Pope Leo XIV - a mathematics major

 

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On May 8, 2025, the Cardinal Robert Francis Prevost was elected as the 267th leader of the Catholic Church. He is the first American to hold the position. He has taken the name of Pope Leo XIV. In college, he earned a Bachelor of Science in Mathematics in 1977 from Villanova University.

Grok was asked about prior popes who had college degrees in mathematics or science. Response:

To determine whether any popes prior to Pope Leo XIV had college degrees in mathematics or science, we need to examine the educational backgrounds of the 266 popes who preceded him, from St. Peter to Pope Francis, focusing on those with formal degrees in these fields. Pope Leo XIV, elected on May 8, 2025, is noted for having a Bachelor of Science in Mathematics from Villanova University (1977), making him a rare case among popes with a formal degree in a scientific discipline. The question requires identifying other popes with comparable academic credentials in mathematics or science, which typically means a university degree or equivalent formal study in fields like mathematics, physics, astronomy, chemistry, or related disciplines.

### Historical Context and Challenges

**Education in Earlier Eras**: 

Formal university degrees, as we understand them today, were not common until the establishment of universities in the Middle Ages (e.g., Bologna, Paris, Oxford). Before this, education was often informal, through monasteries, cathedral schools, or private tutors, and focused on theology, philosophy, or the liberal arts (including the quadrivium: arithmetic, geometry, astronomy, and music).

 **Quadrivium and Science**: 

In the medieval period, mathematics and astronomy were part of the quadrivium, studied by many educated clergy, including some popes. However, this was not equivalent to a modern college degree, which involves specialized, structured study and a formal credential.

**Modern Era**: 

From the 17th century onward, universities began offering degrees closer to modern standards, and some clergy pursued studies in natural sciences. We’ll focus on popes from this period for potential degree-holders, while also checking notable earlier popes known for mathematical or scientific expertise.

### Analysis of Popes with Mathematical or Scientific Backgrounds

Based on historical records and recent sources, we’ll evaluate popes known for their education or contributions in mathematics or science, particularly those with formal degrees. The sources highlight Pope Sylvester II and Pope Leo XIV, with some mention of Pope Francis, so we’ll start with these and expand to others.

#### 1. Pope Sylvester II (999–1003)

**Background**: Born Gerbert of Aurillac (c. 946–1003), he was a renowned scholar in the 10th century, often considered one of the most learned men of his time.

 **Education**:

  - Studied at the monastery of Saint-Gerald in Aurillac, France, where he likely learned the basics of the quadrivium.

  - From 967 to 970, he studied in Catalonia (Vich, Spain), under Bishop Atto, where he was exposed to Islamic mathematics and astronomy, including the abacus and Hindu-Arabic numerals. This was advanced for Europe but not a formal degree program, as universities did not yet exist in this form.

  - Later, in Rheims, he taught and studied further, possibly at cathedral schools, focusing on mathematics, astronomy, and music theory. His education was equivalent to the highest scholarly training of his era but not a college degree, as no such credentials were awarded.

**Contributions**:

  - Reintroduced the abacus and armillary sphere to Western Europe, advancing mathematical and astronomical education.

  - Wrote treatises on arithmetic, geometry, and astronomy, used as educational guides for students.

  - Promoted the Hindu-Arabic numeral system, a significant mathematical advancement.

**Degree Status**: No formal college degree. His studies were conducted in monastic and cathedral schools, not universities, and no evidence suggests he received a degree-like credential. His expertise was exceptional but based on self-directed learning and mentorship, not a structured academic program.

**Sources**: Wikipedia entry on Sylvester II and “A Mathematician Who Became Pope” from The Renaissance Mathematicus confirm his mathematical and astronomical expertise but do not mention a degree.(https://en.wikipedia.org/wiki/Pope_Sylvester_II)(https://thonyc.wordpress.com/2012/05/12/a-mathematician-who-became-pope/)

#### 2. Pope Leo XIV (2025–present)

**Background**: Born Robert Francis Prevost in 1955, elected May 8, 2025, he is the first American pope and an Augustinian friar.

