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The word algorithm sounds like modern tech jargon, but it is actually a centuries-old Latin rendering of one ninth-century scholar's name. This deep dive follows al-Khwarizmi, a Persian-heritage mathematician who wrote in Arabic and worked as an astronomer and head of the library at the House of Wisdom in Baghdad under the Abbasid Caliph al-Mamun.

We explore how messy Islamic inheritance disputes pushed him to write al-Jabr, the book that gave us algebra, and why his shift from geometry to abstract operational logic mattered more than solving any single equation. Then we follow his work on Hindu-Arabic numerals and zero, his astronomical and trigonometric tables, and a 70-person project that redrew Ptolemy's map of the world.

• How al-Jabr (restoration) and al-muqabala (balancing) turned inheritance math into a universal method written entirely in prose
• Why scholars still credit him over Diophantus and Brahmagupta: six standard equation forms and geometric proofs
• His text on Indian computation, the sand-covered dustboard, and how 'Dixit Algorithmi' became the word algorithm
• The Zij al-Sindhind astronomical tables and the sine and cosine values behind prayer times and navigation
• Using lunar eclipses as a global clock to shrink Ptolemy's Mediterranean from 63 to 50 degrees of longitude

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Winslow Homer was born in Cambridge, Massachusetts, in 1836. His mother Henrietta, an amateur watercolorist, was his first teacher, while his father Charles left the family hardware store for the California gold rush and later schemes in Europe. At 19 Homer was apprenticed to a Boston commercial lithographer, drawing sheet music covers in reverse on limestone, and when he quit to freelance for Harper's Weekly he vowed never to have a master again. In 1861 he joined George B. McClellan's army on the Potomac.

His war pictures, including Sharpshooter on Picket Duty and Prisoners from the Front, showed waiting and exhaustion rather than battle, and A Visit from the Old Mistress set freed people and their former enslaver on equal footing. In Paris in 1867 he ignored the Impressionists, and from 1873 watercolor gave him steadier sales. After two years in Cullercoats, England, he settled in 1883 at Prouts Neck, Maine, 75 feet from the Atlantic, painting Undertow, Eight Bells, The Gulf Stream, and The Fox Hunt.

• Henry James called Homer's subjects unpictorial but conceded the paintings were incontestably successful.
• One critic wrote that a child with an ink bottle could not have done worse than his watercolors.
• Undertow earned Homer only $400, and he relied on his brother Charles for financial support.
• His Bahamas watercolor Children Under a Palm Tree was rediscovered on Antiques Roadshow in 2008.
• He died at Prouts Neck in 1910 with Shooting the Rapids unfinished on his easel.

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Winfield Scott, born in Virginia in 1786 and standing six foot five, studied law and watched General James Wilkinson give self-serving testimony at the 1807 Aaron Burr treason trial. Commissioned an artillery captain in 1808, he was sent to New Orleans under Wilkinson, who camped troops in a disease-ridden swamp he owned. Scott's public criticism brought a court-martial, a one-year suspension, and a pistol duel with Dr. Upshaw in which a bullet grazed his scalp. He spent the suspension studying French military manuals.

In the War of 1812 he was captured at Queenston Heights, then drilled his brigade 10 hours a day at Buffalo and beat British regulars at Chippewa before a musket ball shattered his shoulder at Lundy's Lane. The episode covers the nullification crisis in Charleston, nursing cholera victims during the Black Hawk War, and his role in the Cherokee removal. It then follows the Mexico City campaign, his 1852 loss to Franklin Pierce, and the 1861 strategy the press mocked and Union leaders later used.

• At Chippewa the British commander reportedly cried out, Those are regulars, by God, at Scott's gray-clad troops.
• His love of uniforms and etiquette earned him the nickname Old Fuss and Feathers.
• He let Cherokee Chief John Ross take over the removal contract, angering Andrew Jackson.
• In Mexico he ordered troops to pay for supplies and salute Catholic priests, and Robert E. Lee scouted the path around Cerro Gordo.
• The Duke of Wellington called him the greatest living general.

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The Zouaves began in French-occupied Algeria in 1830, named for the Zwawa, Berbers of the Djurdjura Mountains. The first recruits included Kabyles, Turks, Moors, and Arabs, but desertion was severe, with 46 percent leaving over one 15-month span. By 1842 the ranks were entirely European and Jewish, largely Algerian-born settlers, yet they kept the chechia cap, buttonless jacket, baggy sarouel trousers, and a sash about 10 feet long. Their open-order tactics and prone loading drill made them feared shock troops.

