Blaise Pascal was born on June 19, 1623, in central France. As a child, Pascal was often unwell, and this sickly nature would stay with him throughout his life.

Pascal’s father, Étienne Pascal (a member of the *Noblesse de robe*), moved to Paris with his children in the early 1630s. There, Étienne focused on furthering the education of his children. He believed that if he exposed his son to mathematics, Pascal would become so enthralled that he wouldn’t be able to focus on other subjects. To attempt to give Pascal a balanced education, Étienne held off on his son’s study of mathematics.

Unsurprisingly, this seemed to have the opposite effect on the young Pascal, who simply began to teach himself about math. On his own, Pascal apparently found that a triangle’s interior angles add up to the sum of two right angles. Since trying to delay Pascal’s mathematics education was obviously not working, Étienne eventually gave in and started teaching his son the subject.

*Blaise Pascal. Image in the public domain in the United States, via Wikimedia Commons.*

Impressed with Pascal’s skills, his father introduced him to an academic circle in Paris called the *Académie libre* when Pascal was around 13 years old. This was the start of his involvement in the academic community. Throughout his life, Pascal would pursue both academic and religious knowledge, producing important works in both areas. While Pascal was a master of the written word and is known for his *Lettres Provinciales* and the *Pensées*, we focus on his various academic works here.

When Pascal was 16 and involved in the *Académie libre*, he presented a one-page essay called the “Mystic Hexagram”. The paper stated that if a hexagon is inscribed within a circle or conic, then the intersection points of three opposite sides will reside on a line (now known as the Pascal line). This work contributed to the field of projective geometry and is known today as Pascal’s theorem.

*Pascal’s theorem. In this example, the intersection points B1, B2, and B3 are collinear. Image in the public domain, via Wikimedia Commons.*

Another goal of Pascal’s was to make mathematical calculations quicker and easier. The idea began when Pascal observed his father working on taxes. This caused Pascal to wonder: Could he invent a device to simplify this process? Eventually, Pascal designed the *Pascaline*. This early calculator was capable of performing additions and subtractions via movable dials or gears. Pascal would continue to work on this device in the years after he created it.

*A Pascaline. Image by Mirko Tobias Schaefer — Own work. Licensed under CC BY-SA 2.0, via Wikimedia Commons.*

Another area that Pascal is known for is the study of probability. In this field, Pascal came across a couple of probability and gambling questions; in short:

- How many times do you have to throw a pair of dice before you can expect to get two sixes?
- If a wager game of dice isn’t completed, how can you divide the stakes?

Intrigued, Pascal set about solving these problems and discussed his answers with the mathematician Pierre de Fermat. Pascal and Fermat’s exploration of the topic enabled them to develop the basis of the modern theory of probability.

Related to this is Pascal’s paper *Treatise on the Arithmetical Triangle*, which discusses what is known today as “Pascal’s triangle”, a tool that can be used to solve such probability problems. While Pascal was far from the first to discover this triangle, he helped further our knowledge of it.

Interestingly, dice were not the only modern gambling-related tool Pascal was involved in. While trying to invent a perpetual motion machine, Pascal also created an early version of a roulette wheel.

Besides mathematics, Pascal was also interested in a variety of other subjects. For example, he was inspired by work from Evangelista Torricelli to investigate pressure and the existence of vacuums. Pascal ran experiments using mercury barometers to investigate atmospheric pressure. Using some of the findings from this work, Pascal wrote *New Experiments Concerning the Vacuum*, which suggested that a vacuum existed in the barometer tube.

In addition, Pascal’s hydraulics and hydrodynamics work led to him developing a syringe and hydraulic press.

Today, you can find mentions of Pascal in many different places. Just a few of his namesakes are the standard unit of pressure, the pascal (Pa); Pascal’s principle or law; and the Pascal programming language developed by Niklaus Wirth in the 1970s.

Happy birthday, Blaise Pascal!

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Henry Darcy was born on June 10, 1803, in Dijon, France. His father was a tax administrator who passed away when Henry was 14, leaving young Henry’s mother to raise him and come up with the funds to send him to school. In 1823, Darcy enrolled at the L’École Polytechnique in Paris. From there, he entered the School of Bridges and Roads.

*Henry Darcy. Image in the public domain in the United States, via Wikimedia Commons.*

In 1826, Darcy earned his degree in civil engineering and joined the Corps of Bridges and Roads. Rather than stay in Paris, the young engineer returned home to Dijon, where he thought he could do the most good. Based on the talent and insights he’d demonstrated as a student, the Corps tasked him with solving Dijon’s major problem: The city was infamous for having an ongoing water shortage, and the water Dijon *did* have was poor in quality. Darcy set out to design a system that would help sustain his hometown — and ended up doing much more than that…

Many engineers before Henry Darcy had tried to design a water supply system for the city of Dijon, but the design plans always had significant flaws. Darcy was assigned to work on a well drilling project in 1828 that led to only a modicum of success. Water was found, but there wasn’t enough to go around for Dijon’s entire population. Instead of feeling defeated, Darcy took it upon himself to find a way to supply the city with water from a clean, reliable source.

After researching and learning from previous design plans that had failed, Darcy plunged into studies of fluid flow. He experimented with different material for pipes, analyzed water flow across the landscape, and ran filtration tests and field experiments in open channels. In this way, he gained a better understanding of velocity, slope, and cross-sectional area and how they are related. Later, he would develop these findings into the Darcy-Weisbach equation, which addresses pressure and head loss in pipe flow. He was also able to provide theories that explained why a well’s water production changes seasonally, and how water pressure causes artesian wells to occur.

*A water fountain in the Jardin Darcy in Dijon, France. The garden is built on a reservoir. Image by Arnaud 25 — Own work. Licensed under CC BY-SA 3.0, via Wikimedia Commons.*

In 1834, Darcy revealed his plans for the public water supply, which consisted of a 13-km aqueduct running under the city that could transport water from the Rosoir Spring to enclosed reservoirs in Dijon. With a series of distribution lines, water could be provided to buildings, hydrants, and fountains. The system relied on gravity, which meant water pumps weren’t needed. As a means of purifying the supply, Darcy used mostly sand as a filter.

