Paul Erdos

Hungarian born Paul Erdos is considered one of the greatest mathematicians of all time in society. As a young man, Erdos had to deal with the struggle of life as he endured the times of World War II. During this time, he came to a love of mathematics, solving multiple types of problems and gaining mastery on them. Throughout the rest of his life, he never was married, never truly lived in a house or had any possessions for that matter, and dedicated his life to solving more complex mathematical problems. He sought to teach the world more about mathematics and how it can help in life for more fruitful and interesting years to live. He was and still is loved by fellow mathematicians in today’s time as Erdos numbers were and are assigned to people, one would designate that the person actually consulted with Erdos to write a paper, and two would be assigned to someone who consulted with a Erdos number one person etc. In his true and pure dedication to the love of his life, mathematics, Erdos would travel university-to-university and door-to-door of other high-minded mathematicians and would want to learn from them or teach them constantly saying, “ my mind is open for thought.” Through his life, he made many extreme advances in mathematics and actually contributed to the learning and elements of Computer Science. These advances include those of combinatorics, his multiple mathematical theories and the graph theory.
One major contribution that Erdos gave to the computer science community was the idea and expansion of combinatorics which deals with the manipulation and probability of sets of numbers which can obviously be used in the idea of arrays in Computer Science such as Java and C#. This is the question of how many possibilities of numbers can be in a set and be arranged in a set and also how to make the set more favorable through manipulation such as moving numbers around and sorting them again a major part of computer science. This idea of combinatorics came into fruition in the seventeenth and eighteenth century in the statistics of games such as cards which is one of the cool aspects of usage of combinatorics in real life to predict card hands to see how many combinations of cards can be in persons hand at one time in games such as blackjack and poker. But, more importantly is the usage of combinatorics in computers and the immense amount of code that it has made without us actually knowing this. For example, such as previously stated, arrays can use combinatorics to manipulate it and its elements contained within it with the multiple possibilities of its elements if they are filled at random. Speaking of filling arrays and array lists at random, the Math.random when used with the index filling in for loops actually uses combinatorics as it puts an element in a random index which further creates randomness of order of numbers which is what combinatorics deals with. The sort methods such as BinarySearch and other manual searches also are contributed by combinatorics to find either elements that are the maximum, minimum, or target element that is desired to be found within a set that could be random which cuts down the amount of time to take in order to find the required element manually.
The main idea of combinatorics in computer science deals with the randomness of the elements in the set of an array such as for example, if one filled an array with objects of playing cards in a normal deck of cards randomly, how many possibilities could there be of the array in order? This would use combinatorics to find that the answer is 52!. Also, another idea of this subject is not just the dealing and finding of the multiple possibilities in a set of numbers or objects, but it also finds optimal ways to get from point A to point B in an equation through Boolean expressions and tables. To make this easier to understand, I will explain this in a normal easy problem to find the easiest way to solve a problem that deals with this simple idea. Let’s say one would want to go from Los Angeles, California to Tokyo, Japan by airplane. To find out the easiest, shortest, and most efficient way to get to the destination, the multiple amounts of possibilities would be analyzed and eventually, through Boolean expressions, one way would be determined to reach the destination the quickest. This is the same through computer science in wanting an optimal and desired number or outcome, and how through equation and such could one get to the desired outcome the quickest through the least amount of calculations to get there and can be achieved through the likes of Boolean algebra and Boolean logic. Another name for this process of finding the optimal and most efficient and quickest way to get to a desired outcome is called linear programming. This linear programming would cut down the run time of a project, which is always a want for programmers to finish as quickly as possible with the least amount of code used. Just from discussing these simple, yet very important ideas and concepts used in computer science, which have been contributed by combinatorics, one can see that Paul Erdos’ pure dedication to the further discoveries of certain topics that all subjects such as computer science have benefitted due to this. The advances made by Paul Erdos in mathematics was great in his lifetime as all he did for his whole life was work with numbers, create theories, and help make advances in the ideas and concepts such as combinatorics. This subject has effected the overall thought process of computers when working with arrays and searches by going through the arrays with binary search to find a desired number or object in that array or list. He was and still is considered one of the greatest and most dedicated mathematicians of all time that has contributed more to community learning grow in the field of mathematics than most other people have in their lifetimes. To go against and try to prove any of the theories or advances that have been given by Paul Erdos would require a great amount of information and to contribute more to the field of computer science and mathematics that Erdos did in his life would almost seem as a dream. Imagine, all Erdos would do was work out math problems and form theories and carry them out to contribute to not only math but to other subjects such as computer science and even sciences such as physics and chemistry. Just to think that one man would dedicate his life to solve mathematical problems and create theories is unimaginable, Erdos didn’t just contribute to computer science greatly through helping with the concepts of array lists and arrays and the optimal and quickest way to search through linear programming just by expanding on the current ideas of combinatorics. Also he created a numerous amount of theories in mathematics such as the prime number theory which he created that states that with any number greater than one, if one would double that number, there would be at least one prime number in between. This theory and many others would prove to be invaluable to mathematicians in the future.
Lastly, and one of the greatest feats and accomplishments that Paul Erdos provided not just only to mathematics but to computer science is that of the expansion of the idea of graph theory. This might seem as it could be a complex idea about graphs, but this is not so, it is the idea and the usage of graphs in multiple studies of computer science using graphs to sort and organize all of the computing data received through a user and even networks of communication. Ever heard of “the grid” referring to the multiple ways and sources to communicate within the Internet on the computer? Well a grid is exactly a graph and Paul Erdos helped expand on the ideas to help make a usage of graphs not only on paper to make a visual example of a mathematical problem, but to help organize the Internet and its ways of communication whether it’s through a social network or a business network. Paul Erdos helped extremely in the idea of communication in computer science and in today’s world with the explosion of users of social media websites. Also, especially in Java, one of the basic ways of learning and understanding code (which personally helped me throughout the year) was the program GridWorld that dealt with a simple bug in a grid (aka a graph) but it wasn’t as simple as it may have been perceived. This project had method calls, creating new objects, and even creating graphics on the screen when the program was ran and the visual of the bug on the grid would appear. This was all due to graph theory that Paul Erdos helped expand on tremendously. Overall, Paul Erdos was an amazing and dedicated man to the subjects of which he loved, mostly being that of mathematics and solving its many mysterious and challenging problems. He made a link between math and computer science through his discoveries of ideas such of that as combinatorics dealing with the multiple possibilities of the arrangement of elements in a list (or array) and helping the linear programming side of finding the optimal way to get to a desired answer or element within the array in the least amount of time as possible. Also, through the graph theory that Paul Erdos expanded on, this would prove invaluable to the computer science world through “the grid” or network of communicational organization, and through the helpful and understanding program of that of GridWorld which is a base program used to understand the computer language of Java.
Bibliography
Sources used:

* http://cr.yp.to/2005-261/bender2/GT.pdf copyright 2005, Edward A. Bender and S. Gill Williamson (pdf file) * http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter3.pdf
Dartmouth College Textbook (pdf file) * http://www.nndb.com/people/401/000032305/ copyright 2012 Soylent Communications * http://www.britannica.com/EBchecked/topic/191138/Paul-Erdos copyright 2013 Encyclopedia Britannica, written by Paul Hoffman