 **Education**:

  - Earned a Bachelor of Science in Mathematics from Villanova University in 1977, a formal undergraduate degree from an accredited institution.

  - Also studied philosophy at Villanova and earned a Master of Divinity from Catholic Theological Union (1982), plus licentiate (1984) and doctorate (1987) degrees in canon law from the Pontifical University of Saint Thomas Aquinas in Rome.

 **Relevance**: His mathematics degree is well-documented and directly answers the question as a benchmark. We’re looking for popes before him with similar credentials.

 **Sources**: Multiple sources confirm his mathematics degree, including Villanova University, Times Now, and Wikipedia.(https://www1.villanova.edu/university/media/press-releases/2025/pope.html)(https://www.timesnownews.com/education/pope-leo-xiv-vatican-bsc-math-graduate-educational-qualifications-article-151594036)(https://en.wikipedia.org/wiki/Pope_Leo_XIV)

#### 3. Pope Francis (2013–2025)

**Background**: Born Jorge Mario Bergoglio in 1936, he was pope until his death in 2025.

**Education**:

  - Studied at the Inmaculada Concepción Seminary in Buenos Aires, focusing on humanities and philosophy.

  - Earned a licentiate in philosophy from the Colegio Máximo de San José in San Miguel, Argentina.

  - Before entering the seminary, he studied chemistry and worked as a chemical technician at a food science laboratory in Buenos Aires. Some sources, including social media posts, claim he had a “degree in chemistry,” but this is inaccurate. He completed a technical diploma or training in chemistry, not a university degree.

**Degree Status**: No college degree in chemistry or any science/mathematics field. His chemical technician training was vocational, not equivalent to a bachelor’s or advanced degree. His formal degrees are in philosophy and theology.

**Sources**: The Express Tribune mentions speculation about a chemistry degree for a prior pope (likely Francis), but Vatican biographies and reliable sources clarify he was a chemical technician, not a degree-holder.(https://tribune.com.pk/story/2544754/did-pope-leo-xiv-study-math-at-villanova-social-media-fuels-debate)

#### 4. Other Popes with Potential Mathematical/Scientific Interests

To ensure completeness, let’s examine other popes noted for intellectual pursuits, especially in the modern era when degrees became common, or earlier popes known for scientific contributions.

**Pope Gregory XIII (1572–1585)**:

**Background**: Known for commissioning the Gregorian calendar, which required advanced mathematical and astronomical calculations.

**Education**: Studied law at the University of Bologna, earning a doctorate in canon law. He was a professor of law before becoming pope.

 **Scientific Connection**: Worked with astronomers like Christopher Clavius, a Jesuit mathematician, to reform the Julian calendar. The Gregorian calendar, introduced in 1582, corrected inaccuracies in leap years, requiring precise astronomical knowledge.

 **Degree Status**: No degree in mathematics or science, only in canon law. His involvement in the calendar was administrative, relying on experts like Clavius.

 **Source**: General historical knowledge; no specific web source needed.

**Pope Benedict XIV (1740–1758)**:

**Background**: Known as a scholar-pope with interests in science and medicine.

**Education**: Studied at the Collegio Clementino in Rome and earned a doctorate in canon and civil law from La Sapienza University.

**Scientific Connection**: Promoted scientific inquiry, corresponded with Enlightenment thinkers like Voltaire, and supported medical studies (e.g., anatomy). He encouraged the study of Newton’s physics in papal universities.

**Degree Status**: No degree in mathematics or science, only in law. His scientific interests were intellectual, not formal academic training.

**Source**: Catholic Encyclopedia (public domain).

**Pope Pius IX (1846–1878)**:

 **Background**: Longest-reigning pope, known for modernizing the Papal States.

 

**Education**: Educated at the Piarist College in Volterra and in Turin, focusing on theology and philosophy. No evidence of university degrees.

**Scientific Connection**: Oversaw the establishment of the Vatican Observatory in 1868, showing interest in astronomy, but this was administrative.