Sure enough, the experiments paid off and the water supply designs were successful. The project was completed 10 years later, 20 years before Paris installed a similar service. Darcy’s system supplied water to hospitals and municipal buildings all over Dijon. He also designed a series of fountains (142 fountains spaced 100 meters apart) that varied in shape and height while running, which was quite a feat for the time period.

Due to the resounding success of Henry Darcy’s water system and other urban renewal efforts, he became the chief engineer for the department of Côte-d’Or and was appointed to an even higher position in Paris as the chief director for water and pavements. In these roles, he devoted much of his time to further hydraulics research. One of the results of this research is Darcy’s law.

Because Darcy had performed so many experiments with groundwater movement, he started thinking about the way fluid flows through sand and soil. He discovered that the fluid flow rate in a porous medium is proportional to the hydraulic force applied to it. This principle is now known as Darcy’s law.

Also related to Darcy’s study of porous materials is a surface’s permeability, or the measure of a porous medium’s ability for fluids to pass through it. The unit of measurement for fluid permeability is called the *darcy*.

Besides the water system, Henry Darcy devoted his engineering skills to other public service projects. One of his major accomplishments was putting Dijon on the map as a destination by constructing a railway line from Paris to Lyon. In the past, Dijon had been bypassed because mountains and other geographical obstacles proved too difficult to travel through. Darcy was not discouraged: After consulting with a geologist, he showed his engineering prowess by digging a 4-kilometer tunnel through the mountains.

Darcy’s mission to improve quality of life had a ripple effect. By introducing the new water system, he made Dijon a pioneer in technology that led other cities to follow its example. Today, the groundwork he provided contributes to continuing improvements in water resource management.

As a civil servant, Darcy thought more about the people who could benefit from his work rather than his own personal gain: Upon completing the Dijon water system, he was offered a payment of 55,000 francs, which would be worth over $1 million today. He wouldn’t take a franc of it and, at the public’s insistence, accepted a medal instead.

*A bust of Henry Darcy, located in the Jardin Darcy in Dijon, France. Image by Christophe.Finot — Own work. Licensed under CC BY-SA 3.0, via Wikimedia Commons.*

For these reasons and more, Darcy is widely celebrated. The first public garden in Dijon, built on top of a reservoir, is named after him. If you’re ever in Dijon, stop by the *Jardin Darcy* and admire the monument built in his honor. Until then, join us in wishing Henry Darcy a happy birthday!

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Gustave-Gaspard Coriolis was born on May 21, 1792, in Paris, France. While little is known about his childhood, he was clearly a studious young man: In 1808, he took the entrance exam to École Polytechnique and placed second out of all of the entering students. Later, he was an assistant instructor at the school and made strides in advancing friction and hydraulics. Eventually, Coriolis became a mechanics professor at École Polytechnique, where he stayed until 1838.

*Portrait of Gustave-Gaspard Coriolis. Image in the public domain in the United States, via Wikimedia Commons.*

During his years as a teacher, Coriolis wrote a textbook, *Du calcul de l’effet des machines*, in which he explained how to calculate mechanical action. In this text, he adapted theoretical principles and demonstrated how they could be applied in mechanics across various industries. It was in this book that Coriolis also introduced the terms *work* and *kinetic energy* in their modern scientific context — work being the transfer of energy by a force acting through a distance and kinetic energy being an object or particle that possesses energy because it is in motion.

Coriolis suggested that if you perform work by applying a net force on an object, the object speeds up and gains kinetic energy, which depends on both the motion and mass of the object. He gave the correct expression for kinetic energy as 1/2 *mv*^{2}, where *m* is the mass and *v* is the velocity.

After establishing ideas about work and kinetic energy, Gustave-Gaspard Coriolis began to think about how they relate to movements like rotations. He explained some of these ideas in an 1832 paper about the transfer of kinetic energy in rotating machines, then in a famous paper a few years later, *Sur les équations du mouvement relatif des systèmes de corps*.

In his famous paper, Gustave-Gaspard Coriolis acknowledged the general effects of motion on a body on a rotating surface, but showed that there is an additional, inertial force that acts on the body at a 90° angle to the direction of motion. Usually, the body’s path would be straight, but due to this inertial force, the path curves instead. He said that this force, known as the Coriolis force, must be included in the equations of motion.

Initially, Coriolis connected these ideas with rotating machinery, specifically how energy is transferred in waterwheels. However, they became associated with other scientific fields as time went on, with applications in astrophysics and meteorology. Among the stars, the Coriolis force determines the directions of rotation in sunspots. On Earth, the Coriolis force influences wind directions and the rotation of storms, hurricanes, and tornadoes. This force not only affects atmosphere but also the rotation of ocean currents.

*A low-pressure system demonstrates the Coriolis force in the Northern Hemisphere, manifesting in a counterclockwise direction of movement. Image in the public domain in the United States, via Wikimedia Commons.*

The Coriolis force has an interesting effect, which occurs when there is an apparent deflection of the path of an object in a rotating coordinate system. In actuality, the object doesn’t deviate from the path — it only appears to do so because of the rotating motion of the system.

The rotating reference frame for the Coriolis effect is most often associated with the earth. Because the earth spins, completing one rotation per day, scientists must account for this force when analyzing the motion of objects. You can observe the Coriolis effect most noticeably in the path of an object moving longitudinally and for larger movements such as wind patterns and ocean water. The reason this deviation is so apparent along Earth’s longitude is because it rotates toward the east, and the tangential velocity has to do with latitude, since it’s close to zero at the poles and reaches maximum velocity at the equator. (Tip: Check out a PBS *Nova* video showing the Coriolis effect in action.)

