Mathematics is fundamentally the study of numbers, with this study having been ongoing for thousands of centuries and is still being studied in the modern day, making up the basic education curriculum thus reflecting its vitality in society. Considering the broad focus of maths, my essay will essentially be on; the first use of mathematics, the western and eastern ideas of maths and the modern applied mathematics. Mathematics is a subject that covers a range of topics and is seamlessly integrated into a lot subjects because it helps the foundation to work.

The origin of maths can be linked back to middle east, specifically Egypt however the Egyptians didn't use maths for ‘academic purposes' [Hodgpeth, 2017] but rather used it practically for tasks such as dividing bread between men, food for livestock as well as calculating the value of metals. Egyptians are credited for their focus on the importance of maths such as ‘written mathematical communication' [Hodgpeth, 2017] which is the implementation and more so the understanding of maths when applied to society. They used index notation using base number 10, a system described as ‘additive' [Hodgpeth 2017] this could very likely have been the first recorded instance of index numbers which again has stayed consistent with the use of mathematics and is still being taught in classrooms till this day. Many prominent mathematicians worked in Egypt during the Islamic Golden Age, due to the ‘practical uses in the Islamic world' [Greenwald, 2011], with their primary focus on algebra (used for calculating inheritance) and the astronomical side of maths (important to include that the Islamic calendar is lunar and so the study of the moon was essential in the practise of their religion). An example would be Ahmed ibn Yusuf (c. 835 – 912) who wrote a book on ratio and proportion [Greenwald, 2011] as well Kamil Shuja ibn Aslam (c. 850 – 930) who's contributions during his time in Egypt are still relevant to this day, he studied numbers (real and irrational) and combinatorics, his technique was even acquired by Fibonacci [Greenwald, 2011] an indication to how the early study of mathematics was the foundation to the mathematics that we know of now. The father of maths accredited in Ancient Egypt is Archimedes, a mathematician, who is best known for his work with the hydrostatic principle and the Archimedes screw. It is well known that Ancient Greece is also responsible for maths, in particular the mathematics philosopher Pythagoras who came up with Pythagorean theorem, a mathematical theorem still prevalent on the curriculum with every fourteen-year-old in the nation taught it in classrooms. Pure mathematics has been owed to Pythagoras, his work on ratios and the ‘fixed numerical relations' between planets and stars [Downey, 2017 pg. 2]. In history, mathematics was used as a way to support and provide answers for the way in which society works. Specifically, the ancient Egyptians used maths with astronomy to analyse astronomical patterns, using their calculations work out when certain planets and stars would be visible. These studies help to further the understanding and depth that they used back then, and to see how far maths has come and changed.

In modern day, mathematics is used quite differently with it majorly emphasised in classroom education. In both the Western and Eastern worlds, it makes up a third of the syllabus however the level of knowledge and intensity is clearly a dividing factor. In the media, there is constant comparison between the teaching and how East-Asian students outperform the Western students [Leung, Graf and Lopez, 2006]. The mathematics taught in education in Eastern countries is far more intense, hence why the outperformance. It is well known that the Eastern countries are incredibly smart, very competitive and a lot of emphasise is cast onto high achievers. A link can be made to how these countries are world leading in technology and the use of maths folds well into this. Tying into this, the UK has recently adopted an education system similar to the Eastern countries, in order to raise standards and improve their teachings. The cultural difference is apparent, in the UK there are different paths that can be taken if the students have failed their GCSE's a complete 180 as Eastern countries such as Singapore, China and Japan, failure is not an option. This high expectation encourages the students to be more motivated and in turn ranks their country top in the world. Lately the British education system has come under fire for the GCSE's being too difficult for students to grasp, outrage pouring from not only students, parents but also teachers too.

The migration of the Asian idea of maths into the Western classroom is very important to show how even after thousands of years, application of mathematics is constantly being further improved. Integrating a whole new curriculum is bound to be difficult, especially the calculation methods used in China, Japan and Singapore are dissimilar to what British students have been used to. Learning maths and then being told what you've learnt isn't right will always be unfavourable but it allows future generations to have a better life and to be on an equal playing field for them to compete for some of the best educations available at great universities. The long-term effect is highly beneficial even though short term may be distasteful for the students. The implementation of the Singaporean methods in British schools has been criticised by the teachers and parents on many different basis; they don't understand it well enough to help their children with school work, it leads to a nation of majorly failing their maths qualification. The expectation from the two cultures is the important factor, and shows high achieving mathematicians are at their place because of determination.

Mathematics is used in everyday life, in fact it's so vital for our society and the way everything works. As well as the everyday use of it involving financial management (calculating change, budgeting and savings), renovating (measurements needed for whether furniture fits or how many floorboards needed to fit the area) plus used in cooking and baking. It can be said that maths is sewn into everyday task and it can go as far as saying that it is needed for survival. We see the use of maths everyday although the simple calculations are very basic, maybe even primary school knowledge but that shouldn't limit its importance. We see maths everywhere; in computer software, technology, algorithms used in marketing, robots and in hospital equipment. As mentioned in the introduction, mathematics is a broad subject and so there is leeway in the way that it's used. An in-depth example of modern day use of maths would be how in architectural planning, the paramount would be maths in order for everything to work out perfectly. Mathematics in hand with physics helps to determine the shape and size of the building, it also plays a factor when deciding on which materials to use and how well they'll hold up in relation to the rest of the building. Just like in Ancient Egypt, we still use maths to divide assets in wills and to find the worth of belongings. Thus, showing the continuity in the use of maths from ancient history to now. Another example of the use of maths would be in algorithms used to determine the bus, train and tram times, which uses 2 separate algorithms to help the public transports operate smoothly [Shalaby and Farhan, 2004]. The speed, departure and arrival time are all calculated beforehand and a timetable is used to keep within these times, this use of mathematics is often overlooked and not expected to be as detailed and explicit due to it how used we are to the workings of public transport.

To conclude, the application of mathematics throughout history has evolved but the purpose has stayed consistent; to aide lives. From the use of maths in the Ancient world to divide bread between men to the modern world of using simple maths when cooking a recipe. Maths has come so farm, and it's constantly being improved and adapted to fit into modern society. It has allowed us to go forward in society and also helped improve the quality of life we experience, we would virtually be nowhere without the use of maths.

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