John Forbes Nash Jr.: Mathematician and Modern Genius

John Forbes Nash, Jr. will go down in history as a Math God of his time. His contributions to game theory, differential geometry, and the study of the partial differential equations paved a clear way for future mathematicians. He provided keen insight into the factors that govern chance and decision-making inside complex systems that we use in everyday life. It is because of Nash that today, we have a clear understanding of how to apply certain theories in math.

He’s the answer to that pupil who raises his hand and annoyingly asks “Why do we even need math?!”

He earned a Ph.D. in 1950 with his dissertation on non-cooperative games. The Nash embedding theorem is also one of his infamous contributions to math and his contributions to the theory of nonlinear parabolic partial differential equations and singularity theory. 

Nash served as the Senior Research Mathematician at Princeton during the later parts of his life. In 1994 he was the recipient of the Nobel Memorial Prize in Economic Sciences and recipient of the Abel Prize for his work on nonlinear partial differential equations. He is the only person to have ever received both words. 

Nash grew up in West Virginia living with a father who worked as an engineer and a mother who served as a school teacher. His parents got him involved in advanced math courses at local community colleges during his final year of highs school. He later attended Carnegie Institute of Technology majoring in chemical engineering. Later on he graduated in 1948 at the young age of 19 with a B.S. and M.S. in mathematics. 

Ten years go by and in 1959, Nash began to display signs of mental illness and was treated for paranoid schizophrenia. His continued improved but the illness continued. This was actually vividly illustrated in the biography by Sylvia Nasar titled, A Beautiful Mind; later on becoming a film starring Russell Crowe as Nash. Nash later passed away in 2015 leaving behind two sons and a longstanding understanding of mathematics. 

Credits: The image pictured in this article is from Wikipedia.

Real life uses of LCM and GCF

In math, the GCF is better known as the Greater Common Factor. The greatest common factor is commonly used to simplify a fraction by dividing both the numerator and denominator by the greatest common factor of both. This is very common in math computation when considering fractions. 

The LCM is better known as the least common multiple of the denominators. This is often called the lowest common multiple. It is helpful to find the lowest common denominator, since each of the fractions can be shown as a fraction with the denominator. When using addition and subtraction to compare fractions, it is useful to use the LCM. 

Now, considering your real life, did you even realize that LCM and GCF plays into your real life? Think about it…when dividing something equally, you subconsciously are using GCF and LCM. For example, when the children ask for slices of pie, a parent will divide the pie to equally among the children. Without even thinking of it in mathematical terms, you’ve used fraction formulas to solve a problem. And make the children smile!

Now, consider counting and dividing your money. When standing at the counter, you decide how to use certain amounts as fractions to get the job done. You consider dividing your money for the best utilization. For example, when spending, you are recommended to put aside a fraction of money to save, and a fraction to spend. 

You also use GCF and LCM in comparing prices. When thinking of buying a pound of bananas for a cheaper price, you’ll use fractions to determine which price is cheaper. You do this to save money and most times get the best bargain. Coupons also help save and this is also a real-life example of using GCF and LCM in your day to day life. 

Time…an element of life that we of course use in our daily lives. Understanding time, however, is just fractions! Think about how you determine time. When determining time, to learn the minutes of the clock, you determine the fraction of the clock. Without even realizing you’re using GCF and LCM, you are using fractions to determine time! Again, another real-life use of GCF and LCM.

So, when you hear someone tell you that math isn’t necessary, think twice! You use fractions in your everyday life, subconsciously. When considering time, money, comparing prices, and dividing items equally, you are using GCF and LCM. To learn more about GCF and LCM and, visit https://math.tools/calculator/lcm/ & https://math.tools/calculator/gcf/). The Math Tools website allows for you to learn more about fractions, numbers and computing both. 

Significant Numbers and Their Meanings

Math is particularly special because of the array of significant numbers. There are certain numbers and formulas that has likely stuck with you since high school math class – and they always will. Some of these significant numbers are necessary in certain computations. Some of these numbers are used in physics to help explain natural things, such as speed, and depth. 

