Mario Fiorentini, Italy’s most decorated resistance fighter, died at age 103 this week, and his mourners want his legacy to live on.

# Tag Archives: Mathematics

# The Mysterious Dance of the Cricket Embryos

A team of biologists and mathematicians studied hours of video to learn how insects take shape in the egg. The secret is geometry.

# The Elusive Origin of Zero

Who decided that nothing should be something?

# How Florence Nightingale Changed Data Visualization Forever

The celebrated nurse improved public health through her groundbreaking use of graphic storytelling

# Comey and McCabe Audits: How Likely That They Were a Coincidence?

The chances are minuscule. But minuscule is not zero.

# Ukrainian Mathematician Becomes Second Woman to Win Prestigious Fields Medal

# Mathematicians Are Trying to ‘Hear’ Shapes–And Reach Higher Dimensions

# Mathematicians Are Trying to ‘Hear’ Shapes

# How Anonymous Is Bitcoin, Really?

In myth, the cryptocurrency is egalitarian, decentralized and all but anonymous. The reality is very different, scientists have found.

# China Orders Investigation Into Children’s Textbooks

The discovery of what some viewed as disturbing illustrations in books for elementary school students set off a national furor.

# I Just Want My Kid to Learn Algebra. Does That Make Me a Culture Warrior?

Americans still underperform in math. That, not debates about testing and social emotional learning, should be our focus.

# A Look at the Textbooks Rejected by the Florida Department of Education

The state rejected dozens of math textbooks. The New York Times reviewed 21 of them to figure out why.

# Introducing WordleBot, the Upshot’s Daily Wordle Companion

It will tell you how skillful or lucky you were, and it could help improve your results.

# Try your hand at Quantum Go Fish

*Adapted from Math Games with Bad Drawings (2022) by Ben Orlin. You can read our latest interview with Orlin here.*

Of the thousand games I encountered in researching my book *Math Games with Bad Drawings*, only one of them truly frightened me. It’s a finger game. But trust me: It is the most cognitively taxing finger game that the human race has yet devised—a cross between a logic puzzle, an improv comedy session, and a collective hallucination, played with the strangest deck of cards you’ve ever seen (or not seen). Keep your aspirin at the ready.

## How to play

**What do you need**? Anywhere from three to eight players. Each begins the game by holding up four fingers. These are the “cards” in the deck.

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# Hate math? You’ll still love this cornucopia of simple-yet-seductive math games

In 1974, a geneticist named Marsha Jean Falco devised an ingenious research tool to help determine whether epilepsy in dogs was an inherited trait. She drew a series of symbols on index cards, where each card represented a dog and each symbol represented a DNA sequence, to create her own coding system. But as she shuffled and reshuffled the index cards over time, she began seeing the deck in terms of pure abstract patterns and combinations.

Eventually her personal coding system became the game of *Set*—just one of the many math-y games included in math teacher and bestselling author Ben Orlin’s new book, *Math Games with Bad Drawings*. (You can read an excerpt and try your hand at a game of *Quantum Go Fish* here.)

Orlin’s first book, *Math with Bad Drawings*, after his blog of the same name, was published in 2018. It included such highlights as placing a discussion of the correlation coefficient and “Anscombe’s Quartet” into the world of Harry Potter and arguing that building the Death Star in the shape of a sphere may not have been the Galatic Empire’s wisest move. We declared it “a great, entertaining read for neophytes and math fans alike, because Orlin excels at finding novel ways to connect the math to real-world problems—or in the case of the Death Star, to problems in fictional worlds.”

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# Math in 3-D: Q&A with Abel Prize Winner Dennis Sullivan

# Turing Award Won by Programmer Who Paved Way for Supercomputers

In the 1970s, Jack Dongarra created code and concepts that allowed software to work easily with the world’s most powerful computing machines.

# Virtuoso Mathematician Who Reshaped Topology Wins Abel Prize

# Abel Prize for 2022 Goes to New York Mathematician

Dennis P. Sullivan of Stony Brook University and the City University Graduate Center won an award that is the equivalent of the Nobel Prize for math.

# Is Geometry a Language That Only Humans Know?

Neuroscientists are exploring whether shapes like squares and rectangles — and our ability to recognize them — are part of what makes our species special.

# The Evolving Quest for a Grand Unified Theory of Mathematics

# 3 Revolutionary Women of Mathematics

# Mathematicians Protest Russia Hosting Major Conference

# How Covid Stole Our Time and How We Can Get It Back

‘Depressing Math’ can help you live a more fulfilled life.

# ‘The Man From the Future’ Recounts the Life of a Restless Genius

In his new book, Ananyo Bhattacharya writes about John von Neumann, who played an essential role in the development of quantum mechanics, computing and the atom bomb.

# A simple mathematical model can account for lizard’s green-and-black pattern

Zebras and tigers have stripes, cheetahs and leopards have spots, and the ocellated lizard (*Timon lepidus*) boasts a labyrinthine pattern of black-and-green chains of scales. Now researchers from the University of Geneva in Switzerland have demonstrated with a simple mathematical equation the lizard’s complex patterns, according to a recent paper published in the journal Physical Review Letters.