**Degree Status**: No degree in any field, let alone mathematics or science.

**Source**: Vatican Observatory history.

**Pope Pius XII (1939–1958)**:**Background**: Pope during World War II, known for intellectual rigor.

**Education**: Earned doctorates in canon law and theology from the Pontifical Gregorian University in Rome.

**Scientific Connection**: Had a keen interest in science, delivering speeches on cosmology and quantum physics (e.g., 1951 address to the Pontifical Academy of Sciences). Supported the Vatican Observatory and engaged with scientists.

**Degree Status**: No degree in mathematics or science, only in law and theology.

**Source**: Vatican archives; Pius XII’s speeches.

**Pope John Paul II (1978–2005)**:

**Background**: A scholar-pope with a broad intellectual background.

**Education**: Earned a doctorate in theology from the Angelicum in Rome and another in philosophy from the Jagiellonian University in Kraków.

**Scientific Connection**: Promoted dialogue between science and faith, issuing statements on evolution (1996) and supporting the Vatican Observatory. Studied philosophy, which included logic, but not mathematics or natural sciences.

**Degree Status**: No degree in mathematics or science, only in theology and philosophy.

 **Source**: Vatican biographies.

### Systematic Search for Other Candidates

**Medieval Popes**: Most popes before the 13th century were educated in monastic or cathedral schools, not universities. None are recorded as having degrees, as these institutions didn’t award them. Figures like Pope Leo IX (1049–1054) or Gregory VII (1073–1085) were scholars but focused on theology and canon law.

**Renaissance to Modern Popes**: From the 15th century, popes like Nicholas V (1447–1455) founded libraries and supported scholarship, but their education was in humanities or law. The rise of Jesuit education in the 16th century produced scientifically inclined clergy, but no popes from this order (except Francis, a Jesuit, discussed above) had science degrees.

**19th–20th Century Popes**: Popes like Leo XIII (1878–1903), who inspired Pope Leo XIV’s name, were educated in theology and law. Leo XIII studied at the Academy of Ecclesiastical Nobles in Rome, earning a doctorate in theology, not science.

**Vatican Observatory Connections**: Popes since the 19th century supported astronomy, but none studied it formally. Jesuit priests like Angelo Secchi worked under papal patronage, not as popes.

### Social Media Claims

Recent X posts claim Pope Leo XIV is the “second mathematician pope” after Sylvester II, suggesting only these two have mathematical backgrounds. However, these posts are inconclusive without evidence of other popes. Sylvester II’s lack of a formal degree undermines the claim’s precision, and no other popes are named in these posts or sources as having mathematics/science degrees.

### Conclusion

After examining historical records, notable popes, and recent sources:

- **Pope Sylvester II (999–1003)** is the only pope before Leo XIV with significant mathematical and scientific expertise, but he did not have a college degree, as formal degrees didn’t exist in his era. His studies in mathematics and astronomy were advanced but not credentialed.

- **No other popes** among the 266 before Leo XIV are recorded as having college degrees in mathematics or science. Many had interests in these fields (e.g., Gregory XIII, Benedict XIV, Pius XII), but their formal education was in theology, law, or philosophy.

- **Pope Francis** had chemical technician training, not a degree, so he doesn’t qualify.

- **Pope Leo XIV** is the first pope with a confirmed college degree in mathematics (BSc, Villanova, 1977).

Thus, **no popes prior to Pope Leo XIV had college degrees in mathematics or science**. Sylvester II is the closest, with equivalent expertise but no degree.(https://www1.villanova.edu/university/media/press-releases/2025/pope.html)(https://en.wikipedia.org/wiki/Pope_Sylvester_II)(https://thonyc.wordpress.com/2012/05/12/a-mathematician-who-became-pope/)

Proving the Existence of God

 

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I recently read an article about Kurt Gödel's proof of the existence of God. This blog has included other posts about religious mathematicians, including: 

https://jamesmacmath.blogspot.com/2023/12/book-review-zero-biography-of-dangerous.html

https://jamesmacmath.blogspot.com/2023/10/how-does-math-formula-highlight-creator.html

https://jamesmacmath.blogspot.com/2023/09/anniversary-of-eulers-death.html

https://jamesmacmath.blogspot.com/2022/09/alec-wilkinson-staff-writer-for-new.html

https://jamesmacmath.blogspot.com/2022/02/perfect-number-generator.html

https://jamesmacmath.blogspot.com/2022/01/maths-true-source-man-or-nature.html

https://jamesmacmath.blogspot.com/2020/05/george-lemaitre-and-big-bang.html

https://jamesmacmath.blogspot.com/2020/05/thomas-bayes-attempt-to-prove-existence.html