After introducing major ideas about motion and energy, Gustave-Gaspard Coriolis was recognized for his achievements. In 1836, he became the mechanics chair at École des Ponts ParisTech (formerly called École Nationale des Ponts et Chaussées) and was inducted into the French Academy of Sciences. Two years later, he was appointed the director of studies at École Polytechnique. (In contrast to his other works, Coriolis also published research about the physics of billiards, in which he detailed a method for aiming massé shots!)

In 1844, the Coriolis effect and other mechanical principles were published posthumously in a collection called *Traité de la mécanique des corps solides*. Because his ideas and equations are so important in many areas of science, Coriolis received a great honor: You’ll find his name as one of only 72 names engraved on the Eiffel Tower (Jean-Charles de Borda is also among those listed). Today, let’s wish Gustave-Gaspard Coriolis a happy birthday!

- Read more about Gustave-Gaspard Coriolis on Brittanica.com
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Inge Lehmann was born on May 13, 1888, in Copenhagen, Denmark. Her early education was spent at the first coed high school in the country, a progressive idea for the time. Lehmann’s future studies and career did not offer the same inclusive environment. Thankfully, this did not stop her from performing great work throughout her life.

*A drawing of Inge Lehmann, located at her memorial in Copenhagen.*

An early interest in mathematics drove Lehmann to study the subject at the University of Copenhagen, where she would eventually earn her master’s degree in mathematics. Around this time, Lehmann also performed actuarial work, which helped her fine-tune her mathematical skills.

*University of Copenhagen in Frue Plads.*

In 1925, Lehmann started a job that set her on a life-changing career path: She became an assistant to Niels Erik Nørlund, the head of the Royal Danish Geodetic Institute. In this position, Lehmann oversaw the installation of seismological observatories. However, she didn’t just perform these duties; she also taught herself seismology, receiving her degree in geodesy in 1928.

Due to her impressive motivation, Lehmann was appointed chief of the Royal Danish Geodetic Institute’s Seismological Department in 1928, a position she would keep until 1953. While in this role, she investigated a seismological mystery…

Before Inge Lehmann’s research, the true inner structure of the earth remained unknown. At the time, many seismologists thought that Earth’s core was a single molten or liquid sphere that was surrounded by a solid mantle and crust. This theory was backed by recordings of two types of seismic waves released by earthquakes:

- P-waves (primary or pressure waves)
- S-waves (secondary or shear waves)

In short, if Earth’s core was molten, there would be “shadow zones” behind the core where P- and S-waves wouldn’t be able to reach because they would be deflected. Seismic recordings showed that these shadow zones existed, indicating that Earth had a molten core. However, there were inconsistencies in this theory. Namely, a few faint P-waves were recorded in areas that should have been shadow zones if the liquid core theory was true.

Lehmann’s interest in these inconsistencies was peaked when a 1929 earthquake near New Zealand produced P-waves that were faintly detected in places where they shouldn’t have existed if Earth had a molten core. Curious, she set out to investigate this question.

During her investigation of Earth’s core, Inge Lehmann spent years manually studying data from seismometers. According to her cousin, Lehmann would record data by hand on pieces of cardboard torn from oatmeal boxes. She would then spend the day in her garden, surrounding herself with pieces of data-filled cardboard.

Lehmann’s investigation culminated in a 1936 paper titled “*P*“. In her paper, she argued that Earth’s center was actually a solid inner core surrounded by a molten outer core. When using this theory, the seismic waves that had previously baffled scientists made sense. The solid inner core within the molten outer core would reflect some P-waves, which would result in them entering shadow zones. Lehmann’s findings rocked the seismological community and were tested and eventually confirmed by other scientists.

*Schematic of the layers within the earth. Image in the public domain, via Wikimedia Commons.*

In addition to discovering Earth’s inner core, Lehmann also discovered a discontinuity in its upper mantle, which is now called the Lehmann discontinuity. (Note that the term “Lehmann discontinuity” is also used to refer to the boundary between Earth’s inner and outer cores.)

Due to her groundbreaking work, Lehmann became known as a world expert on Earth’s upper mantle.

Inge Lehmann lived to be almost 105 years old, possibly making her the longest living female scientist. During her long seismological career, Lehmann earned many awards and honors, such as:

- A gold medal from the Danish Royal Society of Science and Letters
- Being elected as a fellow of the Royal Society
- Becoming the first woman to win the William Bowie Medal, the highest honor of the American Geophysical Union
- A medal from the Seismological Society of America

Upon receiving the William Bowie Medal, Lehmann was praised as “the master of a black art for which no amount of computerizing is likely to be a complete substitute.”

*Snapshots of the Inge Lehmann memorial.*

In 2017, 24 years after she passed away, Lehmann also received a memorial dedicated to her achievements. The memorial is located on Frue Plads in Copenhagen and is next to memorials for other notable Danish scientists, like Niels Bohr.

- Learn more about Inge Lehmann:
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On May 4, 1733, Jean-Charles de Borda was born in Dax, a city in southwest France near the Bay of Biscay. His parents were part of the French nobility and had strong ties to the military. Borda was the tenth of sixteen children and, not surprisingly, many of his brothers ended up having military careers.

As for Borda himself, his education involved studying at the Collège des Barnabites in Dax; the Jesuit college at la Flèche; and the École du Génie at Mézières, where he ambitiously finished a two-year course in only one year.

Borda’s military career began when he entered the army as a mathematician. Later on, after he had joined the navy, he also took part in the American Revolutionary War.

*Painting of Jean-Charles de Borda at work. Image in the public domain in the United States, via Wikimedia Commons.*

In his late 40s, Borda was granted charge of six vessels for the French Navy. This assignment did not go as planned. After one year, he was defeated in battle and captured by the British Royal Navy. Luckily for Borda, he was returned to France on parole, possibly due to his reputation as a scholar. After returning to France, Borda was appointed as France’s inspector of naval shipbuilding.

