking for ways to stretch yourself in order to achieve the very best results or are still a little uncertain and unsure how you might secure the grade you need, your tutors can provide you with the support you require. Here are a few simple strategies every student should try in order to boost the benefits of the contact they have.
Put simply, meet their expectations! If they provide a task, complete it. If they set a deadline, meet it. If you have a meeting, be there. Programmes of study and assessment schedules are in place to meet the needs of everyone; ensuring that there is adequate time for covering all of the content, assessing progress and providing feedback. A tutor works with many students and if you don’t adhere to the plan then you are unlikely to get the time you deserve. If there is a problem with the schedule set out for you, talk to your tutor in advance so that they can make any amendment they possibly can in order to make sure that everyone’s needs are met. If a tutor sees you are committed to your learning and doing what is required they are likely to go above and beyond in the ways in which they support you.
As already mentioned, the tutor is the subject expert. They have the knowledge of the subject but also the ways it is assessed and how to ensure you can demonstrate it when required to do so. Listen to their advice. Take notes where required. Follow their suggestions. However, if there is something you are unsure about, don’t be afraid to ask! Questioning is key to developing a deeper understanding and mastery of a subject but is also a great tool in ensuring there have been no miscommunications or misunderstandings. Your tutor will respect your ability to really engage with the content you are covering together and look for ways to address your questions in more detail.
Receiving feedback is one of the most important parts of the learning journey. However, many of us find getting feedback something that is really, really hard! Instead of thinking about what is said by your tutor as being ‘good’ or ‘bad’, try to consider what you can learn from it instead. If you are given praise for a certain aspect of your work, think about what you did that made this so effective. If there are comments relating to something that hasn’t worked out so well then think about what you might do differently next time. Reflection is key to making progress. Also, apply the same thought process when it comes to your attitude to learning. If a tutor comments on this, avoid taking it personally and think of how you might use what they have said to become a more effective learner.
Don’t forget that any contact that you have with your tutor is designed to benefit YOU. If you are in need of something specific from that contact then, again, do not be afraid to ask! In reality, this involves planning and preparing for any contact you have before you have it. Make a note of any questions you have when studying independently. If you need to revisit any material with them, ask in advance. If you have found a subject area particularly easy or hard, let them know. Remember, your tutor will be looking to support you in a way that is personalised to meet your needs too, so the more effectively you’re able to communicate these, the better they will be able to do this.
Of the 9 million school-aged pupils in England in 2019, it was estimated that around 52,000 were home-schooled*. These numbers have been steadily on the rise in recent years as home-schooling becomes a more popular choice for parents. Whilst one might associate learning at home with younger pupils, home-schooling is actually most common within the key stage 3 age range. But is educating your child at home the right decision for you? Here we take a look at some of the benefits, and potential challenges, to home-schooling your child at key stage 3.
Why Key Stage 3 Home Schooling?
Home-schooling allows you to create a bespoke programme of education for your child which may better suit their needs. Families can be much more flexible regarding the “school” week with educational sessions taking place at a time and place that better suits those involved. Families are free to start learning in the mid-afternoon if that works better for the student, and many parents take advantage of quieter, mid-week, times at museums, libraries and sports facilities. One-to-one teaching also means that sessions are much more efficient. Often, a whole day’s worth of learning can take place in just a couple of hours due to the individual attention that students receive.
For parents whose child lacks confidence, or who worry about potential bullying at school, home-schooling provides an opportunity for a student’s academic confidence to develop without the anxiety that a classroom environment can cause. Lacking the distractions that other students in a noisy classroom can cause, the home can provide a quieter environment where it is easier for students to concentrate.
The increasing numbers of home-schooled children means that there is now a vast and supportive community of parent-teachers who can provide support and advice to anybody new to home-schooling.
Many parents worry about the lack of social interaction that their child may experience if they are home-schooled, particularly as they become a teenager. Many teenagers form strong friendships with the people they go to school with, and home-schooled children certainly miss out on developing these relationships. However, there are numerous other ways in which children can make friends and so this need not be a problem as long as families encourage and provide opportunities for their children to make friends elsewhere. From sports teams to music groups, extra-curricular activities provide children with a way to make friends with many like-minded young people.
The cost of home-schooling can also be a concern to parents. Many families opt to provide a tutor to deliver at least part of their child’s education and a qualified key stage 3 tutor may charge around £40 per hour. Many families also purchase online courses for their child which may form part of their home education curriculum. There are numerous options available, but you should always consider prices carefully before enrolling on courses. At the same time as considering the expense, families should think of the value for money a quality online course potentially provides. Using a tutor and/or home-schooling course provides structure, consistency and a secure route to take GCSEs, should you wish to pursue formal qualifications.
