February 2019 - Missing the Forest for the Tree: A Worldview Grounded in Science

3000 BCE: Number Systems

Posted on February 26, 2019May 2, 2020 by Dan

The invention of number systems designated another high mark for the civilization. Its development led to formal mathematics just as the development of writing systems led to reading and literature. These two tools are responsible for preserving and transmitting the vast, accumulated knowledge humanity has attained in the past 5000 years. These disciplines form the foundation of our modern academic curriculum.

For tens of thousands of years there was not an organized number systems. People counted things using their fingers and toes, if they needed to count anything at all. Around 25,000 ago there is evidence that people started placing marks on wood and bone, a practice known as tally systems, to keep track of things. Later on people used markers, counters, or tokens in what is called a token system. These tokens corresponded directly to the goods and things that they represented. Tally systems followed by token systems were proto-numeral systems. This proved was useful for counting and keeping track of smaller amounts but it was not very practical when counting large numbers or attempting to complete more complex mathematical operations.

When humans were hunter-gathers there was not a pressing need to tally items. People lived in smaller groups and generally shared goods in the community. Human emotions such as resentment and distrust were sufficient to regulate fairness in the community. With the advent of agriculture the human condition changed. Soon their were sprawling city-states with tens of thousands of people and a division of labor. Accountants were needed to record debts and taxes owed. This necessity provided the kindling spark to devise a more capable system of keeping track items than a tally system.

Number Systems Take Their Position in Civilization

Babylonian Number System — Babylonian Sexagesimal Number System

Around 3000 BCE the Babylonians developed one of the first known positional number systems. It was written in cuneiform and was a sexagesimal (base 60) number system. The major achievement of the Babylonian number system over previous number systems was that it was positional. This mean that the same symbol could be used to represent different orders of magnitude, depending on where the symbol was located within the number.

The Babylonian system was a significant advancement in the development of mathematics. It provided for the addition and subtraction of numbers and allowed for fractions. It did have some many shortcomings. One such shortcoming is the absence of the number zero. Today we use a base 10 positional number system however there are still some relics of the base 60 number system in our culture. For example, the circle is 360 degrees and there are 60 seconds in a minute.

Many other civilizations further developed number systems. They Chinese, Egyptians, Aztecs, Mayans, and Inca’s all made use of them. The Greeks in particular showed an intense interest in math. When the conquests of Alexander the Great spread Greek culture throughout the ancient world it marked a turning point in science and math that still lingers, along with so much else from the Greek culture, with us today.

The Story of our Number System

The number system we used today is referred to as Arabic Numerals despite its oldest preserved samples being discovered in India from around 250 BCE. It is uncertain whether this system developed entirely within India or had some later Phoenician and Persian influence. What is certain is that the Arabic’s fully developed and institutionalized this system. A book written around 820 by the mathematician Al-Khwarizmi provides us with the oldest fully developed description of this system. Titled On the Calculation with Hindu Numerals, it is responsible for introducing this Hindu-Arabic numeral system to Europe.

The Arabic’s designed different sets of symbols which can be divided into two main groups – East Arabic numerals and West Arabic numerals. Although the Arabic language is written from right to left, Arabic numerals are arranged from left to right. The European numeral system was primarily modeled on the now extinct West Arabic numeral system.

The Importance of Number Systems

We would be lost in our world without numbers. They are used to represent goods and things.. They allow the measurement of objects. They are used in the tracking of time. But maybe most importantly, number systems are necessary for mathematics, the bedrock of science.

Pythagorean Theorem
(Credit: www.mathworld.wolfram.com)

Much of the world can be expressed in mathematics. It has been echoed by many great scientists that nature speaks to us in the language of mathematics. This is why science depends so much on math. Math has wide-ranging applications ranging from engineering, accounting and finance, navigation, physics and cosmology, computers and coding. Geometry and calculus allows us to construct buildings to live in. Algebra allows us to calculate our loan payments when we purchase that new home. The examples the benefits of using math, just like are numbers, are infinite.

