Hacker culture is defined as a group or subculture of individuals who enjoy creatively overcoming the limitations of software to achieve 'clever' outcomes. Whatever these 'clever' outcomes may be, the word 'hacker' does not have positive connotations for most people. Nowadays, 'hacking' could mean a whole company goes completely bankrupt from one exploitation in their code or an individual is victim to cyber identity theft. With today's rates of cybercrime incidents, law enforcement is struggling to keep up, and these incidents are no longer easy to identify and prosecute. However, the origins of hacker culture were quite different. In the 1960s at MIT, the word "hacker" originated as an extremely skilled individual who practised what we now may think of as ancient computing languages like FORTRAN or LISP. Hackers used to be people who were locked up in a room, programming all day, and no one seemed to mind them in the 60s. Most people did not even own a personal computer or laptop, let alone know what hacking was. Yet, people who knew about these programmers viewed them positively and welcomed them to challenge computer systems and software to improve them. However, in 1971, the first major hacking was carried out by a vet named John Draper, who figured out how to make free phone calls and this act later became known as... phreaking. Although this may not be similar to the overscaled hacking you may be used to, at the time, it was considered completely groundbreaking. Those who followed John Draper were groups called "Legion of Doom" and "Choas Computer Club", two of the largest and most respected hacker groups ever found, and Kevin Mitnick still the world's most famous hacker. As technology and code progressed, so did hacker culture. Hackers can find more ways of exploiting holes in software and remote machines; most things you would not even think you could hack, like a boiler system or an electric iron. Hackers can also find and release vulnerabilities that can be very useful for software engineers to know about and fix before those vulnerabilities cause even worse problems. Although hackers are commercialised as the evils of cyberspace, real hackers only want to learn more about a program and tend to be more helpful than problematic. While it is often true that hackers do commit malicious attacks, their acts should not be considered as part of 'hacker culture', something that originated from a place of curiosity and love for programming. By Ailin
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Updated: Oct 19, 2022
Background Maryam Mirzakhani was an Iranian-born mathematician and professor at Stanford University, born in Tehran, Iran. By her own estimation, she was fortunate enough to grow up after the Iran-Iraq war, when the political, social, and economic situation had stabilised, so she could focus on her studies. As a teenager, she showed her mathematical skills by winning gold medals in 1994 and 1995 in the International Mathematical Olympiad. Mirzakhani first gained her bachelor’s degree in mathematics from the Sharif University of Technology in Tehran in 1999 before going on to earn her PhD in 2004 from Harvard University. She then became a Clay Mathematics Institute research fellow at Princeton University before finally becoming a full-time professor at Stanford University in 2008.
Research Her PhD was concentrated on the topic of Riemann surfaces and by the time she became a professor, she was considered to be a leader in the fields of hyperbolic geometry, topology, and dynamics. Her contributions to her field also led to her being awarded a Fields Medal, often regarded as one of the highest honours a mathematician can receive, in 2014, in which the award committee commended her for her ‘outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces. She is the first and to date only female winner of the Fields Medal since its inception in 1936. Her technique involved using the moduli spaces of surfaces. In 2014, the Mirzakhani Society was founded by students at the University of Oxford, a society for women and non-binary students studying Mathematics at the university in which Mirzakhani met whilst visiting Oxford back in 2015. Mirzakhani also became a member of the National Academy of Sciences in 2016, which made her the first Iranian woman to be officially a part of the academy. Mirzakhani said she enjoyed pure mathematics the most, due to the elegance and longevity of the questions she studied. Death Mirzakhani was diagnosed with breast cancer in 2013 and unfortunately ended up passing away on 14 July 2017 (at the age of 40) at Stanford Hospital. Many paid tribute to her in the days following her passing, with Mirzakhani’s birthday (12 May) being agreed by the International Council for Science to be International Women in Mathematics Day. On 4 November 2019, it was announced that The Breakthrough Prize Foundation had created the Maryam Mirzakhani New Frontiers Prize which was to be awarded to outstanding women in Mathematics annually.
By Samantha and Saachi
- Mathematics
- 2 min read
Updated: Oct 19, 2022
Niels Fabian Helge von Koch (1870-1924) was a Swedish mathematician famous for his discovery of the Koch snowflake curve. The Koch snowflake is built-in iterations, in a sequence of stages.
Starting with an equilateral triangle, you create another, smaller, equilateral triangle in the centre of each side. This is repeated indefinitely, and during this, a snowflake shape would be created. The Koch snowflake is an example of a fractal curve (in fact, it was one of the first fractals to have been described), a shape that has a similar pattern at any magnification. For example, if you look at one part of the shape in its third iteration, you would be able to see a very similar structure at a later iteration, when the snowflake is magnified.
The Koch snowflake has quite unique properties: it has an infinite perimeter, but a finite area. As iterations happen infinitely, the perimeter and area keep increasing. With every iteration, the perimeter of the shape increases by a factor of 4/3. As the number of iterations tends to infinity, the perimeter keeps on increasing, reaching infinity. As the number of iterations increases, the triangles added get smaller and smaller. With the area, the snowflake would never exceed the area enclosed by the orange hexagon, as the triangles being added are so small. For this reason, the Koch snowflake has a finite area.
Following the same concept, many other mathematicians created variants of the Koch snowflake, using different initial shapes, angles, and planes. After many iterations, intricate and beautiful shapes can be created.
Tessellations can also be created using snowflakes of the same or different sizes. In the gaps, the same snowflake is created, demonstrating its repetitiveness and versatility.
The Koch snowflake is used to illustrate that ‘it is possible to have figures that are continuous everywhere but differentiable nowhere’. Fractals are used to understand important scientific concepts, for example, the way in which bacteria grows and brain waves.
By Samantha and Saachi
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