Oxford Home Schooling provides Key Stage 3 courses for under 18 students, in English, Geography, History, Maths, P.S.H.E., Science and Spanish, and details of these can be found on our relevant site page by clicking on the link here.
Our own Key Stage 3 course prices can be found by clicking here.
*Figures from www.gov.uk
Think of Pythagoras and you’ll probably recall studying his theorem at school, where a right-angled triangle the sum of the squares on the other two shorter sides equals the hypotenuse squared. The theorem is believed to have been known to the Babylonians 1000 years earlier, but the Greek Philosopher and mathematician may have been the first to prove it.
In the field of Mathematics, Pythagoras’ work led to great leaps forward in our understanding of numbers and geometry, and of importance in many other branches of mathematics, including trigonometry.
Pythagoras was taught mathematics by ancient Greek Philosopher Thales, who brought the subject to the Greeks from Ancient Egypt, and by Anaximander, who was an earlier student of Thales. He was founder of the Pythagorean brotherhood, a group devoted to the study of mathematics.
Pythagoras was certainly not an ordinary mathematician, by any means. He believed that science and religion were connected. It is thought that he believed that he had already lived four lives, all of which he could remember. Others claimed that he was able to travel through space and time and could talk to plants and animals.
His work linked his subject with the universe at large. Pythagoreans believed that everything could be reduced to numbers, that the whole universe had been built using mathematics. They said the truth behind the everyday reality we experience lies in numbers.
Modern-day physicists who seek the ‘theory of everything’ or the ‘grand unification’ are Pythagoreans. They subscribe to the thought that the universe can be completely understood through mathematical equations, and they are committed to a quest to find these equations. To Pythagoreans 10 was the supreme number, as it can be made by adding the first four numbers, 1,2,3 and 4. These numbers form a tetractys – the perfect, equilateral triangle.
Pythagoreans also used science in the areas of mystery and spiritualism. Their beliefs were based on the power of numbers. The monad (a unit), spoke of the birthplace of all things, and the number two, the dyad, referred to matter. The number seven was considered sacred because it was the number of strings on a lyre, the number of planets, and the seventh day of the Greek calendar was sacred to Apollo, all the feasts were celebrated on the seventh of the month.
Pythagoras also recognised the healing powers of music. He thought it was possible to align the souls to their perfect nature, and through music he performed what he called ‘soul adjustments’. He was the first person to prescribe music as medicine.
Widely considered as the ‘father of philosophy’, Pythagoras’ teachings, theories, philosophies and life’s work show that he was truly an outstanding polymath, and his learnings and teachings made him one of the greatest thinkers of his time.
Everyone is talking about virtual reality. It has been around for years, but it could soon be time for it to hit the mainstream. Companies such as Immersive VR Education can even generate a lifelike spaceship in the classroom, and their capabilities are expanding with the growth of Big Data.
One of the key benefits VR offers is a truly interactive and connected classroom experience. This could take students away from the classical model of education, which relies on the teacher to impart knowledge on often passive students. Effectively, it means the amount of personalised interaction is not dependent on dividing the time of one person. If you consider that most class sizes in the UK state education sector consist of around 30 students, one teacher dividing their time equally for an hour would give each student 2 minutes. For students who don’t grasp topics easily, this is clearly not optimal.
In the context of the current global pandemic, VR could also allow students to interact with teachers without being physically present in the room. In this sense, the dilemma of how to maintain social distancing in an oversubscribed system could be answered by embracing this new technology.
With VR, schools with poor resources could still teach practical skills such as car mechanics, with each student participating for the whole lesson – and safely. Maths could become tactile, languages could become a chat in a French cafe. It could be a revolution, bringing a level of interactivity the students are already used to at home to the classroom.
The most important transition, however, will be in mentality, with teachers moving from the centre of the classroom to the role of facilitator.
Big Data refers to using large data sets to establish patterns and make connections. Tech giants such as Google can, for example, use this to discover trends in commuting habits by using data points from Google Maps.
Big Data can, in many cases, mimic or even surpass human intuition. This means students can keep track of learning, and therefore learn in a more self-directed way. In a traditional environment, a teacher has to monitor the test results of individual students, breaking down their weaker sub-skills into a learning plan. This is an essentially impossible task given that many teachers are responsible for hundreds of students. In a Big Data environment, these subskills can be easily tracked to identify areas for growth.
Some studies have indicated that VR could be harmful, particularly for very young learners (for whom it could cause profound confusion.). Even for older learners, VR could signal the advent of an increasingly detached society, where the social side of learning could be overlooked. Even if VR professes to be social in its scope, phones and social media have created increased levels of introversion and depression in children and adults alike.
The price, at first, could also be a prohibitive factor, with many schools unable to afford the equipment. This could give a further competitive advantage to more wealthy areas.