Throughout his lifetime, Jean-Charles de Borda studied fluid flow and fluid resistance as they pertained to ships, scientific instruments, pumps, and waterwheels. Through this work, he generated information that could be used to enhance these devices. His research would go on to inspire Lazare Carnot’s future mechanics work.

*Borda made improvements to devices like waterwheels. Image by Jared. Licensed under CC BY 2.0, via Flickr Creative Commons.*

One important point of study for Borda was investigating Newton’s theory of fluid resistance. When doing so, he found that the theory was untenable. He proposed that the resistance is proportional to both the square of the fluid velocity and the sine of the angle of incidence.

A great French surveyor, Jean-Charles de Borda helped develop navigational tools. Among them was his repeating circle, which could measure the distance between different points at sea. To function, the circle used two telescopes and relied on the surveying technique of triangulation. Another one of the scientific instruments Borda developed was used to perform a meridian arc measurement, important in the field of geodesy.

*The Borda repeating circle (top) and a schematic depicting its operation (bottom). Top image in the public domain in the United States, via Wikimedia Commons. Bottom image in the public domain via Wikimedia Commons.*

In conjunction with his surveying techniques, Borda also developed a series of trigonometric tables and traveled to the Caribbean to test chronometers, another type of device that can be used for marine navigation.

Tip: Learn more about modern navigation tools, like ring laser gyroscopes, in this blog post.

In 1756, when Jean-Charles de Borda was in his early 20s, he wrote about the physics of projectiles as part of his work as a military engineer. His work catapulted him into the world of science and, as a result, he was elected into the French Academy of Sciences. While a part of this organization, Borda created a ranked preferential voting system called the Borda count, which enabled members to vote for multiple candidates for positions. The French Academy of Sciences is said to have used this method to elect members for almost two decades. Borda is also known for his work with the metric system and for helping to install a uniform system of weights and measures.

Due to his many accomplishments, Jean-Charles de Borda’s name can be found in the Eiffel Tower along with 71 other scientists. Today, let’s wish him a happy birthday!

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Claude Shannon was born on April 30, 1916, in Petoskey, Michigan, and spent most of his childhood with his family in Gaylord, Michigan. From a young age, Shannon showed a keen interest in mechanical and electrical engineering, constructing model planes and a radio-controlled boat. He also showed an aptitude for communications technology. Inspired by Thomas Edison’s improvements to the telegraph, Shannon built a telegraph of his own out of barbed wire and connected it from his house to a friend’s house.

*Claude Shannon. Image by Jacobs, Konrad. Licensed under CC BY-SA 2.0 DE, via Wikimedia Commons.*

After earning bachelor’s degrees in both mathematics and electrical engineering from the University of Michigan, Shannon began his graduate studies in 1936 at the Massachusetts Institute of Technology (MIT). He went on to earn a master’s degree and PhD from MIT. His master’s thesis, written when he was 22 years old, forever changed how we use digital circuits in computing and automation.

Claude Shannon spent his time at MIT industriously. A summer internship with Bell Laboratories secured a lifelong affiliation with the company and deepened his interest in electrical engineering. He also worked at MIT as a research assistant to acclaimed researcher Vannevar Bush, with whom Shannon designed switching circuits on Bush’s differential analyzer, an early analog computer. He based the design of these circuits on the concepts of mathematician George Boole.

In 1937, Shannon wrote his master’s thesis, “A Symbolic Analysis of Relay and Switching Circuits”. Drawing from his experience with the differential analyzer, he used Boolean algebra to establish the theory behind digital circuitry. This revelation gave engineers the ability to test circuit designs with Boolean algebra before investing time and money into building a prototype. In addition, Shannon was able to prove that Boolean algebra and binary arithmetic could be used to arrange circuits in a simplified way.

*A partial view of a two-layer printed circuit board geometry. The file is provided through the courtesy of Hypertherm, Inc., Hanover, NH, USA.*

Previously, engineers used ad hoc methods for digital circuit design, but Shannon’s applied theory made more intentional connections with a focus on network synthesis. With Shannon’s simplified arrangements of electromechanical relays, such as those used in telephone switches, electrical switches could perform logic. This ability laid the foundations for the basic functions of a computer.

During World War II, Claude Shannon was working at Bell Labs under contract with the National Defense Research Committee (NDRC), where he specialized in fire-control systems and cryptography. As a cryptographer, Shannon used digital codes to protect sensitive information. He realized, as the war was coming to an end, that he could also use digital codes to address a signal noise interference problem he often encountered, and thereby protect messages from such interference. He started thinking about cryptography’s relationship to communications theory and began developing mathematical formulations that explored the nature of the transmission of information.

Claude Shannon’s work up to this point served as the basis for his landmark 1948 paper, “A Mathematical Theory of Communication”, which introduced information theory as a definitive field. He was able to establish the results for information theory so completely that his framework and terminology are still used today. He was also the first to use the word “bit” to mean a single binary digit. The bit is now also referred to as the *shannon* (Sh), a unit of information and entropy.

In this paper, Shannon poses two key questions:

- What is the most efficient encoding of a message using a given alphabet in a noiseless environment?
- What additional steps should be taken when noise is present?

To answer these questions, Shannon came up with a way to efficiently transmit messages and measure the efficiency of transmissions. All messages, he purported — whether conveyed via telephone, television, or radio — might be delivered inaccurately due to the presence of noise. The aim, then, is to find a way around the noise. He suggested that a message should be constructed as a sequence with statistical properties — in other words, in bits, or binary digits (ones and zeros). In this way, the message’s coding can be minimized and transmitted more effectively, regardless of the presence of noise, and then easily reconstructed and interpreted by a recipient device.

As a way to measure the efficiency of a communications system, Shannon developed information entropy. The higher the entropy of the message, the more effort it takes to transmit it.