 

I had a goal of writing a post that summarizes these many theories, however, during my research, I found an article by Manon Bischoff in Scientific American that already has a very good summary. It includes many of the theories of the scientists and mathematicians from the above links and the summary of Kurt Gödel's proposed proof. I recommend readers of this blog to his article.

Book Review: Zero, The Biography of a Dangerous Idea by Charles Seife

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Charles Seife, professor at New York University, wrote Zero, The Biography of a Dangerous Idea in 2000. Zero tells the story of how different cultures have used, or refused to recognize, the number zero in their mathematics. In telling this story, Seife also walks the reader through the history of mathematics including geometry, algebra, and calculus. A theme throughout the book is also the relationship of infinity and zero. In addition to the mathematical history, the book includes how zero and infinity link with many scientific concepts, including the future of the universe, absolute temperature, string theory, and quantum mechanics.

How Does a Math Formula Highlight the Creator?

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The Ken Ham Blog recently had a thought-provoking post about the Golden Ratio: see link. It speaks how this ratio is related to many things in nature. A video by the Institute for Creation Research presents their argument for God as evidenced by intelligent design in the Fibonacci series and the Golden Ratio.

See also:

Speed Limit Conversions 

OEIS Sequence

Anniversary of Euler's death

(Image: Jakob Emanuel Handmann - Kunstmuseum Basel, Public Domain)

Yesterday, September 18, 2023, was the 240th anniversary of the death of the Swiss mathematician Leonhard Euler. He was born in 1707 in Basel, Switzerland.

A more complete description of his life was recently published by Breakpoint Colson Center: Leonhard Euler: Called to Mathematics - Breakpoint (Includes an audio version).

Other posts in this blog related to Euler:

Math Vacation: Euler's Identity (jamesmacmath.blogspot.com)

(More on Euler’s Identity: Euler's identity - Wikipedia)

Math Vacation: Euler Characteristic of Polyhedra (jamesmacmath.blogspot.com)

Math Vacation: Project Euler (jamesmacmath.blogspot.com)

Math Vacation: Using Random Numbers to Estimate Pi (jamesmacmath.blogspot.com)

Math Vacation: Perfect Number Generator (jamesmacmath.blogspot.com)

More on Euler: Leonhard Euler - Wikipedia

 

 

Book Review: A divine language : learning algebra, geometry, and calculus at the edge of old age.

Alec Wilkinson, staff writer for The New Yorker magazine, recently wrote about his quest to study math later in life. Here is a link to his September 6, 2022, article: How Mathematics Changed Me | The New Yorker. He started his quest five years ago at age 65. He also writes about this in his book, A divine language : learning algebra, geometry, and calculus at the edge of old age. I have the book on order and look forward to reviewing it.

From his article, I understand much of what Wilkinson learned during his quest as I started this math blog late in my life. This blog started as a Covid project two years ago when I was 61. We both learned strangeness of different types of infinities, mystery of design of our world, and how God in unknowable.

11/8/2022 Update - my local library got this book, and I just finished it. Wilkinson included stories about many of my favorite mathematicians. I liked that he was able to interview Chris Ferguson, who won $1,000,000 in the World Series of Poker in 2000, shortly after earning his PhD from UCLA. 

Perfect Number Generator

 

A perfect number is a positive integer which equals the sum of all its divisors, excluding itself. The first perfect number is 6 since 6 = 1 + 2 + 3. The next perfect number is 28 since 28 = 1 + 2 + 4 + 7 + 14.

Over two thousand years ago, Euclid found a formula for generating perfect numbers. The product of
(2^p-1) and (2^p-1) is a perfect number when p is a prime and 2^p-1 is also a prime number. Many high prime numbers can be found using the formula 2^p-1, but the formula doesn’t always produce prime numbers. When the formula does produce a prime number, it is called a Mersenne prime named after the French Friar, Marin Mersenne (Marin Mersenne - Wikipedia).

