Happy Birthday Numero Unus

Today is the birthday of Theodore Olivier born 1793 in France. Olivier was a mathematician who specialized in geometry. He is known for his string models of ruled surfaces.

Today's quote is by Al Jolson, Billy Rose, and Dave Dreyer.

"Like wall paper that sticks to the wall

Like the seashore clings to the sea

Like you'll never get rid of your shadow

You'll never get rid of me

Let all others fight and fuss

Whatever happens, we've got us

We're closer than pages that stick in a book

We're closer than ripples that flow in a brook"

There are many problems that deal with shadows. Usually these problems use the relationships found in trigonometry or similar triangles. I have listed below three of my favorite shadow problems,

1) If I am 6 feet tall (in my dreams) and I cast a 5 foot shadow, how tall is a flagpole that casts a 10 foot shadow? Answer: 12 feet

2) A street light is mounted at the top of a 15 foot pole. I am walking away from the pole at a rate of 5 ft/second. How fast is the tip of my shadow moving when I am 40 feet from the pole? Remember: I am 6 feet tall. :-) Answer: 25/3 ft/second

3) My favorite problem that applies the use of shadows is the calculation of the Earth's circumference by Eratosthenes over 2000 years ago. Eratosthenes estimate was 25,000 miles. The actual circumference is 24,902 miles.

Today, I complete my Sibling Bond series. My previous blogs were tributes to my sister and younger brothers. The day to day conflicts and agreements with these three siblings acted as a rock tumbler, shaping and polishing me in my progression to adulthood.

Today is my brother, Russ' birthday. Today, he is a decade older than I am. Unlike my other siblings, Russ was a comet, following an unpredictable, elliptical path that when his intersected mine, his effect on my growth was more transitory but not any less impactful.

Russ was sixteen when I was six. The memories of my family became more distinct for me at that age. My younger brothers were energetic, four year old playmates and my sister was the ever present baby sitter. My brother, however, had his driver license, was involved in sports in high school, and was working with my father in his shop. He flew in my view like a bird at my window feeder, who departs to locations unknown as soon as I am aware of its presence.

I treasured any time I had with him. I adored this mysterious, independent, good natured brother. He occasionally included me in his excursions. I was oblivious to the task at hand and eagerly followed behind at a pace that could quite never keep up to his confident gate. I recall many times that I was introduced to his friends, as "his little shadow", a description that caused me to grin and swell with pride.

When I was nine, Russ was a senior in high school and his orbit grew. I saw him less often but desired his attention even more. During this time, I was watching shows such as Dennis The Menace and the Little Rascals. Each of these shows had booby traps involved in their plots. I was captured with the idea of setting traps and Russ became my victim. For a period of three months, a series of pranks greeted him when he came home from his late night excursions. As he entered his room, a barrage of novelties fell from a precarious bucket perched at the top of the door. Books, shredded paper, and water were all items that landed on my brother's unsuspecting head. Throughout this period of time, Russ never raised his voice. He took it in stride. He was patient with his annoying brother.

I became a teenager in the early 1970's and Russ was in his early 20's. He invited me to stay with him in Minneapolis for a weekend. I recall walking through Dinky Town, encountering the sights, sounds, and smells that defined the 70's. Those sensory inputs opened the eyes of this naive, small town kid. That evening, we decided to go to a movie. Our choices were: Magnum Force, Paper Moon, The Paper Chase, and Papillon. We chose Papillon. The night ended, falling asleep while watching Rat Patrol, and I, dreaming of my urban life.

As I have grown older, Russ is no longer the super hero that I thought he was when I was younger. He, like us all, is flawed and complex, but he is wise. He is patient and calm. He has the gift of diminishing my failings and applauding my achievements. He is someone I aspire to be.

As I write this blog about my brother, I am surprised about the details I can recall about our times together. I feel his interactions with me were intentional. I believe he wanted to impact me differently than what I experiencing at home.