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Dmitri Mendeleev

Posted on February 24, 2019January 23, 2024 by Dan

Dmitri Mendeleev (1834 – 1907) was a Russian chemist who is most famous for publishing his periodic table of elements. The period table is one of the most recognizable symbols in science.

Mendeleev was born in the Russian province of Siberia in 1834, the youngest of seventeen siblings. At the age of sixteen Mendeleev moved with his family to the the Russian capitol of St. Petersburg and enrolled in his father’s old school, St Petersburg’s Main Pedagogical Institute. At age 21 he got a teaching job in the Crimea but soon returned to St. Petersburg to study for a master’s degree in chemistry from the University of St. Petersburg which he obtained in 1856.

Mendeleev was becoming more passionate about science and more concerned that Russia was falling behind Germany in the field. He believed improving Russian educational textbooks was one way to close the gap. In 1861 he published the 500-page textbook Organic Chemistry which won him the Demidov Prize of the Petersburg Academy of Sciences. He continued to be a a teacher of chemistry and write additional textbooks over the next few decades.

During his time teaching and writing textbooks Mendeleev began to notice patterns and relationships among the known elements. He found many similar properties in groups of elements such as the halogens and the alkaline earth metals. He noticed the atomic weight’s of the elements could be used to arrange elements within groups, and also to arrange groups themselves. In 1869 he published publish The Relation between the Properties and Atomic Weights of the Elements, revealing his periodic table to the world.

Mendeleev’s periodic table was impactful for its predictive power. Due to its ordering, it predicted that some of the atomic weights of known elements may be wrong. It also predicted the existence of unknown elements and it predicted what properties these elements would possess. Both of these predictions ended up being true.

Mendeleev received substantial fame and recognition for his periodic table. In 1905, the British Royal Society awarded him its highest honor, the Copley Medal. The same year he was elected to the Royal Swedish Academy of Sciences. He died just after the turn of the century in 1907 from the influenza virus. Element number 101 is named Mendelevium in his honor.

1869: Mendeleev’s Periodic Table of Elements

Posted on February 23, 2019March 7, 2025 by Dan

The periodic table of the elements is a cornerstone of modern chemistry and an iconic visual representation almost all school children are familiar with. Its origins trace back to 1869, when Russian chemist Dmitri Mendeleev, the inventor of the periodic table in 1869, published his groundbreaking system. Aside from a few minor changes we still use Mendeleev’s system of organization for our modern periodic table.

The Development of the Periodic Table of Elements

Title Page to Volume I of Dmitri Mendeleev's Principles of Chemistry — Title Page to Volume I of Dmitri Mendeleev’s Principles of Chemistry

By the middle of the 19th century scientists had discovered dozens of elements, but there was no way or organizing them. By 1869 there had been a total of 63 elements discovered and isolated. As the number of known elements was increasing, several scientists began to notice relationships among some of elements and patterns in how they combined with each other. Scientists had been trying to develop a classification system of elements for decades for the known elements for decades but no agree upon system had been reached. For one example, an English scientist named John Newlands proposed the Law of Octaves in 1865. He noticed that every eighth element shared similar characteristics when arranged by atomic weight, much like the notes in a musical octave. In music, an octave consists of eight notes, with every eighth notes a repetition of the previous note just at a higher pitch.

There were however limitations to his law. It has limited applicability, working reasonably well for the lighter elements but breaking down for heavier elements. It also had limited predictive power as it made no room for undiscovered elements. For these and other reasons it was not accepted by all scientists of the time, although it did have a role in the evolution of the periodic table by emphasizing the importance of looking for patterns in the elements of nature.

The Inventor of the Periodic Table in 1869: A Visionary Approach

Enter Dmitri Mendeleev, a chemistry professor at the University of St. Petersburg and the true inventor of the periodic table. In 1861, at age 27, he earned his doctorate after studying abroad in Heidelberg, where he worked with leading chemists like Robert Bunsen, sharpening his analytical skills. A few years later, in 1867, he began working on publishing a chemistry textbook titled Principles of Chemistry. It was his research for this textbook that led him develop this relationship between the chemical properties of the elements to their atomic weights.