*A schematic of Shannon’s communication system from his 1948 paper. Image in the public domain, via Wikimedia Commons.*

Furthermore, Shannon was able to show that bandwidth and noise are factors characterizing any communications channel, and the maximum rate at which data can be transmitted with zero error for a given channel can be calculated. This is known as Shannon’s channel capacity, or Shannon’s limit.

In subsequent articles on information theory, Shannon introduced sampling theory. Sampling converts a signal into a numeric sequence, and sampling theory bridges continuous time signals (analog signals) and discrete time signals (digital signals). Shannon’s version of the theorem proved a dual of fellow engineer Harry Nyquist’s results. The Nyquist-Shannon sampling theorem, often used in wave optics studies, honors the scientists for this reason.

It’s obvious that Claude Shannon worked hard — but he had a reputation for *playing* hard as well. He was known for taking rides through the halls of Bell Laboratories and MIT on a unicycle (while juggling four balls, no less). In his home near Boston, which he dubbed “Entropy House”, he displayed a framed paper certifying him as a “doctor of juggling” among his legitimate diplomas and awards.

One of his inventions stands above the rest as a step toward artificial intelligence: “Theseus” or Shannon’s mouse. Theseus is a magnetic mouse controlled by an electromechanical relay circuit that allows it to move around a special maze with 25 squares. Each of the partitions can be moved around to reconfigure the maze, and the mouse’s “goal” is to go through the maze until it reaches a prize.

*Theseus and its maze at an MIT Museum exhibit. Image by Daderot. Image in the public domain, via Wikimedia Commons.*

The genius of Shannon’s design shows in the mouse’s programming: Once the mouse goes through the maze, it can be picked up and put back inside the maze anywhere it has already been and find its way to the prize based on its prior knowledge. If Theseus is placed in an unfamiliar location within the maze, it finds its way to a known location. Once reaching familiar territory, Theseus resumes its prime mission of finding the target. The Theseus experiment set a precedent for the machine learning systems we’re familiar with today.

Besides riding a unicycle and programming a magnetic mouse, Shannon was always tinkering with computer machinery and automation, as the following list of his inventions proves:

- Computerized chess
- Automated pogo stick
- Rocket-powered frisbee
- “Mind-reading” machine built out of mechanical relays that could predict a player’s behavior
- THrifty ROman numeral BAckwards-looking Computer (THROBAC), which calculates in Roman numerals
- “Ultimate” or “Useless” machine, in which you flip a switch to turn it on and mechanical hand pops out of the box to turn it off again (Watch a video to see it in action!)
- Device that solves the Rubik’s Cube® puzzle

Claude Shannon is widely celebrated for his many contributions to the field of computing. His master’s thesis is considered one of the most important of the 20^{th} century and won Shannon the Alfred Noble American Institute of American Engineers Award. While the Nobel Prize is not offered in his specific field, he won the Kyoto Prize, Japan’s equivalent award. He was also awarded the IEEE Medal of Honor. On his centenary in 2016, the IEEE Information Theory Society coordinated worldwide events and activities in his honor.

Shannon was truly ahead of his time in 1948. While his revolutionary information theory was not seen as immediately applicable, we now see its influence in every device containing a microprocessor or microcontroller. He established the parameters for compressing and transmitting digital information, which enables you to access and read this COMSOL Blog post — perhaps even from your mobile device.

Let’s wish Claude Shannon a happy birthday!

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*Rubik’s Cube is a registered trademark of Rubik’s Brand Ltd. Corporation.*

Leonhard Euler (pronounced “oiler”) was born on April 15, 1707, in Basel, Switzerland. By age 13, he was already studying at the University of Basel, and by 16, he earned a Master of Philosophy degree. During his time at the university, he studied intensively with family friend and famed mathematician Johann Bernoulli, who encouraged Euler to pursue a career in mathematics.

Euler wrote a dissertation a few years later on the propagation of sound, titled *De Sono*, which was the first of many published mathematical works. In fact, by the end of his lifetime, Euler’s total collected works filled 60 to 80 quarto volumes, a larger collection than anyone else’s in the field. More success soon followed: In 1727, Euler placed second in an annual Paris Academy prize problem competition, a prize he came to win a total of 12 times.

*A portrait of Leonhard Euler. Image in the public domain in the United States, via Wikimedia Commons.*

After spending some time in St. Petersburg, Russia, as both a medic in the Russian Navy and a professor of physics at the Imperial Russian Academy of Sciences, Euler moved to Berlin, Germany, to accept a job offer from Frederick the Great of Prussia. Euler spent 25 years at the Berlin Academy before returning to Russia, and it was in Berlin where he wrote his most groundbreaking work.

It’s hard to solve formulas or talk about mathematical theories without referencing Euler’s work in one way or another. Euler contributed to topics such as functions in number theory and angles that define rotations in space. It’s no wonder that Pierre-Simon Laplace reportedly said “Read Euler; he is the master of us all.”

There are two well-known numbers named after Euler:

- The “
*e*” mathematical constant in calculus stands for “Euler”, and is approximately equal to 2.71828 - “Euler’s constant”, or γ (gamma), is approximately equal to 0.57721

While Euler published many textbooks, two he published in Berlin made him famous in his field: *Introductio in analysin infinitorum* (1748) on functions and *Institutiones calculi differentialis* (1755) on differential calculus.

In his textbooks, Euler was the first mathematician to introduce the concept of a function in mathematical analysis, as well as the first mathematician to write the function *f* as applied to the variable *x*: .

Other notations created or popularized by Euler include:

- Sum or total of a set of numbers, denoted by the Greek letter Σ
- “Imaginary” unit, equal to the square root of -1, denoted by the letter
*i* - Ratio of a circle’s circumference to its diameter, denoted by the Greek letter π (popularized after originating from Welsh mathematician William Jones)
- Trigonometric functions for sine, cosine, tangent, cotangent, secant, and cosecant
- Constants;
*a*,*b*,*c* - Variables or unknowns in an equation;
*x*,*y*,*z*

His attempts to standardize many of these symbols helped mathematicians collaborate and solve problems together. Euler himself collaborated quite often with famous mathematicians, including Joseph-Louis Lagrange.