I have learned from him that family allows its members to find their own way and encourages them to stitch their own block on the family quilt. He has taught me that family welcomes all its members, and, if necessary, rejoices on the return of its members to the fold, and that as members of the family, we should refrain from casting judgement.

Happy Birthday Numero Unus!

O Tannebaum

Today is the birthday of mathematician, Mary Cartwright, born 1900 in Aynho, Northamptonshire, England. Cartwright was the first woman mathematician to be elected to the British Royal Society.

Today's quote is from The Littlest Christmas Tree: A Tale of Growing and Becoming by Janie Jasin. "Thank you, Dear Creator, for Life. Thank you for Dreams. Thank you for Ideas and Thoughts and Feelings. Most of all, thank you for choosing me to grow - just for today - and to know the wonder of Your World and its many Possibilities."

A tradition that has been established in our family is the assembly and decorating of our artificial Christmas tree on the day after Thanksgiving. Early in our marriage when my wife and I were hanging the lights on the tree, I noticed I struggled with the project. My placement of the lights as we circumnavigated the string about the tree just wasn't quite right. I had too many lights in the back of the tree or the plugin wasn't situated in accordance to our electrical outlet. As my children grew older, I happily abdicated my role of string assistant to more capable and eager hands.

This year my eldest son, Jacob, asserted his birthright, erected the tree, and hung the lights. I assisted. I had been on administrative leave for about 25 years and I thought now is the time for redemption. I thought, "I can do this!" I also searched for another moment to atone for those instances that I was less than the parent I should have been. Jake is my practice child. What I mean is that I practiced being a parent on him.  There are several classes of students that graduated from Lake City Lincoln High School that I was allowed to practice on prior to my first teaching job. I did not have that convenience with Jake. I made mistakes. Mistakes that I still regret to this day. Our relationship has become more than father and son. We have become friends. He has become my confidant. I value his opinion. I look forward to our time together. I look forward to moments of redemption.

He had progressed to the finality of the tree construction when I began this annual event. Quickly a philosophical discussion emerged between my wife and son as to where to start the string of lights. 

"At the bottom," my wife insisted, "closer to the power source. The plug should be on the bottom right."

"At the top," countered my son, "next to the star. It can guide me to that source."

 My wife relented. Sometimes perseverance can appear as stubbornness.  Jacob and I weaved the lights counterclockwise about the tree. This weave appeared as a dance - a dance of a couple in which one is trying to lead and the other, not confidant in the placement the of step or the rhythm, is trying to follow. After a few rotations, a pirouette, and a few string entanglements, Jacob stopped me. "Dad, you're hanging them too low and you need to wind them around the tree so the strings rise and fall. They should make a wave", he instructed. I grew silent. "Dad, are you ok? Are you upset?", he inquired.

"No, I'm ok", I responded. He paused and placed the bubbler in the center of the tree. He regrouped, "Are you thinking about math?"

I smiled slyly. He sighed.

When we were done, he began hanging his ornaments. The ornaments that he was carefully placing on the tree marked his life. My wife and I choose ornaments for each member of the family that signify an event that we view as significant for that year. These ornaments have accumulated for the past 29 years.They can represent moments as exhilarating as birth and marriage or as humbling as rowing a boat across a lake after the motor stopped running.  Each member has their spot on the tree where their bauble is placed. These assortment of symbols, delicately removed from their containers and carefully hung above and below the periodic function of string of lights that winds itself, top to bottom or bottom to top, (depending on your view) around the tree.

His phrase "rise and fall of the strings" resonated in my mind. I have never thought about the mathematics in a Christmas tree. Years ago, I taught seventh graders. During this time of year, I taught prime factorization I would croak the tune "O Tannebaum" and insert the words "O Factor tree, O Factor tree, How beautiful are your factors!". The tree is obviously conical in shape and and the Greeks had described parabola, circle, ellipse, and hyperbola as planes intersecting a cone, but those words, "rise and fall" kept haunting me.