Mendeleev’s journey to becoming the inventor of the periodic table in 1869 was not without its quirks and obstacles. Legend has it that Mendeleev conceived the periodic table’s structure in a dream after struggling with the problem for days, arranging element cards on his desk like a game of solitaire.

In any case, his key breakthrough came when he organized his table in order of increasing atomic weight. He placed elements with similar properties underneath each other. In a few instances where it made sense, he swapped some elements out of order of increasing atomic weight to better line up the chemical properties. In doing this he inadvertently set up his table by increasing atomic number rather than atomic weight. By the time his table was finished he had discovered what is now called the Periodic Law, which means that the physical and chemical properties of the elements repeat in a periodic manner.

Mendeleev's Periodic Table of Elements — Mendeleev’s Periodic Table of Elements

Mendeleev’s true genius came in the fact that he left spaces on his table, correctly predicting the existence of elements that had yet been discovered. He even predicted the properties of these missing elements based on their position in his table. For instance, he correctly predicted the existence of elements that would later be known as gallium, scandium, and germanium. Although his table was initially met with skepticism, when these elements were eventually discovered and their properties closely matched Mendeleev’s predictions it provided a strong validation of his table, quickly leading to its acceptance.

The Modern Periodic Table

Mendeleev’s table has continued to evolve as new elements were discovered and the understanding of the atomic structure increased. It is a product of the collaborative efforts of many scientists involving a few important changes and additions.

Most notably, thanks to the work of Henry Moseley, we now organize the table by atomic number, which is the total number of protons in the nucleus. This change happened as a result of the discovery of isotopes and lead to the realization that atomic number is the fundamental basis for the organization of the elements. In addition to that change the modern periodic table now includes over 100 elements, up from the 63 known to Mendeleev when his first table was published.

The Modern Periodic Table of Elements: The table today contains 118 known chemical elements
(Credit: American Chemical Society)

The are a few other changes and additions to make note of.

Noble gases: the original table did not include the specific group of noble gases as these elements were not yet discovered.
Electron structure: the modern periodic table is often presented with electron configurations for each element.
Improved measurements: significant advances in technology have allowed for more precise measurements of atomic weight and structure.
Filling of d- and f- blocks: these blocks were not fully understood during Mendeleev’s time and have been refined to reflect their electronic structures and chemical properties.
More comprehensive periodic trends: the modern periodic table provides more information about periodic trends such as atomic radius, ionization energy, and electron affinity.

The Importance of the Periodic Table

The periodic table is an indispensable tool for chemists and educators worldwide. Its organization captures the complexity of the natural world in a simple framework that easily shows the relationships, properties, and reactivity between the chemical elements.

The periodic table also provides a wealth of information about the chemical elements. It contains information about the atomic structure and weight, electron configuration, valence electrons, and chemical reactivity. All of this information provides insights into studying the elements and for manipulating matter at the molecular level. One area of study where this information is particularly useful is in the field of material science. By understanding the periodic trends, scientists have been able to design and engineer new materials with specific characteristics for a wide range of applications such as in electronics, energy production, agriculture, and medicine.

The periodic table of the elements was a triumph in scientific reasoning due to its predictive power. It stands as one of the most celebrated foresights in the history of science, serving as a prime example of the power of science to uncover hidden order in the universe.

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Alessandro Volta

Posted on February 23, 2019January 23, 2024 by Dan

Alessandro Volta (1745 – 1827) was an Italian physicist and chemist who was a pioneer in electricity. He is best known for inventing the battery, which was the first artificial source of continuous electrical current.

Volta was born in Como, Italy, was educated first at home and then at a Jesuit school. He became interested in electricity at an early age and began publishing papers on the topic in his early twenties. By 1774 he had became a professor of physics at the Royal School in Como. One of his first major accomplishments was the discovery and isolation of methane gas.

