Voevodsky (left) is awarded the Fields Medal — mathematics' highest prize — in 2002. Photo: Greg Baker / AP

Vladimir Voevodsky, a groundbreaking computer scientist and mathematician, died in his home in Princeton, New Jersey on Sept. 30. Voevodsky was 51 and had been a professor at Princeton University for 15 years.

The Russian-born Voevodosky is credited with pioneering the "motivic homotopy theory" field of mathematics and ushering in the use of computers to check scholars' proofs. Voevodsky's work in computer science was so revolutionary that it shifted the meaning of the = sign, the New York Times reports.

From Voevodsky's colleagues, per the Times:

  • His work "changes the very meaning of what the equals sign means in mathematics ... The foundations of math are like a constitutional document that spells out the governing rules all mathematicians agree to play by. He has given us a new constitution." —Thomas Hales, University of Pittsburgh
  • "His contributions are so fundamental that it's impossible to imagine how things were thought of before him." —Chris Kapulkin, University of Western Ontario

Go deeper: The New York Times' obituary of Vladimir Voevodsky

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Roger Marshall wins Republican Senate nomination in Kansas primary

Rep. Roger Marshall. Photo: Mark Reinstein/Corbis via Getty Images

Rep. Roger Marshall won the Kansas Republican Senate primary on Tuesday evening, beating former Secretary of State Kris Kobach and a slew of other candidates, AP reports.

Why it matters: Following GOP Sen. Pat Roberts' retirement announcement, some Republicans worry that if Kobach won the primary it would endanger the party's chances of keeping the seat and maintaining a majority in the Senate.

Updated 1 hour ago - Politics & Policy

Primary races to watch in Arizona, Kansas, Michigan, Missouri, Washington

Photo: Michael B. Thomas/Getty Images

Primary elections on Tuesday in fives states see crowded fields of both Republicans and Democrats hoping to make the ballot in 2020.

What to watch: Rep. Rashida Tlaib (D-Mich.) is "fighting for her political life" in a tight primary race against Detroit City Council President Brenda Jones, who Tlaib beat by 900 votes in 2018, The New York Times writes. Senate Republicans are also watching the primary race in Kansas to see who could replace retiring Republican Sen. Pat Roberts.

Updated 2 hours ago - Politics & Policy

Coronavirus dashboard

Illustration: Sarah Grillo/Axios

  1. Global: Total confirmed cases as of 8:30 p.m. ET: 18,448,084 — Total deaths: 698,023 — Total recoveries — 11,048,174Map.
  2. U.S.: Total confirmed cases as of 8:30 p.m. ET: 4,765,170 — Total deaths: 156,668 — Total recoveries: 1,528,979 — Total tests: 57,543,852Map.
  3. States: New York City health commissioner resigns in protest of De Blasio's coronavirus response — Local governments go to war over schools.
  4. Public health: 59% of Americans support nationwide 2-week stay-at-home order in NPR poll.
  5. Politics: Trump's national security adviser returns to work after coronavirus recovery Republicans push to expand small business loan program.
  6. Sports: Indy 500 to be held without fansRafael Nadal opts out of U.S. Open.