I searched for mathematics in the seemingly infinite Google search engine and found Treegonometry, a series of mathematical formulas that would compute the "perfect" amount of trimmings for ideal Christmas tree. These formulas were derived by students at the University of Sheffield in the United Kingdom. The formulas are as follows:

1) Number of ornaments = Square Root of (37) ÷ 20 x (height of tree in cm)

2) Length of tinsel (cm) = 13 x pi ÷ 8 x (height of tree in cm)

3) Length of lights (cm) = pi x (height of tree in cm)

4) Height of star/angel (cm) = (height of tree in cm) ÷ 10

A six foot tree would 37 ornaments, 919 cm of tinsel, 565 cm of lights, and a star that is 18 cm tall.

I realized in my blog, The Circle of Geometry, I had described the helix as my best symbol of life and there was helix of lights that wound about the tree but this helix, as life, is more complex.

Above, I have provided a top view of the lights and a three dimensional view of the lights traversing the tree. The top view is a spiral. The second view is a conical compression spring often referred to as a tapered spring. I have seen these springs in faucets, holding in the gaskets. The advantage of these types of springs, is the stability they provide when placed on structures such as battery contacts or push buttons. Does the spring start at the bottom or the top?

In my son's description of "rise and fall" and "make a wave", he was expressing the sinusoidal curve which can be shown by stretching a spring.

Unlike the helix, I described in a previous blog, this tapered spring is a better symbol of life, with one addition. I would include "the rise and fall" of the spring as it rotates about its axis. The "ups and downs" that we encounter each day add to the overall wisdom we gain as each year passes.

The tapering of the spring represents the acceleration of time. When my children were born, my wife and I were excited about the brief celebrations of solid food, walking, no diapers, and eventually, no daycare. The time before each of those events were anticipated and calculated.

As a child, the days before the holiday break and ultimately, Christmas, could be excruciating long. I marked the days on my calendar and again, those days were anticipated and calculated.

My first year of teaching was, in my mind, the longest of my career. I made the mistake of marking each day of school and highlighted my last day of the year. Calculated? Yes. Anticipated? Very much so.

Now, I don't measure the day. I do not look forward to the last day of school. I don't calculate and I avoid anticipation.

My parents are in the twilight of their lives. They have often remarked about how time has quickly passed. As the tapered spring reaches the apex, time is rapidly revolving.

I believe the wavy tapered spring is life. As each year turns, and each experience raises the rotation, the circumference of the circle becomes smaller. Time shortens. Opportunities to mend torn moments pass by. Children become adults. The time spent with them becomes rarer and more treasured.

The Dark Side of Math: A PHS Gopher Tale

Today is the birthday of Lene Hau born 1959 in Vejle, Denmark. Hau is famous for her experiments to slow down light. Her team was able initially slow light to 17 meters/second and, in 2001, were able to stop light to one-thousandth of a second.

The first quote of the day is from Steven Wright. He quipped, "It doesn't matter what the temperature of the room is, it's always room temperature."

The second quote is from Brian Holland, Lamont Dozier, and Eddie Holland.

"It's like a heat wave

Burning my heart (it's like a heat wave)

I can't keep from crying (it's like a heat wave)

It's tearing me apart"

When I was in high school, I was a self absorbed student that waffled between nonconformity and the compliance of peer expectation. I liked mathematics and was a motivated student in that subject, but I was rather fickle in other subject areas--my motivation was dependent on the connection I formed with my teachers.  I made strong connections with my Language Arts teachers but not so much with my science teachers.