The look spread to the Papal Zouaves defending Pius IX, the black-uniformed Zouaves of Death in the 1863 Polish uprising, and units in Spain, Brazil, and the British West Indies. In the United States, Elmer Ellsworth's touring Zouave Cadets helped inspire more than 70 Union Zouave regiments and about 25 Confederate companies. Rifled muskets made the bright uniforms deadly targets, World War I ended the colorful dress by 1915, and the French Zouave regiments were disbanded in 1962 after Algerian independence.

• Paris uses a 17-foot Zouave statue on the Alma Bridge to judge how high the Seine is flooding.
• Putting on the sash took two men, with the soldier spinning himself into it.
• Notable American units included the 11th New York Fire Zouaves, the 5th New York, and the Louisiana Tigers.
• At Second Bull Run the 5th New York lost about 120 killed and 330 wounded out of 525 men in under 10 minutes.
• Legend says a Zouave at Sevastopol rolled tobacco in gunpowder paper, inspiring the Zig-Zag logo.

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James Longstreet, Robert E. Lee's old war horse, was born in South Carolina in 1821 and raised on the Georgia frontier by his uncle Augustus. He finished near the bottom of his West Point class but befriended William Rosecrans, George Pickett, and Ulysses S. Grant, whose wedding to Longstreet's cousin Julia Dent he attended. In January 1862 scarlet fever killed three of his children in a single week, and the jovial poker player became the stoic commander his staff called a rock.

Longstreet favored a strategic offensive with tactical defense, and at Gettysburg he argued against the assault Lee ordered on the third day. After the war he urged Southerners to accept defeat, joined the Republican Party, and in 1874 led a biracial militia against the White League at the Battle of Liberty Place in New Orleans. Jubal Early and William Pendleton then blamed him for Gettysburg. The episode covers his wounding in the Wilderness, his post as diplomat to the Ottoman Empire, and his marriage at 76 to Helen Dortch.

• Wounded in the thigh at Chapultepec, Longstreet handed his regiment's colors to George Pickett.
• He told Lee that no 15,000 men ever arrayed for battle could take the position at Gettysburg.
• In front of Jefferson Davis, he said Braxton Bragg knew nothing of the business of war.
• His Wilderness flank attack used an unfinished railroad bed before friendly fire paralyzed his right arm.
• William Pendleton's claim that Lee ordered a sunrise attack at Gettysburg has no supporting evidence.

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Cold Harbor was not a port but a rural Virginia crossroads about 10 miles northeast of Richmond, named for a Burnett family tavern that offered shelter but no hot meals. In the spring of 1864, during the Overland Campaign, Ulysses S. Grant kept sliding southeast around Robert E. Lee's flank, and both sides raced to the intersection. Grant pulled heavy artillerymen from the Washington forts to bring his strength above 100,000, while Lee gathered roughly 59,000 to 62,000.

A small Union gain on June 1 led George Meade to order an army-wide assault, but exhausted night marches pushed it back 24 hours. Lee's men used the delay to build seven miles of zigzag earthworks with interlocking fields of fire. At 4:30 a.m. on June 3 about 35,000 Union troops attacked and lost an estimated 3,000 to 7,000 men in hours, and Grant suspended the attack by 12:30 p.m. Nine days of trench fighting followed before Grant slipped away across the James River toward Petersburg.

• The night before the assault, Union soldiers pinned slips with their names and hometowns inside their coats.
• Confederate gunners drove stakes at 200, 300, and 400 yards to pre-set the fuses on their shells.
• General William F. Smith refused Meade's order to renew the assault, calling it a wanton waste of life.
• Grant and Lee exchanged notes for days, and the two-hour truce on June 7 came too late for most of the wounded.
• Grant later wrote that the final assault at Cold Harbor was the greatest regret of his military career.

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In late June 1862 the Union Army of the Potomac was close enough to Richmond to hear its church bells, yet within a week it was retreating to the James River. George B. McClellan had more than 100,000 men but believed Pinkerton reports that he faced 200,000. Robert E. Lee, in command only since June 1 after Joseph E. Johnston's wounding at Seven Pines and mocked as the King of Spades, had about 90,000 men and chose to attack rather than endure a siege.

After Oak Grove on June 25, A.P. Hill's unsupported assault at Beaver Dam Creek was repulsed, yet McClellan decided that night to abandon his railroad supply line. Gaines' Mill, the largest Confederate attack of the war, broke the Union line, and McClellan boarded a Navy gunboat on June 29 without naming a second in command. Lee's trap at Glendale failed, and on July 1 Henry Hunt's massed artillery on Malvern Hill shattered the Confederate assaults. The week cost nearly 16,000 Union and more than 20,000 Confederate casualties.