“These labyrinthine patterns, which provide ocellated lizards with an optimal camouflage, have been selected in the course of evolution,” said co-author Michel Milinkovitch, a theoretical physicist at the University of Geneva in Switzerland. “These patterns are generated by a complex system, that yet can be simplified as a single equation, where what matters is not the precise location of the green and black scales, but the general appearance of the final patterns.”

As we’ve reported previously, a common popular (though hotly debated) hypothesis for the formation of these kinds of animal patterns was proposed by Alan Turing in 1952, which is why they are sometimes referred to as “Turing patterns.” Turing’s seminal paper focused on chemicals known as morphogens. His proposed mechanism involved the interaction between an activator chemical that expresses a unique characteristic (like a tiger’s stripe) and an inhibitor chemical that periodically kicks in to shut down the activator’s expression. The key is that the inhibitor diffuses at a faster rate than the activator, creating periodic patterning.

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# Fermat’s Theorem: The Texas Oil Heir Who Took on Math’s Impossible Dare

James M. Vaughn Jr., wielding a fortune, argues that he brought about the Fermat breakthrough after the best and brightest had failed for centuries to solve the puzzle.

# How a Mathematician Spends His Sundays

Everywhere Steven Strogatz goes in the city, he sees math.

# New Math Research Group Reflects a Schism in the Field

# Shirley McBay, Pioneering Mathematician, Is Dead at 86

The first Black student to receive a doctorate from the University of Georgia, she devoted her life to advocating for diversity in science and math education.

# The Risk-Return Trade-Off Is Phony

A new book says the strongest long-term returns come from reducing the risk in a portfolio.

# Proposed Changes to California’s Math Curriculum Stir Debate

Proposed guidelines in California would de-emphasize calculus, reject the idea that some children are naturally gifted and build a connection to social justice. Critics say math shouldn’t be political.

# Gnarly, Centuries-Old Mathematical Quandaries Get New Solutions

# Simple Mathematical Law Predicts Movement in Cities around the World

# Infinity Category Theory Offers a Bird’s-Eye View of Mathematics

# The Godmother of the Digital Image

The mathematician Ingrid Daubechies’ pioneering work in signal processing helped make our electronic world possible — and beat a path for women in the field.

# Spain’s Factorial raises $80M at a $530M valuation on the back of strong traction for its ‘Workday for SMBs’

Factorial, a startup out of Barcelona that has built a platform that lets SMBs run human resources functions with the same kind of tools that typically are used by much bigger companies, is today announcing some funding to bulk up its own position: the company has raised $80 million, funding that it will be using to expand its operations geographically — specifically deeper into Latin American markets — and to continue to augment its product with more features.

CEO Jordi Romero, who co-founded the startup with Pau Ramon and Bernat Farrero — said in an interview that Factorial has seen a huge boom of growth in the last 18 months and counts more than anything 75,000 customers across 65 countries, with the average size of each customer in the range of 100 employees, although they can be significantly (single-digit) smaller or potentially up to 1,000 (the “M” of SMB, or SME as it’s often called in Europe).

“We have a generous definition of SME,” Romero said of how the company first started with a target of 10-15 employees but is now working in the size bracket that it is. “But that is the limit. This is the segment that needs the most help. We see other competitors of ours are trying to move into SME and they are screwing up their product by making it too complex. SMEs want solutions that have as much data as possible in one single place. That is unique to the SME.” Customers can include smaller franchises of much larger organizations, too: KFC, Booking.com, and Whisbi are among those that fall into this category for Factorial.

Factorial offers a one-stop shop to manage hiring, onboarding, payroll management, time off, performance management, internal communications and more. Other services such as the actual process of payroll or sourcing candidates, it partners and integrates closely with more localized third parties.

The Series B is being led by Tiger Global, and past investors CRV, Creandum, Point Nine and K Fund also participating, at a valuation we understand from sources close to the deal to be around $530 million post-money. Factorial has raised $100 million to date, including a $16 million Series A round in early 2020, just ahead of the Covid-19 pandemic really taking hold of the world.

That timing turned out to be significant: Factorial, as you might expect of an HR startup, was shaped by Covid-19 in a pretty powerful way.

The pandemic, as we have seen, massively changed how — and where — many of us work. In the world of desk jobs, offices largely disappeared overnight, with people shifting to working at home in compliance with shelter-in-place orders to curb the spread of the virus, and then in many cases staying there even after those were lifted as companies grappled both with balancing the best (and least infectious) way forward and their own employees’ demands for safety and productivity. Front-line workers, meanwhile, faced a completely new set of challenges in doing their jobs, whether it was to minimize exposure to the coronavirus, or dealing with giant volumes of demand for their services. Across both, organizations were facing economics-based contractions, furloughs, and in other cases, hiring pushes, despite being office-less to carry all that out.

All of this had an impact on HR. People who needed to manage others, and those working for organizations, suddenly needed — and were willing to pay for — new kinds of tools to carry out their roles.

But it wasn’t always like this. In the early days, Romero said the company had to quickly adjust to what the market was doing.