*One of Euler’s illustrations from his famous paper on topology and graph theory, “The Solution of a Problem Relating to the Geometry of Position”, first published in 1744 in the scientific journal* Acta Eruditorum*. Image in the public domain in the United States, via Wikimedia Commons.*

Euler is also known for developing Euler’s identity, the equality *e ^{iπ}*+1 = 0. It shows a connection between the most fundamental numbers in math and is a case of Euler’s formula,

What’s interesting about Euler’s identity is that it is considered the epitome of mathematical beauty. It was voted by *Mathematical Intelligencer* readers in 1988 as the “most beautiful” theorem and even won beauty contests in brain scans.

Euler solved many real-world problems analytically and developed efficient tools to address them. A famous example is a thought problem known as the *Seven Bridges of Königsberg*. Königsberg, Prussia (now Kaliningrad, Russia), is situated between both sides of the Pregolya river. The city includes two islands that, during Euler’s time, were connected to each other by seven bridges. The problem’s objective was to come up with a path through the city that only crosses each bridge once.

Euler was able to prove, via satisfactory analysis involving many tests and graphs, that the problem has no solution. His methods laid the foundations for graph theory and topology.

*The seven bridges of Königsberg, Prussia, shown in green. Image by Bogdan Giuşcă, based on a map of Königsberg in the public domain. Licensed under CC-BY-SA-3.0, via Wikimedia Commons.*

Besides textbooks, Euler published a work that propelled him to stardom beyond the praise of his fellow mathematicians. In the early 1760s, Frederick the Great asked Euler to tutor his niece, Friederike Charlotte of Brandenburg-Schwedt, the Princess of Anhalt-Dessau. Euler wrote the princess over 200 letters, which were later compiled and published. In the letters, Euler discussed math and science in simplified terms, which made them wildly popular among the public because they helped make mathematical concepts easier to understand.

Later in life, Euler’s eyesight deteriorated, but it did not limit his prolific output. In fact, he said that his blindness made him less distracted so that he could focus on his work. In 1775, several years after losing his eyesight, Euler wrote an average of one mathematical paper per week!

Euler opened up a world of possibility with his fundamental symbols and equations. He established many areas of mathematics and contributed to structural mechanics and astronomy, including the creation of accurate longitude tables. He also applied mathematics to optics and music theory.

*Euler on an old Swiss 10-franc banknote. Image in the public domain, via Wikimedia Commons.*

For his many gifts to mathematics, Euler has been commemorated on a Swiss 10-franc banknote and on Swiss, German, and Russian postage stamps. For his contributions to astronomy, the asteroid 2002 Euler was named after him.

Today, let’s wish Leonhard Euler a happy birthday!

- Learn more about Leonhard Euler:
- Read more about the application of Euler’s equations in modeling:

Inspecting the storm-ravaged beaches after one of 2018′s many winter storms, locals of Orleans, Massachusetts, noticed strange impressions in the peat beds close to the ocean. Some of these impressions were U-shaped imprints, while others were long, narrow striations. Where did these weird marks come from? The answer lies in history.

As it turns out, in the late 1800s, the peat bed area of Orleans was a road that villagers used to enter the beach. And what mode of transportation was most popular in the late 1800s? Horses and carriages!

*While hourglasses use sand to mark the passage of time, sand can tell us about details forgotten over this passage.*

How horse and buggy tracks were preserved on a beach for over two centuries comes down to a process similar to fossil formation. First, an impression is made in the ground, whether by a foot, tire, or animal. Then, a storm comes along and creates waves that cover the coast in a layer of sediment, preserving the imprint like a cast. Years go by and another storm hits. This time, the resulting coastal erosion removes layers of sand and exposes the tracks.

When waves crash on the coastline and the tide changes, it wears away the sediment and sand. This phenomenon, called coastal erosion, occurs gradually over time. When an intense meteorological event like a winter storm occurs, it can cause the coast to erode in a more rapid fashion. Although erosion can damage coastal habitats, it attempts to make up for the damage by preserving tracks and footprints — and uncovering them later so we can learn more about our history.

*Top: Tracks of a Moa bird, native to New Zealand and extinct since 1445. Image by K. Wilson — National Library of New Zealand. Available under public domain in New Zealand, via Wikimedia Commons. Bottom: 2100-year-old human footprints found on the shore of a Nicaragua lake. Image by Dr d12. Licensed under CC BY-SA 3.0, via Wikimedia Commons.*

Preserved footprints, animal tracks, and transportation marks are useful in the study of archaeology, paleontology, and anthropology. For instance, dinosaur tracks are studied by researchers to determine the behavior patterns and traits of different species. Human footprints from prehistoric periods paint a picture of how our early ancestors looked, behaved, and — in the case of Orleans, Massachusetts — traveled. While these disciplines are concerned with what preserved footprints tell us about the feet they belonged to, in the field of geomechanics, engineers are more interested in the sediment *around* the footprints. The layers of sediment and sand that preserve these impressions reveal information about the soil mechanics and rock mechanics in the surrounding area over time.

There is a problem, though. As quick as the ocean’s waves can uncover footprints from long ago, they can also wash them away. If researchers want to preserve these impressions in a more permanent manner, they need to work quickly to beat the rising tides. Potential tactics for this purpose include creating casts, using digital scans to capture 3D data, and good old-fashioned photography.

Next time you take a walk along the beach, think about how the footprints you leave behind could be preserved for years to come!