Computations like the ration of a circle’s circumference to its diameter is universally recognized as pi. The significance of pi is that it is always approximately equal to 3.14159. For example, for any circle, when dividing that circle’s circumference by its diameter, it will give you the answer of 3.14159. Pi is an irrational number, meaning that its value cannot be precise, like a simple fraction. Pi is widely known in mathematical studies including geometry and algebraic equations. 

Sounds cool, right? To checkout more about the significance of Pi, visit https://math.tools/api/numbers/ and get lost in the meanings and significance of numbers! 

The power in numbers and how some have meaning should be recognized. For example, the speed of light, better known as C, computes at exactly 299792458 meters per second. The C stands for celeritas, which comes from the Latin word speed. The number is a universal constant in physics. The precise value is what makes it significant and has been studied for centuries. Understand that some of these numbers break down exact and were discovered by early day mathematicians who paved the way for an understanding of how to use numbers to measure.

Ever heard of the number to everything, also known as the number of the Universe? 42 is said to be the number of the universe, later known to the number of everything. It gets its significance from a famous radio show that eventually was turned into a novel then a movie “The Hitchhiker’s Guide to the Galaxy” by Douglas Adams delved into in the book, he wrote that the number 42 is “The Answer to the Ultimate Question of Life, the Universe, and Everything”. It is said that the answer was determined by the supercomputer Deep Thought after 7.5 million years of calculations. The number is considered a perfect number, which means a number that is a positive integer that is equal to the sum of the number’s suitable divisors.  The number 42 became a staple in math culture after the movie appeared in 2005. However, buzzfeed reported that Adams went on record to say it was all centered around a joke and he just randomly chose the number 42. The answer remains unknown. However, people still hold a great belief that there is some truth to the number 42 being the number and the answer to the universe. 

Some numbers are like household names, you’ll know its significance the moment you hear it. It becomes a natural knowing. In fact, pi is such a special thing in the math culture that it has its own day – March 14th (3.14) of every year is considered “Pi Day”. To learn more about significant numbers, checkout out https://math.tools/ . The website has built in calculators, math tables, information on formulas, flashcards and more! Math Tools is your virtual math tutor, right at the palm of your hands!

The meaning of Pi

As a child, you may recall learning about Pi in math class. Remembering the term may have triggered a smell of your grandmother’s baked pies. However, that isn’t quite what your math teacher meant during that lesson.

It was first called “pi” in the year 1706 by William Jones, the Welsh mathematician.  Pi is the first letter in the Greek word perimitros, which means “perimeter.”

Pi is approximately 3.142 and it is the circumference of any circle that is divided by its diameter. The word Pi comes from the Greek letter π. It is pronounced “pie” and is one of the most common constants in math.

To arrive at pi, you must correctly use the formula. The circumference of a circle is found using the formula C= π*d = 2* π*r. When using a calculator to compute pi, the results should always be approximately 3.14. 

Several math lovers have dubbed March 14 or 3/14 as the day to honor the infamous mathematical constant. However, unlike the date, Pi cannot be written like a fraction since it is an infinite number

Pi is usually used in the subjects of both science and math, but mostly associated with math. When determining the area or circumference of a circle or a round object, students use the Pi formula

No other math formula is as popular as Pi. It was discovered long ago that Pi turns out as an irrational number and its exact value is not known. However, its formula stands strong in mathematics for centuries. 

Teaching math in today’s century

If you’re a parent raising a child in the 21st century in the public-school system, you’re most definitely no stranger to the idea that the way math is taught has changed. The methods in which we were taught how to do math has significantly taken a turn and it’s no secret that some parents can barely keep up with their child’s math homework.

Like Shakespeare said:

Though this be madness, yet there is method in’t. – William Shakespeare

Here’s why: In several states, a new idea of Common Core State Standards was adopted to create a new and improved (so, the government promised) way of how we taught young people in this country. Common Core State Standards is an initiative that began in 2010 that details how students in grades K-12 should understand and learn English language arts and math at a certain level.

Common Core math standards has received much criticism over the years. The common core standards offer a new approach. What it does is a bit more complicated for students, parents, and even educators. Common Core State Standards, especially in math, created a national uproar. What is happening in math is an emphasis more on concepts of understanding the numbers and problems. The breakdown of numbers has become more explicit and takes more time to solve problems. This became a challenge and created an evolution in mathematics.