In 1791 his friend Luigi Galvani published his views of animal electricity, a form of electricity Galvani believed to be generated in the bodies of animals which would flow through the nerves, causing muscles to move. Galvani experiments showed that when two different metals came into contact with a dead frog, the frogs muscles would twitch. Volta disagreed with Galvani on his animal electricity hypothesis as he believed that it was the through the contact of two dissimilar metals that caused the electric current to flow. In an attempt to prove this Volta built what he called the Voltaic pile, the first ever electric battery.

The Voltaic pile provided a powerful too for other scientists to made additional observations and discoveries in the field of electricity. It was easy enough for anyone to make. Within weeks it was used to dissolve water into hydrogen and oxygen and within a few years newer and more powerful batteries were being created and used to isolate new chemical substances.

In 1791 Volta was already deemed an expert in electricity and he was elected to be a Fellow of the Royal Society. Impressed by his battery and work on electricity, Napoleon Bonaparte made him a Count in 1809. Volta died in 1827 but his legacy would live on. In 1881 in recognition of his fantastic contributions to electrical science the term volt would be the official SI unit of electric potential.

Luigi Galvani

Posted on February 23, 2019January 23, 2024 by Dan

Luigi Galvani (1737 – 1798) was a pioneer of bioelectricity who made important contributions in physics, chemistry, and biology. He was the first person to demonstrate the electrical basis for nerve impulses when he made a dead frogs muscle move when he jolted it with electricity.

Galvani was born in Bologna, Italy and obtained a degree in medicine at the University of Bologna in 1759. After graduation he applied for a position at the university and became a lecturer of anatomist of the university. In the 1770s Galvani had started to become interested in the relationship between electricity and life.

During experiments he conducted, Galvani realized that he could use electricity to make the dissected legs of a frog contract. For example, when Galvani used a scalpel made of steel to cut through the leg of a frog hanging from a brass hook, the leg visibly twitched. Based on his observations Galvani concluded that the body contained a type of electrical fluid which he dubbed animal electricity. He knew that his conclusions would be controversial and he delayed publishing his work until 1791 when he published Commentary on the Effect of Electricity on Muscular Motion.

Some of his scientific colleagues accepted his views, but he received opposition from the Italian physicist Alessandro Volta. Volta believed that it was through the contact of two dissimilar metals, such as the steel in the scalpel and the brass of the hook, that caused the electric current to flow. In response to Galvani Volta invented the Voltaic Pile, the first battery. He realized that the frog’s leg served as a conductor of electricity (electrolyte) and he replaced the leg with brine-soaked paper placed in between to pieces of metal. Volta’s conclusion ultimately proved correct however Galvani was still correct in attributing the muscular contractions to the electrical stimuli. Where Galvani was wrong was in the idea of an inherent animal electricity operating within the body.

Galvani continued to investigate animal electricity until the end of his life. It is his work that inspired Mary Shelly to write her famous work Frankenstein in 1818. Galvani died at his brothers home in December 1798.

James Lind

Posted on February 22, 2019January 23, 2024 by Dan

James Lind (1716 – 1794) was a Scottish doctor who is famous for his medical insight that eating citrus fruits will prevent and cure scurvy. He instituted other recommendations which stressing the importance of ventilation of ships and hygiene to the Royal Navy.

Lind was born in Edinburgh and began his education as an apprentice at the College of Surgeons at Edinburgh University before entering the Navy as a surgeons mate. In 1747 he had become surgeon of the 50 gun vessel HMS Salisbury.

As surgeon he carried out experiments, or clinical trials, to discover the cause of scurvy. Scurvy was a disease that was extremely deadly to sailors during the Age of Exploration. It is estimated that over 2 millions sailors were killed by the disease. Its symptoms weakness and fatigue, muscle soreness, loose teeth, bleeding gums and hemorrhages. It is caused by a lack of Vitamin C in the diet which is why citrus fruits prevent and cure it.