- Learn about analyzing coastal erosion by solving shallow water equations
- Interested in geomechanics? Check out these blog posts:

On March 23, 1749, Pierre-Simon Laplace was born to a bourgeois family in Normandy, France. He took an early interest in theology, and his aptitude for argumentation motivated his wealthier neighbors to fund most of his education. Laplace discovered that he was especially gifted in mathematics and decided to pursue this study in earnest. When he was just 18, he was hired as a college professor in his town — although he was not content to stay there long.

*Pierre-Simon Laplace. Image in the public domain in the United States, via Wikimedia Commons.*

Within his first year of teaching, one of Laplace’s mentors wrote him a letter of recommendation to give to Jean le Rond d’Alembert, a prolific and famous mathematician. Laplace figured that d’Alembert’s support was all he needed to launch a successful career, so he went straight to Paris to give d’Alembert the letter and secure his patronage. D’Alembert, however, rejected the young mathematician and commented that he paid “little respect to letters of recommendation.”

Not one to be easily discouraged, Laplace himself wrote d’Alembert a letter, this time writing about the principles of mechanics, and sent it to him of his own accord. Impressed, d’Alembert responded that Laplace’s second attempt was done “in a more appropriate manner” and offered his support. Thanks to d’Alembert’s influence, Laplace was hired as a math professor at the Military School of Paris, and at age 24, he was accepted at the French Academy of Sciences.

Pierre-Simon Laplace’s years at the French Academy of Sciences, from 1771 to 1787, were fruitful. He contributed to a number of studies in various fields, including optics, acoustics, and heat transfer. While his contributions in these areas are valuable, his research on astronomy was revolutionary.

While at the Academy, Laplace published a three-part memoir on planetary inequalities. Through mathematical proofs, he was able to solve a problem that puzzled observational astronomers at the time: Jupiter’s orbit appears to be always shrinking, while Saturn’s orbit seems to be always expanding.

*A graphic depiction of the solar system. Image in the public domain in the United States, by Harman Smith and Laura Generosa, contractors to NASA’s Jet Propulsion Laboratory, via Wikimedia Commons.*

Laplace explained these perturbations with algebra and proved that Jupiter and Saturn cannot bring about significant changes in their orbits from their mutual action. He concluded that perturbations in the planets’ orbital motions will always remain small, constant, and self-correcting. Ultimately, Laplace was able to establish that the solar system is made up of rigid bodies that exist and move in a vacuum under the effect of mutual gravitational attraction.

In 1796, Laplace finished writing a book on the history of astronomy, as well as a general nonmathematical explanation of the solar system and gravity, known as *Exposition du système du monde*. The explanation of the solar system was an important foundation for his later work, *Mécanique céleste*.

*Exposition du système du monde* focuses on Laplace’s version of the nebular hypothesis, which suggests that the solar system began as a mass of incandescent gas that rotated around its axis and broke off into rings around its outer edges. According to the hypothesis, these rings eventually cooled and formed the planets, while the remaining gaseous core made up the sun. The nebular hypothesis, while flawed, inspired future work on planetary origins. In addition, the hypothesis expanded our understanding of stellar evolution by featuring the idea of a protosolar nebula. Laplace also briefly postulated on the existence of black holes.

*An illustration of planetary nebula formation. As strong stellar wind (red arrows) expels the outer layers of the red giant star, the hot white dwarf is revealed at its center. Image in the public domain, via Wikimedia Commons.*

From 1799 to 1825, Laplace published a five-volume treatise containing calculations for planetary motions, *Mécanique céleste*. He analyzed spherical harmonics (now called Laplace coefficients) that account for gravitational attraction, as well as tidal dynamics that consider friction and natural periods of ocean basins. During this time, Laplace also issued an essay on probability theory and expanded upon these theories in *Mécanique céleste*.

These volumes on celestial mechanics rely heavily on Newtonian laws of gravity and motion, but fill in the details through differential calculus. Laplace applied Newton’s laws to the stability of the solar system by computing the motion of the planets as well as their satellites and perturbations. He also corrected the velocity of sound in Newton’s theory of vibratory motion.

In the decades that Laplace was working on *Mécanique céleste*, the political climate changed drastically. By the time *Mécanique céleste* was completed in full, the French Revolution had ended, the Bourbon Restoration occurred, and the Bourbons even named Laplace a marquis.

Laplace was something of a philosopher. In 1814, while working on *Mécanique céleste*, he introduced the idea of causal determinism, which precludes free will. This type of determinism proposes that there is an unbroken chain of events going back to the origins of the universe, and that the future is determined by a combination of prior states of the universe and the laws of nature.

In a thought experiment now known as “Laplace’s demon”, a hypothetical intellect (or demon) of atomic proportions sorts out molecules of different velocities in order to counter the laws of thermodynamics. According to Laplace, this imaginary intellect knows the location and momentum for every atom in the universe and can calculate the past and future values for each atom at any given time using the laws of classical mechanics.

Many philosophers have argued for and against Laplace’s demon. The topic has also motivated scientists to make strides in the development of statistical thermodynamics and applications of chaos theory.

Laplace worked with renowned scientists during his lifetime and inspired many others thereafter. His collaboration with chemist Antoine Lavoisier led to several experiments on the expansion of metals and a paper on the kinetic theory of molecular motion. With Thomas Young, Laplace worked to describe a pressure across a curved surface with the Young-Laplace equation. And in 1862, many years after Laplace’s death, William Thomson (Lord Kelvin) built upon Laplace’s theory of capillary attraction.

Among his many honors and achievements, Laplace was president of the Board of Longitude and helped organize the metric system. There is also an equation named in his honor, the solutions of which are harmonic functions. Laplace’s equation, , is a second-order partial differential equation that is prevalent in many areas of applied and theoretical mathematics.

Today, let’s wish Pierre-Simon Laplace a happy birthday!

- Learn more about Pierre-Simon Laplace:
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A passionate and curious intellectual, Albert Einstein is considered one of the most influential physicists of the 20^{th} century. The German-born mathematician and physicist made numerous discoveries throughout his lifetime. Most notably, he developed the special and general theories of relativity. For discovering the law of the photoelectric effect, he earned a Nobel Prize in Physics in 1921.