I also had a fear that I was underprepared for the rigors of college and that fear drove me to take an array of academic classes. One of those classes, German, I studied my junior year. I was really not aware of what I was getting my self into and very quickly, I was in a conundrum. Learning a foreign language was, well, foreign to me. I was already struggling with the verbal portion of the English language. Why did I think that speaking German would be any different? In addition, I had to memorize. I don't learn by rote. I develop connections that lead from one point to another. Some people believe these connections are linear, but I view them as a web. When I encounter a new idea it vibrates a single string and the entire web pulsates. That pulsation allows me to find the connections to other concepts. This process wasn't working for me in German. I struggled with Der, Die, and Das. I was briefly gratified to find out that these articles are assigned to the gender or neutrality of the subject but was as quickly mortified to realize there are a seemingly endless assortment of exceptions to the rule.

In addition, I was required to join German Club.  German Club was more than a social club for the students. The underlying purpose of the club was to market world language and a student exchange program, AFS. I am not typically a joiner and I was a reluctant participant. This reluctance was transformed to paralyzing dread when I found out I was a founding member of the Schottische Dancers. Our first public performance was surprisingly witnessed by a large audience that included my younger brothers and girlfriend.

This combination of attitude, self prophesying  experiences, and personal characteristics that included cantankerousness and defiance contributed to a student that simply did the minimum requirements. I was complacent but had an underlying frustration that was waiting for its moment to surface. That moment came when the class discussion moved to the measure of temperature.

 Temperature was not new to me. In my mathematics classes, students were already taught how to convert Celsius to Fahrenheit and vice versa. My mathematical education also include that each resulting formula was an inverse of each other, a reflection over the line y = x, and an intersection at -40°. I ask you to examine the table of temperatures.

My German teacher was demonstrating how to convert Celsius to Fahrenheit using the formula, F = 9/5C + 32. She was selecting nice, positive values that were divisible by 5, 15°C = 59°F, 10°C = 50°F, and 35°C = 98°F (body temperature). She was on a roll but then a mistake. "As you notice students", the youthful teacher quipped in a confident, almost "cocky" air, "the Celsius temperature is always a lower number than Fahrenheit." My head perked up. I raised my hand. She smiled in the achievement of drawing me in, yet another mistake. "Could you convert -40°C for me", I inquired. "Negative numbers?", she murmured, somewhat shaken. "I can do this", she responded energetically. "Uh, the answer is ... -40°F that's not possible, I must of made mistake. Give me another one." Eagerly, I made my play in the game. "Oh, how about -50°?" I inquired, again. "-50°C is ... oh, my, a -58°F, how can that be?" she responded with sweat on her brow and a quivering lip. The blinds rattled  ominously above the closed windows. I leaned back, closed my eyes, and let the piranha feast.

Our German teacher wasn't in class until the following Monday. I don't know if her absence was the result of the failed lesson plan on temperature, the loss of credibility with our class, or a preplanned absence. On Monday, she retaught the lesson and explained how negative numbers had impacted her calculations. She did admit she needed a brief lesson from a resident math teacher. I am sure that with each preceding year, she used this experience as a building block to advance her teaching skill.

Celebrating the Conjugate Twins

Today is the birthday of Richard Schoen born 1950 in Celina, Ohio. Schoen is a notable mathematician that has made contributions in the area global differential geometry. In a collaborative effort with Shing-Tung Yao, he proved the fundamental positive theorem in general relativity.

Today's quote is from the cat in The Cat in the Hat by Dr. Seuss.

"... 'I will show you

another game that I know!'

and then he ran out.

and, then, as fast as a fox,

the Cat in the Hat

came back in with a box.

A big red wood box.

It was shut with a hook.

'Now look at this trick,'

said the cat.

'Take a look!'

Then he got up on top

With a tip of his hat.

'I call this game FUN-IN-A-BOX,'

said the cat.

'In this box are two things

I will show to you now.

You will like these two things,'

Said the cat with a bow.

'I will pick up the hook.

You will see something new.

Two things. and I call them

Thing One and Thing Two.

These Things will not bite you.

They want to have fun.'

Then, out of the box

came Thing Two and Thing One!' ..."