• Pinkerton's agents estimated enemy strength partly by counting Confederate campfires.
• Stonewall Jackson arrived hours late at Mechanicsville and spent a day at White Oak Swamp trying to rebuild a bridge.
• Benjamin Huger had his men cut a new road through the woods around felled trees and missed Glendale.
• Henry Hunt massed 250 cannons on Malvern Hill, and Confederate infantry never got within 200 yards of the Union center.
• Lee reorganized his army into two corps under James Longstreet and Stonewall Jackson after the campaign.

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George B. McClellan rebuilt the Army of the Potomac after First Bull Run, ringing Washington with 48 forts and 480 heavy guns, and in November 1861 told Lincoln he could do it all as general-in-chief. Instead of marching overland, he pushed his Urbanna Plan to move the army by water around the Confederates, defending it in a 22-page letter to the president. Joseph E. Johnston withdrew in March 1862, leaving behind Quaker guns, and Lincoln removed McClellan as general-in-chief on March 11.

McClellan shipped more than 120,000 men, 15,000 horses, and 1,150 wagons to Fort Monroe, but the CSS Virginia kept the Navy from covering his flanks. At the Warwick Line, John B. Magruder's roughly 11,000 men held him for a month while Allan Pinkerton's inflated estimates put the enemy near 100,000. The episode follows Williamsburg, Hanover Court House, Seven Pines and the Grapevine Bridge, Johnston's wounding, Robert E. Lee's arrival, and the retreat to the James River after Malvern Hill.

• Magruder marched a single company in a continuous loop through a clearing to simulate endless reinforcements.
• McClellan prepared more than 70 siege guns, and the Confederates left the night before the bombardment.
• He dismissed escaped enslaved people who reported that the Confederates were evacuating their lines.
• Edwin Sumner's men crossed the Grapevine Bridge at Seven Pines just before it washed away.
• J.E.B. Stuart's cavalry rode completely around the Union army in three days.

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In 1863 a piece of sheet music was deposited in the Library of Congress under the name Louis Lambert, a pseudonym for the Irish-American bandleader Patrick Gilmore. Published by Henry Tolman and Company in Boston, the lyrics were reportedly written for his sister Annie, who was waiting for Union light artillery captain John O'Rourke. The words describe church bells, cheering villages, and laurel wreaths for returning soldiers, with no mention of victory or the enemy.

In 1883 Gilmore admitted in The Musical Herald that the melody was a tune he had heard someone humming. The same music had appeared months earlier as the drinking song Johnny Fill Up the Bowl, and historians link it to the Scottish John Anderson, My Jo and the English ballad The Three Ravens. The episode follows the tune from Union and Confederate campfires to Glenn Miller, Morton Gould's American Salute, The Clash's English Civil War, Guns N' Roses, and the children's song about ants marching one by one.

• Gilmore called the melody an orphan tune he had dressed up and rhymed into usefulness.
• A Gilmore publisher printed lyric slips telling buyers to sing the new words to the drinking song's tune.
• Johnny I Hardly Knew Ye was not published until 1867 and was first sung to a different melody.
• Glenn Miller, Guy Lombardo, and the Andrews Sisters all recorded the tune during World War II.
• It appears in a 1979 Bollywood film and in the anime Black Lagoon and Girls und Panzer.

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The Confederate battle cry known as the rebel yell sounded nothing like a cowboy's yee-haw. Soldiers and correspondents described a noise that began low in the diaphragm and climbed through rhythmic crescendos into a high, piercing shriek, comparing it to a dying rabbit, a cougar, or a wolf's howl. Regiments practiced it, and one Virginia cavalry battalion became so known for its coordinated cry that it was nicknamed the Comanches.

The only audio comes from elderly veterans filmed at reunions, including the 75th anniversary of Gettysburg in 1938, and a North Carolina infantryman and a Virginia cavalryman produced nearly identical yells. The episode examines theories that the cry blended Scots-Irish Highland charges, Comanche war whoops, Moorish-influenced ululation, and fox hunters' calls, and that it was heard in Bleeding Kansas before 1861. It also looks at why officers ordered men to holler during charges, and how the name later landed on a bourbon and a Billy Idol song.

• One early written account spelled the yell as a low whoa followed by a long, vibrating hooey.
• A veteran asked to demonstrate it at a society dinner refused, saying it could not be done standing still with false teeth.
• A writer who fought at Chickamauga called it the ugliest sound any mortal ever heard.
• One general ordered his men to yell because they had run out of ammunition.
• A former Confederate surgeon would leap up and give the yell at the opera when the orchestra played Dixie.