Albert Einstein was born on March 14, 1879, to middle-class Jewish parents in the southern German city of Ulm. Two important encounters ignited young Einstein’s curiosity. He described them as the “two wonders”. The first was at age five when his father handed him a compass. He was enthralled by the movements and workings of the compass, sparking his lifelong affinity for invisible forces. Einstein’s second “wonder” came to him at age twelve when he discovered a geometry book, which he fondly referred to as his “sacred little geometry book”. And so began young Einstein’s fascination with physics and mathematics.

In 1896, Einstein entered the Swiss Federal Polytechnic School in Zurich, where he later obtained his diploma in Physics. Much to his chagrin, Einstein was unable to secure a stable job until 1902, when he became a clerk at the Swiss patent office in Bern. In his spare time at the office, Einstein frequently daydreamed and ruminated on scientific theories. Eventually, these daydreams evolved into his most innovative work. The year 1905 is often referred to as Einstein’s “miracle year”. Not only did he obtain his doctor’s degree but he also published four revolutionary papers that launched him into the scientific community.

*Albert Einstein. Image in the public domain in the United States, via Wikimedia Commons.*

Einstein’s visionary theories revolutionized the way we think about energy, mass, gravity, space, and time. His groundbreaking research explored the photoelectric effect, Brownian motion, and the theories of special and general relativity.

The photoelectric effect put to rest a long debate of what light is made of. It explained that light is not a wave propagating through space, but actually wave packets, or photons. The energy of each photon is equal to the frequency multiplied by Planck’s constant. Einstein’s photoelectric effect contributed to the development of quantum mechanics.

Einstein provided the first scientific proof of the existence of atoms with his quantitative theory of Brownian motion. He studied atomic collisions in fluids and demonstrated that the size of atoms can be measured. This was a breakthrough for the atomic realm.

*Particle diffusion in a fluid demonstrating Brownian motion.*

Similar to his icon, Galileo Galilei, Einstein shook the scientific community by challenging its current framework. With the special theory of relativity, he declared that distances in time and space are relative and they change depending on the speed of a material object. Furthermore, he calculated that the speed of light is unchanging and unapproachable by any material object.

Einstein’s famous equation, E = mc^{2}, directly grew out of his special theory of relativity. It shows that tiny particles of mass could be converted into a massive body of energy. The special relativity equation is credited for the genesis of the atomic bomb, although Einstein opposed war and had no involvement in the development of nuclear weapons.

The pioneering physicist felt that his special theory of relativity was incomplete, because it did not account for all types of motion; he wanted to generalize the theory. In 1915, Einstein proudly published the general theory of relativity. It explained that gravity is the result of the distortion of space-time. The acceleration and gravitational field of a material object are not absolute quantities; accelerations could transform into gravitational fields and vice versa.

*Einstein demonstrated his general theory of relativity using gravitational lensing, where mass bends light from a distance.*

Throughout his lifetime, Einstein continued to produce more important inquiries and discoveries. For example, Einstein discovered stimulated emissions in 1916. His inquiries have inspired other scientists to explore major scientific theories and observations, including the Big Bang theory and gravitational waves.

With the rise of antisemitism, Einstein fled Germany in 1932. He spent the remainder of his life questioning scientific theories and denouncing racism. Einstein is not only remembered for his scientific contributions, but also for his humble nature, witty humor, and affinity for mankind. As a member of the NAACP, he was a passionate supporter of human rights and civil rights. More than 40 years after his death, *Time Magazine* dubbed him Person of the Century.

For all of these reasons, we continue to celebrate the life of Albert Einstein today.

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Joseph von Fraunhofer was born on March 6, 1787, in Straubing, Bavaria. Orphaned at a young age and apprenticed under a strict mirror maker, Fraunhofer’s early life was difficult. At work one day, the building around Fraunhofer collapsed, trapping him beneath rubble. Oddly enough, this incident was a positive turning point for the young glassmaker.

The building collapse and subsequent rescue of Fraunhofer caught the attention of Prince-Elector Maximilian Joseph and a politician named Joseph Utzschneider. The support of these men provided Fraunhofer with funding and enabled him to receive an education while continuing his practical training in optics.

*Joseph von Fraunhofer. Image in the public domain in the United States, via Wikimedia Commons.*

Eventually, Fraunhofer entered the Optical Institute at Benediktbeuern, where he enhanced his glassmaking skills. He was given the task of making achromatic lenses for telescopes, at which he excelled. In 1818, Fraunhofer became the director of the Optical Institute, continuing to perform great work.

During his lifetime, Fraunhofer developed a few important optical devices. One such contribution is the spectroscope, which helped Fraunhofer study light with great precision. He is also known for furthering the development of diffraction gratings.

*Fraunhofer displaying his spectroscope. Image in the public domain in the United States, via Wikimedia Commons.*

One of Fraunhofer’s most significant achievements is rediscovering a set of spectral lines, which would later be called *Fraunhofer lines*. Fraunhofer’s research in this area led him to independently discover over 570 dark lines in the solar spectrum. While these lines had been observed before, Fraunhofer added to this knowledge by measuring and recording the lines.

*Left: Visual depiction of Fraunhofer lines. Image in the public domain, via Wikimedia Commons. Right: A rainbow formed from natural light.*

Due to his influential work, Fraunhofer received various honors. For instance, he earned an honorary doctorate from the University of Erlangen. He was also appointed as a knight of the Bavarian Crown, which gave him the status of personal nobility.

Today, Fraunhofer’s work remains important. For example, his pioneering work on diffraction gratings and stellar spectroscopy has led to the development of modern spectrometers.

In honor of his lasting achievements, let’s wish Joseph von Fraunhofer a happy birthday!

- Learn more about Joseph von Fraunhofer:
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