To carry out his experiment, Lind selected twelve men from his ship who suffered from scurvy and divided them into two groups of six, feeding each group a different diet. One of the groups contained citrus fruit, such as lemons and oranges, and this was the group that showed remarkable recovery results. This can be considered one of the first reported, controlled clinical trials in history. In 1753 he published A Treatise of the Scurvy to little fanfare. Lind recognized the importance of citrus friends in his treatise but he believed that there were multiple causes and hence many cures for the disease. He notes that the group that had the oranges and lemons recovered yet he is unclear on his recommendations to scurvy’s cure.

Lind continued to work on improving the diet and hygene of sailors. In 1762 Lind published an Essay on the Most Effectual Means of preserving the Health of Seamen rehashing some of his recommendations of his first book while adding further remarks on improving sailors heath. It wasn’t until 40 years later that the Navy mandated a supply of lemon juice on all ships, and with the scurvy virtually disappeared. Lind continued to do work on typhus, tropical disease, and other areas until he died in 1794.

1824: Carnot Cycle

Posted on February 21, 2019August 21, 2023 by Dan

The Carnot cycle is the ideal cycle of operations that provides the maximum theoretical efficiency for any engine that utilizes heat. It was first proposed by the French physicist Sadi Carnot in 1824 prior to its expansion by other scientists.

Reflections on the Motive Power of Fire

Nicolas Leonard Sadi Carnot is often referred to as the “father of thermodynamics”. In 1824, at the age of 27, he published his only book titled Reflections on the Motive Power of Fire in which he introduced the concept of the Carnot cycle while laying down the foundations for a new discipline – thermodynamics. By this time the steam engines industrial and economic importance had been established, although little scientific work had been done by studying them. Carnot’s book was one of the first scientific studies of steam engines.

Carnot explore some key ideas in his book. He recognized heat as a form of energy that can be converted from one state to another. This concept eventually led to the first law of thermodynamics, which states that energy is conserved in any thermodynamic process. He introduced the notion of an idealized heat engine, known as the Carnot engine, as a theoretical construct to study the maximum efficiency of heat conversion. This engine could be served as a reference point against which all other real work engines could be compared. Additionally, he noted that the efficiency of a heat engine depends of the temperature difference between the source and the sink, and that maximum efficiency is only achieved when it operates in a recoverable manner.

To understand the principles of an ideal heat engine, Carnot devised the Carnot cycle which is a series of four reversible processes. It is a theoretical cycle that provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work. The Carnot cycle heat engine is not a practical engine that can be made because its processes are reversible, which violate the second law of thermodynamics.

The Four Stages of the Carnot Cycle

The Carnot cycle consists of several operations. First, the engine absorbs energy in the form of heat from a reservoir. Work is done by the heat which causes an expansion. Next is compression where the heat is given out. The net result is that heat is taken from a hot source to a cooler one, while some of the heat does work. The Carnot cycle establishes the highest possible efficiency – measured by dividing the work that is done by the energy absorbed from the reservoir – for any heat engine. In the real work efficiency of an engine is never as high as that predicted by the Carnot cycle due to factors such as friction.

Here are the four stages of the Carnot cycle.

Isothermal expansion – gas expands on its surroundings as heat is transferred from hot reservoir at a constant temperature; work being done = heat supplied.
Adiabatic expansion – gas continues to expand on its surroundings with no heat exchange, causing temperature to cool; work being done > heat supplied.
Isothermal compression – surroundings compress gas as heat is transferred to a low temperature reservoir at a constant temperature.
Adiabatic compression – surroundings compress gas with no heat exchange, resetting the system to its original state (before stage 1).