I teach the idea of conjugates quite often in my classes. Conjugates are two arithmetic expressions that involve two values. As an example, let's suppose I use the two values, 9 and 5. Conjugates using these two values would be: 9 + 5 and 9 - 5. Conjugates are simply two expressions that are formed by adding and subtracting the values in the same order. Conjugates can be generalized to a + b and a - b whose product becomes a^2 - b^2 which math geeks refer to as the difference between squares. A few examples of conjugates that are utilized in mathematics are: confidence intervals (statistics), complex solutions (analytical algebra), and rational expressions containing square roots (limits/calculus).

Today has always been a special day for me. As a child, this day signified the beginning of the holiday season. I marked these dates on my calendar: October 23, October 31, November 22-28, December 25, and January 1. I am sure that four of the five dates listed are obvious to the reader and many may presume that with a mathematics background that I am championing today's date as Mole Day, but the reality is today is my brothers' birthday. I have brothers that are identical twins.

In fact, my brothers are mirror twins. Bruce is right-handed and Bill is left-handed. When I study their facial features, Bruce resembles my mother's side of the family and Bill, of course, my father's. On their birthday, my mother would make a white angel food cake for one and a chocolate devils cake for the other. I was in culinary heaven, two slices in one day! The holiday season had begun!

I have always felt their relationship is one of the strongest I have every encountered. My sons have often mentioned that when Bruce and Bill are together, the sum is much greater than the parts. In my classes, I use stories of my family to form connections to mathematics. I refer to Bruce and Bill as the conjugate twins.

In my blog, The Fabulous Five, I noted that the interactions we have with our siblings shape our personalities. My grandmother would describe to me the befuddlement that overcame me as a toddler when my mother came home with twin babies. I don't really know how much I understood of the complexity that just entered my life as a 18-month-old child, but I would agree their births changed my life significantly from that moment. I was transformed in a short period of time from the baby of the family to something different, not necessarily the middle child but not exactly the oldest either. Like Thing One and Thing Two, two creatures had entered my domain that would bring a new thrilling energy that was a mixture of frustration, fear, and sheer enjoyment.

My brothers became my playmates and my rivals. In the next 16 years, I learned to be competitive, cooperative, assertive, compromising, creative, imaginative, empathetic, and manipulative. We were explorers, warriors, athletes, and builders. We crawled through culverts, shot imaginary intruders with sticks and broken baseball bats, and played endless games of baseball and football. Our teams were easily decided--the twins versus me. We adjusted rules so that two-on-one games were possible through a series of arguments and heated discussions. Any disputes evaporated in our nightly dreams and we began each day anticipating a renewed adventure.

Today, I will celebrate the birth of the Conjugate Twins, Bruce and Bill. I will raise a toast in their honor, give them a call, and enter the holiday season thankful for the impact they have had in my life.

Happy Birthday Sis!

Today is the birthday of Boris Bukreev born 1859 in Lgov, Kursk gubernia, Russia. Bukreev worked in the areas of algebra, mathematical analysis, calculus of variations, differentiable geometry, and complex variable functionality.

Today's quote is from Persi Diaconis relating his transition from a magician to a mathematician. He recalls, "I thought I could do anything...So I bought William Feller's Introduction To Probability Theory and Its Applications and I thought I would just read this book. And I couldn't read it. I didn't know calculus, or at least not enough."

Persi Diaconis

I first discovered Persi Diaconis when I was assigned to give a presentation on a current mathematician in a History of Mathematics course I was taking. I was immediately caught up in his life's journey. He was born January 31, 1945 in New York, New York. His parents were musicians and as a young child he studied violin at Juilliard School in New York. He was interested in mathematics but also highly motivated in the area magic. He used mathematics in many of his magic tricks. He was on track to graduate high school at the age of 15 but dropped out a year earlier to pursue a career as a magician. He eventually left his career in magic, went back to school, and received a doctorate in statistics from Harvard University. Diaconis mathematical pursuits are widely divergent. He has written books and papers ranging from group representations in probability and statistics to Markov chains. In 1992, with Dave Bayer, Diaconis proved that the maximum number of shuffles need to riffle shuffle a deck of cards is seven. By comparison, the overhand method of shuffling would take 2500 shuffles to randomize a deck of cards.