Like many new areas in tech, the march of VR and Big Data seems inevitable. The question will not be whether or not to adopt the technology, but how to do it in a controlled and responsible way. The benefits of this could be unparalleled in the history of education.
The current lockdown has highlighted the huge value of YouTube and social media as a topic-rich, online educational platform. There already existed a wide range of online learning resources, but since lockdown the number of online home learning resources has grown exponentially. As a home-based learner, you can now learn virtually anything you want, when you want, often for free. Here’s some of the most relevant resources for young home-based learners.
This resource has been around a long time, but since Monday 21st April, the team from BBC Bitesize have incorporated ‘Daily Lessons’ into their offering, which aim to provide structured learning to kids at home during lock-down. They offer 3 new lessons every week day for each year group from Year 1 to Year 10, making it an almost one-stop shop for lockdown home learning.
This fascinating, free online resource includes lots of educational activities and games that you can do in the house or garden. If you are interested in biology and natural history then you can access great resources such as their Dinosaur directory which has facts, figures and images for over 300 dinosaurs, or their Open Air Laboratories learning resources. The content is relevant for Key stages 1-4 and post-16.
This is a great online learning resources, enabling children from key stage 1, right through to key stage 4 to develop their mathematics skills in a fun and engaging game-based learning environment. It comes with a 48-hour free trial
National History Museum
BBC Bitesize
https://www.bbc.co.uk/bitesize
Mathletics
Choosing subjects to study is an important consideration, of this there is no doubt. However, in recent years the campaign for jobs and the drive for individuals to study employment-specific STEM (science, technology, engineering and mathematics) subjects has left the arts, the humanities and the social sciences in an undermined position.
From Sociology to Literature, History to Psychology and Geography, these, and many more are all considered to be under the broad umbrella of the Humanities, with Psychology, Sociology, and Geography sub-grouped into social sciences.
So would anyone consider studying a course that sets you up for what some have termed as ‘career suicide’? Is it worth it? What will be achieved other than a confirmed ability to follow a prescribed syllabus and learn the required information to pass exams or produce coursework?
George Anders, in his book entitled You can do anything: The Surprising power of a ‘Useless’ Liberal Arts Education, says “curiosity, creativity, and empathy aren’t unruly traits that must be reigned in to ensure success. The job market is quietly crying out for people who can bring a humanist’s grace to our rapidly evolving high-tech future.”
Tempering the needs of a rapidly growing STEM world needs to be the humanising of The Arts, ensuring that the heart and soul of the species, as well as its stomach and head, are catered for.
So what will studying the Humanities actually, broadly, offer? Aside from all the subject-specific knowledge, ‘training’ in the Humanities and Arts offers an unparalleled depth of personal growth and mental diversification. The development of a student’s ability to critique systems of behaviour, work and politics ensures that individuals are able view their work (and life) situation with a clear and reflective, empathetic yet unflinching gaze.
Being able to hold and ‘apply’ multiple perspectives on a subject and really ‘feel’ the impact of those perspectives offers real-time, realistic views on potential impact and change in any given area. The student is working towards gaining an understanding of the historical, predictive, economic, social and cultural layers that are part of any given situation. It is far from easy, rather it is the equivalent of a mental Olympic sport, and no mean feat.
The training involved in developing these capacities and increasing the knowledge base behind them is not as simple as it is often made out to be. It is a lifelong pursuit in stretching understanding and increasing mental flexibility. To be able to juggle the range of incredible global and individual states and concepts is every bit as important a role as Einstein believed it to be when he is quoted in Phillip Frank’s book, Einstein: His life and times : “the value of an education in a liberal arts college is not the learning of many facts but the training of the mind to think of something that cannot be learnt from textbooks”.
Knowing oneself in relation to the micro of one’s own society and the macro of an increasingly globalised world can be applied to the job market as well as to the after dinner discussion.
To be able to holistically, empathically, and with humanity, understand the multiple situations and issues that humanity faces, and to be able to address them from a standpoint that is complementary with the STEM point of view will always be valuable. The Arts and Humanities offer us more than ‘just’ problem solving, they offer us the movie reel, as well as the means and the reasons for creating the necessary artefact.
Locating the human self in the midst of the need for new technology and adapted processes is a way of ensuring that the species stays positively anchored in more than just a physical, practical way. What does it mean to be human without the arts? Considering a social, economic and political world without the evolving soul of humanity is merely an existence.
So, go ahead and follow the passionate pursuit of intellectual and artistic learning and see which worlds open up for you to explore. A colourful, terrible and incredible past and future of the world awaits.
To find George Enders’ book You can do anything: The Surprising Power of a “Useless Liberal Arts Education, follow this link: https://www.georgeandersbooks.com/
Follow this link to find Phillip Franks’s Einstein: his Life and Times