The Importance of the Carnot Cycle

Sadi Carnot’s work brought about a revolution in our understanding of the underlying principles of heat transfer and energy conversion. Most directly, it set the stage for subsequent advancements in the field of thermodynamics. Work on the Carnot cycle heat engine led to the fundamental thermodynamic principle of entropy, a fundamental concept related the the second law of thermodynamics. Rudolf Clausius introduced the term entropy in the mid-19th century to explain the irreversible nature of energy transfer and transformations in physical systems. Clausius observed that heat naturally flows from a higher temperature region to a lower temperature region and that the process is irreversible. He recognized the importance of Carnot’s work with heat and sought to put in on a more rigorous, mathematical footing.
Another Rudolf was to later be inspired by the Carnot cycle when he was developing a more efficient engine. In 1982 Rudolf Diesel submitted design patents for an internal combustion engine. He knew gasoline engines were very inefficient, wasting around 90% of its heat in the process. He sought to make an engine closer to the theoretical framework of the Carnot cycle engine.

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Theodor Schwann

Posted on February 20, 2019January 23, 2024 by Dan

Theodor Schwann (1810 – 1882) was a German physician and physiologist who proposed the cellular nature of all living things. Along with Matthias Schleiden, Schwann laid down the foundation to Cell Theory.

Schwann was born in Neuss, Germany, attended a Jesuit school in Cologne, enrolled in the University of Bonn, transferred the the University of Wurzburg for clinical training in medicine before he finally moved the the University of Berlin where he obtained his M.D. degree. Much of his moving involved him following physiologist Johannes Muller, a leading physiologist of his time.

After he graduated he began to make a series of discoveries. In 1835 he discovered the enzyme Pepsin. Next he performed experiments with yeast and fermentation. He successfully demonstrated that fermentation was an organic process; that living yeast was necessary to produce more yeast.

Schwann’s most important work was in the development of Cell Theory. He began by taking the idea that all plants are made from cells and extended them to animals. In 1838 Schleiden published Contributions to our Knowledge of Phytogenesis, outlining his theories of the roles of cells in plant development. This influenced Schwann and the next year he published Microscopical Researches into the Accordance in the Structure and Growth of Animals and Plants, a landmark work where he proposed his own Cell Theory. In it he exclaimed ” “All living things are composed of cells and cell products”, extending Schleiden’s idea that new plant cells are formed from old plant cells to the domain of animals. He also coined the term “metabolism” to describe chemical reactions taking place within the cell.

Cell Theory and his work on yeast and fermentation provided strong evidence against the idea of spontaneous generation – the idea that living organisms could develop from nonliving matter. This won him tremendous respect from his peers. In 1879 Schwann was elected to both the Royal Society and to the French Academy of Science. He died three years later.

Matthew Maury

Posted on February 20, 2019January 23, 2024 by Dan

Matthew Maury (1806 – 1873) was an American Naval officer and oceanographer. He is credited with the moniker “Father of Modern Oceanography” thanks to the comprehensive book on oceanography he published in 1855, The Physical Geography of the Sea.

Maury was born into a Huguenot family in Virginia but had moved to Tennessee by the time he turned five. His brother John was a Navy officer and Matthew was determined to follow suit. He obtained a naval appointment at age 19 from Tennessee Representative Sam Houston. He immediately began studying the sea on a four-year voyage aboard the Vincennes that began in 1826. It was the first US Naval warship to circumnavigate the globe. Sadly, his seafaring days came to an abrupt end at the age of 33 after his leg was maimed in a stagecoach accident. Henceforth he would devote his time to studying the ocean.

In 1842 Maury was placed as head of the Depot of Charts and Instruments in Washington DC, which offered him a tremendous amount of maritime data in terms of log books and various other records. He would eventually turn this institution into the United States Naval Observatory and become its first superintendent.

In 1855 he published the first modern oceanography textbook, The Physical Geography of the Sea, describing the winds, currents, climate, and physical geography over the worlds oceans. That same year Maury proposed sea lanes in his book Sailing Directions. This idea was taken up by the major shipping companies to the benefit of lives and dollars saved. He also sent out survey ships to take depth readings on the Atlantic Ocean’s floor, which revealed the Mid-Atlantic ridge. His books and his surveys helped to prove the feasibility of laying a first transatlantic cable, which occurred in July 1866.