Today is my sister's birthday. Marilyn is my only sister and although she looks younger than I, she is seven years my senior. In fact, for much of my preadolescent years, she raised me. I believe her structured guidance was due to my mother's needed attention to my younger brothers. I was a challenging child. I had three noticeable characteristics. I was defiant. I was stubborn. I was argumentative. These notable traits did not go unnoticed by my teenaged sister and many times we butted heads.

I have written previously about the sibling bond and my sister did instruct and direct me to paths that I still travel on to this day. She taught me how to twist to Chubby Checker and she spent an entire afternoon with me detailing the intricacies of riffle shuffling. Most importantly, the summer before my ninth grade year, she pulled me aside, and we had a long talk about what to expect in high school. I have forgotten many of the details of that conversation but one bit of advise has impacted me to this day. She suggested that I get involved in school. She felt that although academics were important, being involved in school activities outside of the classroom would energize me, create an enjoyable experience, and build healthy relationships. I think that her suggestion planted the seed that later grew into my desire to be a teacher. As I reflect on our conversation, it was a touching moment between a twenty-something woman and a teenage boy. I think she was aware that I was a socially awkward introvert that needed a gentle push or more appropriately, to be placed in her hands and riffle shuffled, not seven times, just once.

We receive many gifts as we journey through life. Some gifts come wrapped in bows and boxes on holidays. Some gifts pass us as we wander unaware in this passage of time until we pause and gather our senses. Today, I celebrate one of my gifts.

Mona smiles at a wrinkle in time

Today is the birthday of Jurgen Moser born 1928 in Konigsberg, Germany. Moser was a mathematician proficient in techniques applied to Hamiltonian dynamical systems and generated the "Moser Twist Stability Theorem".

The quote for the day is from Madeleine L'Engel in A Wrinkle in Time. "I don't understand it any more than you do, but one thing I've learned is that you don't have to understand things for them to be."

I recently traveled to France, spent some time in Paris, and had the opportunity to journey to the southern regions of the country. This blog will be a summation of my observations through the tinted lenses of a mathematics cheerleader.

One of the stops touring Paris was the marker, Point Zero. Point Zero is the spot in which all distances from Paris are measured. The distance from Minneapolis, Minnesota to Paris, France is 4203 miles.

Point Zero

The path of a flight from Minneapolis to Paris is an arc that is a portion of a great circle. This arc is called a geodesic.

A great circle is the concept of a line in spherical geometry. Spherical geometry has applications in navigation and astronomy. This type of geometry is termed Non-Euclidean geometry which considers the Euclidean axiom of parallel lines.

Another perspective that I have of point zero is the concept of the origin. The term origin can conjure many meanings. On a Cartesian coordinate system the origin is where the horizontal line (x-axis) and the vertical line (y-axis) meet. This point is designated by the ordered pair (0, 0). Similarly, the Earth has a horizontal line (equator) and vertical line (prime meridian) which intersects in the Gulf of Guinea in the Atlantic Ocean. This point is designated as 0° latitude and 0° longitude.

                           Prime Meridian                Equator

The Mathematical Origin

I also visited the Louvre. The Louvre is massive and impressive but I found a treasure chest of mathematical and scientific wonderments in rooms that displayed items owned by King Louis XIV.

