Descriptive set theorists study the niche mathematics of infinity. Now, they've shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don't need to think about it when they're solving their problems. They can take it for granted that sets behave the way they'd expect, and carry on with their work. Descriptive set theorists are an exception. This small community of mathematicians never stopped studying the fundamental nature of sets--particularly the strange infinite ones that other mathematicians ignore. Their field just got a lot less lonely. In 2023, a mathematician named Anton Bernshteyn published a deep and surprising connection between the remote mathematical frontier of descriptive set theory and modern computer science.

Llamasoft's software helps companies model, design and optimize their supply-chain networks, using AI and algorithms to map out scenarios and mitigate potential risks. The Ann Arbor, Mich., company is backed by private-equity fund TPG Capital, which took a stake in 2017, and counts Boeing Co., Danone SA and Home Depot Inc. among its customers. This is Coupa's third acquisition this year. The company's platform helps businesses manage procurement, invoicing, payments, sourcing and other spending functions and has more than $1.95 trillion in cumulative spending by its customers under management. "We've pulled all these siloed processes together," Coupa CEO Rob Bernshteyn said.

Coupa Software provides real-time analytics for pricing, assortment, demand and competitive metrics in the retail sector. The firm has had a big six months -- in October the firm launched a successful IPO, which saw its shares more than double on its first day of trading. Analysts at the time said the strength of the IPO underscored investors' appetite for technology. On its own, Coupa has already made its first big acquisition -- Spend360, a U.K. firm that provides digital data management solutions, including data analytics, using machine learning and artificial intelligence, for corporate finance and procurement teams. Many think this will be the first of a few upcoming acquisitions as Coupa adjusts to existence in the public markets and pushes forward on its path to profitability (as of its IPO, Coupa still wasn't quite there yet).