mathematics

John Urschel

John Urschel is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand John Urschel rather than just read about it. In short: John Cameron Urschel Jr. (born June 24, 1991) is a Canadian mathematician and former professional football guard.

Key takeaways

John Urschel belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect John Urschel to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of John Urschel from memory before moving on to harder problems.

Reference excerpt

John Cameron Urschel Jr. (born June 24, 1991) is a Canadian mathematician and former professional football guard. He played college football at Penn State and was drafted by the Baltimore Ravens in the fifth round of the 2014 NFL draft. Urschel played his entire NFL career with Baltimore before announcing his retirement on July 27, 2017, at 26 years old. Urschel has bachelor's and master's degrees (both from Penn State) and a PhD (from the Massachusetts Institute of Technology), all in mathematics. Urschel is also an advanced statistics columnist for The Players' Tribune. He served a three-year term on the College Football Playoff selection committee which began in the spring of 2020, and is an assistant professor at the Department of Mathematics of the Massachusetts Institute of Technology.

Early life and education Urschel was born in Winnipeg, Manitoba, Canada. His parents, John Urschel Senior and Venita Parker, were a surgeon and attorney, respectively. He grew up in Buffalo, New York where he graduated from Canisius High School in 2009. At Pennsylvania State University, Urschel earned both a bachelor's degree in 2012 and a master's 2013 degree in mathematics before earning his PhD in mathematics from the Massachusetts Institute of Technology in 2021. While at Penn State, he was awarded the William V. Campbell Trophy, known as the "academic Heisman".

Professional football career

Urschel was selected by the Baltimore Ravens in the fifth round of the 2014 NFL draft. He played in 11 games, starting three, for the Ravens in 2014. He appeared in 16 games, starting seven, for the team in 2015. He played in 13 games, starting three, his final season in 2016. On July 27, 2017, Urschel announced his retirement from the NFL after three seasons. The Baltimore Sun reported that the JAMA study on the prevalence of chronic traumatic encephalopathy (CTE) in deceased players was a factor in Urschel's decision. Officially he stated, "This [CTE] was actually a serious, serious concern of mine. Yes, I am retiring; I did retire. But at the same time, I love the NFL. I love football. I wouldn't trade my experiences for the world. I do believe that football is a great game. I didn't want to be fodder for anti-football establishments." His retirement as an active player was not the end of his participation in the sport. He was appointed to the College Football Playoff selection committee on January 22, 2020, serving a three-year term which began in the spring of that year.

Mathematics career While doing his master's at Penn State, Urschel was involved in teaching vector calculus, trigonometry and analytic geometry, and introduction to econometrics. In 2014, Urschel was named Arthur Ashe, Jr. Sports Scholar by Diverse: Issues In Higher Education. In 2015, Urschel co-authored a paper in the Journal of Computational Mathematics titled "A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians". It includes "a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue." Urschel began a Ph.D. in mathematics at Massachusetts Institute of Technology in 2016, focusing on spectral graph theory, numerical linear algebra, and machine learning. MIT does not allow Ph.D. students to study part-time; while the Ravens knew that he was taking classes, Urschel admitted after retiring from the team that he did not disclose that he was a full-time graduate student, having taken correspondence classes in between games and practices. On January 4, 2017, Urschel was named to Forbes' "30 Under 30" list of outstanding young scientists and owns the following blurb: "Urschel has published six peer-reviewed mathematics papers to date and has three more ready for review. He's won academic awards for his math prowess. All this while playing guard for the Baltimore Ravens." Since 2017, Urschel has had an Erdős number of 4. His PhD thesis on Graphs, Principal Minors, and Eigenvalue Problems was completed in 2021 under Michel Goemans at MIT. He was a member of the Institute for Advanced Study in Princeton, New Jersey. In the Fall of 2023, Urschel joined the faculty of MIT as an assistant professor in the MIT Math department. He is also a Junior Fellow at the Harvard Society of Fellows (currently on leave).

Awards and honors 2009: Mr. Canisius 2013: Senior CLASS Award 2016–2018: Dean of Science Fellowship 2017: Forbes's "30 Under 30" list in science 2024: Doctor of Letters, honoris causa, Dartmouth College

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with John Urschel

Start with the simplest possible case. Write down what John Urschel claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to John Urschel before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about John Urschel ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of John Urschel

In research: John Urschel appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses John Urschel in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: John Urschel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1991 births, 21st-century American mathematicians, American football offensive guards, so understanding it makes those chapters shorter.
In everyday life: Look for John Urschel outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study John Urschel in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what John Urschel means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain John Urschel out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is John Urschel in simple terms?

John Cameron Urschel Jr. (born June 24, 1991) is a Canadian mathematician and former professional football guard.

Why does John Urschel matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study John Urschel?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on John Urschel.