“We target HR leaders and they are currently very distracted with furloughs and layoffs right now, so we turned around and focused on how we could provide the best value to them,” Romero said to me during the Series A back in early 2020. Then, Factorial made its product free to use and found new interest from businesses that had never used cloud-based services before but needed to get something quickly up and running to use while working from home (and that cloud migration turned out to be a much bigger trend played out across a number of sectors). Those turning to Factorial had previously kept all their records in local files or at best a “Dropbox folder, but nothing else,” Romero said.

It also provided tools specifically to address the most pressing needs HR people had at the time, such as guidance on how to implement furloughs and layoffs, best practices for communication policies and more. “We had to get creative,” Romero said.

But it wasn’t all simple. “We did suffer at the beginning,” Romero now says. “People were doing furloughs and [frankly] less attention was being paid to software purchasing. People were just surviving. Then gradually, people realized they needed to improve their systems in the cloud, to manage remote people better, and so on.” So after a couple of very slow months, things started to take off, he said.

Factorial’s rise is part of a much, longer-term bigger trend in which the enterprise technology world has at long last started to turn its attention to how to take the tools that originally were built for larger organizations, and right size them for smaller customers.

The metrics are completely different: large enterprises are harder to win as customers, but represent a giant payoff when they do sign up; smaller enterprises represent genuine scale since there are so many of them globally — 400 million, accounting for 95% of all firms worldwide. But so are the product demands, as Romero pointed out previously: SMBs also want powerful tools, but they need to work in a more efficient, and out-of-the-box way.

Factorial is not the only HR startup that has been honing in on this, of course. Among the wider field are PeopleHR, Workday, Infor, ADP, Zenefits, Gusto, IBM, Oracle, SAP and Rippling; and a very close competitor out of Europe, Germany’s Personio, raised $125 million on a $1.7 billion valuation earlier this year, speaking not just to the opportunity but the success it is seeing in it.

But the major fragmentation in the market, the fact that there are so many potential customers, and Factorial’s own rapid traction are three reasons why investors approached the startup, which was not proactively seeking funding when it decided to go ahead with this Series B.

“The HR software market opportunity is very large in Europe, and Factorial is incredibly well positioned to capitalize on it,” said John Curtius, Partner at Tiger Global, in a statement. “Our diligence found a product that delighted customers and a world-class team well-positioned to achieve Factorial’s potential.”

“It is now clear that labor markets around the world have shifted over the past 18 months,” added Reid Christian, general partner at CRV, which led its previous round, which had been CRV’s first investment in Spain. “This has strained employers who need to manage their HR processes and properly serve their employees. Factorial was always architected to support employers across geographies with their HR and payroll needs, and this has only accelerated the demand for their platform. We are excited to continue to support the company through this funding round and the next phase of growth for the business.”

Notably, Romero told me that the fundraising process really evolved between the two rounds, with the first needing him flying around the world to meet people, and the second happening over video links, while he was recovering himself from Covid-19. Given that it was not too long ago that the most ambitious startups in Europe were encouraged to relocate to the U.S. if they wanted to succeed, it seems that it’s not just the world of HR that is rapidly shifting in line with new global conditions.

# How to Solve Any Problem Using Just Common Sense

Contemplating Fermi problems keeps me curious about the world and how things relate to one another.

# A Deep Math Dive into Why Some Infinities Are Bigger Than Others

# Modern Mathematics Confronts Its White, Patriarchal Past

# Is This Some Kind of Code? You Can Solve the …

Erik and Martin Demaine, a father-and-son team of “algorithmic typographers,” have confected an entire suite of mathematically inspired typefaces.

# Can Geometry Be as Soul-Stirring as Poetry?

In “Shape,” Jordan Ellenberg argues for the importance of geometry as the underlying structure of reality.

# A New Biography of Kurt Gödel, Whose Brilliant Life Intersected With the Upheavals of the 20th Century

“Journey to the Edge of Reason,” by Stephen Budiansky, is an illuminating new biography of the groundbreaking mathematician.

# ‘Shape’ Makes Geometry Entertaining. Really, It Does.

In his new book, Jordan Ellenberg explains how geometric thinking can allow for everything from fairer American elections to better pandemic planning.

# 2 Win Abel Prize for Work That Bridged Math and Computer Science

Avi Wigderson and László Lovász will share the annual prize that aims to be something like the Nobel for mathematics.

# The Latest Wrinkle in Crumple Theory

From studies of “geometric frustration,” scientists learn how paper folds under pressure.

# Triangulating Math, Mozart and ‘Moby-Dick’

Sarah Hart, the first woman to hold England’s distinguished Gresham professorship of geometry, explores the intersections of music, literature and mathematics.

# New World Map Tries to Fix Distorted Views of Earth

You’re going to need some double-sided tape.

# The Lasting Lessons of John Conway’s Game of Life

Fifty years on, the mathematician’s best known (and, to him, least favorite) creation confirms that “uncertainty is the only certainty.”

# ‘The Pandemic Is a Prisoner’s Dilemma Game’

Using game theory, researchers modeled two ways of prioritizing vaccinations, to see which saved more lives.