The American Civil War interrupted his career, sending him to Europe and then to Mexico before he finally returned to Virginia where he took the post of professor of meteorology at the Virginia Military Institute. He stayed there until his death in 1873.

820s: Algebra

Posted on February 19, 2019May 2, 2020 by Dan

Algebra is the study of mathematics by using a combination of symbols and values and the rules for manipulating those symbols and values. In its most basic form, it involves using equations to find the unknown. Linear equations, the quadratic formula, functions, and much more are all familiar examples of algebra. Algebra became recognized as a separate branch of mathematics thanks to work of the Persian mathematician Muhammad ibn Musa al-Khwarizmi.

The Roots of Algebra

The Quadratic Formula with Examples
(Credit: www.onlinemathlearning.com)

This history of any field of mathematics rides on a curvy road. This is no-less true for algebra. The roots of algebra can be traced back to Babylonian and Greek mathematics, at least 2000 BCE. We have evidence of stone tablets from Babylonian mathematicians who were hitting on the same ideas of algebra. The representation was not the same and the symbols they used were unique to their culture, but the fundamental spirit of algebra is evident. The Babylonians used complex arithmetic methods to solve modern algebraic problems. The Egyptians also worked with algebraic ideas but they were much less advanced that the Babylonians and did not advance much past solving linear equations.

The next big reservoir of algebraic thought came courteous of the Greek mathematicians, in particular a person named Diophantus of Alexandria. Diophantus lived in Alexandria, Egpyt in the 3rd century. Little is known of his life except his works and his age. He authored a thirteen book series titled Arithmetica that unfortunately has not survived in its full form. The portions that have survived show algebraic equations being solved. Diophantus and the Greeks devised a system of geometric algebra, using squares to solve for equations.

The Indian mathematician Brahmagupta was another person who influenced the development of algebra. Brahmagupta lived during the 7th century in northwest India. He wrote many influential works with a focus on mathematics and astronomy. His most famous work, Brahmasphutasiddhanta, provided solutions to linear and quadratic equations and is one of the earliest known texts to treat zero as a number. Much of his work moved from India the the Middle East, and was not known by Western Europe until many centuries later.

The Compendious Book on Calculation by Completion and Balancing

These earlier systems, especially the Greek and Indian, provided the inspiration for Persian mathematician al-Khwarizmi. Al-Khwarizmi was born in 780 and fortunate enough to have studied and worked in the House of Wisdom in Baghdad. The House of Wisdom was an enormous library and a major intellectual center of the time. In the 820s he wrote The Compendious Book on Calculation by Completion and Balancing, forming the foundation of algebra and establishing it as an independent discipline from arithmetic and geometry.

The Arabic title of his work is Al-jabr wa’l muqabalah, and it is from “al-jabr” that we get the term algebra. As the title indicates the text stresses the completion and balancing of equations. Here is a simple example of each type of operation:

Completion – Take the equation x+6=36. To complete this equation, we subtract 6 from each side to get x=36-6, or x=30.
Balancing – Take the equation x+y=y+30. To balance this equation we cancel y from both sides and get x=30.

His treatise is important because it presented the first systematic solution of linear and quadratic equations.

Algebra Today

Today algebra is used in a variety of mathematical fields, practical applications, and everyday life situations. Numbers and equations are used in everyday life whether we realize it or not. We use it in finance when we calculate loan interest, our return on investment, or a currency exchange rate. We use algebra when calculating rations. Ratios are relationships between different quantities. Twice as many guests are now showing up to your party? We need to balance the equation and add twice as many ingredients to that soup we are cooking. Are you a United States resident traveling outside the country? Most of the world uses the metric system for measurements and we’d use algebra to convert these measurements. We use algebra in statistics, graphing, computer coding, measuring calculations such as area, volume, and mass, and more.

Intuitively, we use algebra all the time when we solve for unknown variables. Abstractly, algebra helps us with our critical thinking and problem solving skills. Lastly many other branches of mathematics are dependent on algebra. Finding the area under a curve requires the use of calculus, and calculus would not be possible without algebra.

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