Compasses and Calipers      Directional Compasses

Miniature Sundials              Globes and Telescopes

Microscopes                               Scales

Sextants                         I Have No Clue :-)

The painting, Mona Lisa, created by Leonardo da Vinci hangs in the Louvre and is one of most popular sites. Not only was Da Vinci an artist but he also was a scientist and mathematician. In mathematics, a controversial numeric value is the "Golden Ratio". The Golden Ratio is computed from the following proportion: (a + b)/a = a/b which simplifies to the equation a^2 - ab + b^2 = 0. The solution for this quadratic equation is (1 + sqr(5))/2 or 1.61803398875 (this decimal is an approximation since the golden ratio is an irrational number). This ratio is historically called the ratio of beauty and most famous works of art and architecture supposedly have that particular ratio embedded within them. A "Golden Rectangle" has its ratio of longest side to shortest side as an approximation to that ratio. A "Golden Spiral" is a graph of a logarithmic equation that has the Golden Ratio as its growth factor.

The "Mona Lisa" at the Louvre

The legs of the blue triangle originate in the bottom corners of the painting and bisect the width of the top of the painting. The Golden Rectangle is placed on the left side of the painting with its width progressing across the top of her head. The end of that segment lies on the right side of the triangle. The Golden Spiral frames her face.

When I was in sixth grade, I bought the paperback version of A Wrinkle In Time by Madeleine L'Engel. In fact, I still have it. A quote from the book has stayed with me for a long time. A character in the book, Charles Wallace, explains a tesseract in the following manner, "Well, the fifth dimension's a tesseract. You add that to the other four dimensions and you can travel through space without having to go the long way around. In other words, to put it into Euclid, old-fashioned plane geometry, a straight line is not the shortest distance between two points."

Recently, I watched the movie, Interstellar. In this movie, an astronaut explains the concept of a wormhole. In the explanation, two points are drawn on a piece of paper and a straight line connecting them. The paper is bent so that the two points coincide and a pencil is punched through both holes. That punch represents a wormhole, a portal, which connects one dimension with another.

Towards the end of my stay in France, I had the opportunity to visit an old friend from high school. Jean was an exchange student from France my senior year. We became good friends and previously had seen each other about 20 years ago. There was no rekindling of our friendship, we are still great friends. Our conversations were like we had corresponded consistently for 39 years but in actuality, we hadn't. I have had a few friends in which time has placed a wormhole, in which the tapestry of our lives was folded and 1976 and 2015 became one. The shortest distance between two points is not a straight line.

France: Day 17- Cedric Villani

Today is the birthday of Alexis Bouvard born 1767 in Contamines, Haute-Savoie, France. Bouvard is famous for the mathematics he used to discover Neptune.

The quote of the day is by Cedric Villani. In his book, Birth of a Theorem, A Mathematical Adventure, he writes, "Far from moving swiftyly between two points, in a straight line, the mathematician moves forward haltingly, along a long and windy road. He meets with obstacles, suffers setbacks, sometimes he loses his way. As we all do from time to time."

Cedric Villani

Cedric Villani was born 1973 in Brive-la-Gaillarde, France. Villani is currently working on partial differential equations and mathematical physics. He was awarded the Fields Medal in 2010 for his work on Landau damping and the Boltzmann equation.

In the April 14, 2015, edition of The New Yorker, an article entitled The Lady Gaga of French Mathematicians Comes Stateside by Thomas Lin, Lin quoted Villani, "We (mathematics) are the most hidden of all fields. We are the one that typically interact the least with the outer world. We are also the field which is the most emblematic of revulsion in school."

Geoffroy Clavel wrote in the May 7, 2014 edition of the Huffington Post, an articled entitled Cedric Villani, 'The Lady Gaga of Mathematics' Wants To Bring The Joy Of His Discipline To Everyone. In the article, Clavel describes Villani as the current ambassador of mathematics. Villani not only loves mathematics, "he also wants to convince the wider public that this dry subject can be fascinating - - as long as you know how to talk about it."

I have another item to add to my bucket list, meeting Cedric Villani, perhaps on my next trip to France. Passez une bonne journee mes amis, jusqu'a la prochaine fois.