The ancients knew of the first four perfect numbers: 6, 28, 496 and 8128. Through trial division, the list was confirmed with three additional perfect numbers: 33550336, 8589869056 and 137438691328. In 1772 Euler found the eighth: 2305843008139952128 (with no modern computing aids). Euler also proved the converse of Euclid’s original proof, that is even numbers are perfect if and only if they can be expressed in the form (2^p-1) (2^p-1).

It is known that there are an infinite number of primes; however, it is not known if there are an infinite number of Mersenne prime numbers. As of this posting, there have been 51 confirmed Mersenne primes (the largest has over 24 million digits). If one were able to prove the Mersenne primes continue infinitely, then so would perfect numbers. The size of the perfect number associated with the largest known Mersenne prime has over 49 million digits.

Here is a link to a spreadsheet for calculating the first eight perfect numbers.

Math's True Source - Man or Nature?

The British Journal for the Philosophy of Science recently accepted for publication a manuscript by Sam Baron titled Mathematical Explanation: A Pythagorean Proposal. A summary of Baron's paper is given here: Pythagoras’ Revenge: Humans Didn’t Invent Mathematics, It’s What the Physical World Is Made Of (scitechdaily.com).

Baron proposes that our world has an inherent mathematical part in addition to its matter. In this framework, mathematics provides matter with its form while matter gives mathematics its substance.

I believe Baron's proposal is similar to Stephen Wolfram's proposal in A New Kind of Science.

A prior post in this blog wrote about the many examples of fractals found in nature.

Linking nature and mathematics is a common theme in teleological arguments for the existence of God. See prior post on Rev. Bayes. 

 

Georges Lemaître and the Big Bang

George Lemaitre, 1894-1966, was a Catholic Priest who is credited with the theory of the Big Bang (The Primeval Atom). As a PhD candidate, some of his early work was reviewed by Albert Einstein who told him "Your calculations are correct, but your physics is atrocious." Einstein at the time did not like the idea of an expanding universe."

His theory was held by Pope Pius XII to be scientific validation of Catholicism. While Lemaitre preferred to keep neutral on the religious implications of the theory, he did not believe cosmology and religion were in conflict. 

An earlier post featured another minister-scientist, Thomas Bayes, who developed Bayesian Statistics. While few people, outside mathematicians and scientists, have heard of Bayesian Statistics, nearly everyone has heard of the Big Bang.

Shortly before Lemaitre's death in 1966, evidence of background radiation from the Big Bang was detected by microwaves. The image below is a recent mapping of the background radiation.

Image source: NASA https://lambda.gsfc.nasa.gov/product/map/current/pub_papers/nineyear/basic_results/wmap_9yr_basic_results_images.cfm

Additional Notes:

Recent You Tube on Cosmology by Dr. Katie Mack

Forbes Article May 6, 2020

Thomas Bayes - an Attempt to Prove the Existence of God

Thomas Bayes was an eighteen-century Presbyterian minister and gifted statistician. Two of his publications, Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures (1731), and An Essay towards solving a Problem in the Doctrine ofChances (1763), are examples of how he wanted to use his intellect to prove the existence of God. His attempts were unsuccessful, otherwise Thomas Bayes would be a known to all and not just to mathematicians. However, his devotion is honored as his approach was so rigorous that it established a new field of mathematics, now named Bayesian Statistics.

Our current world-wide Covid-19 crisis provides an example of how Bayesian Statistics is applied.

First, here is the nomenclature for revised probabilities:

P(A)       Probability of Event A

P(B)       Probability of Event B

P(A|B)  Probability of A, given B is true

Fictitious Covid-19 problem

Suppose a test for Covid-19 is 95% effective in detecting the disease when present in a patient. The test gives a false positive result 10% of time when the disease is not present. Approximately 4% of the population has the disease. Given a positive test result, what is the probability that a patient actually has the disease.

The three facts stated above can be expressed as:

A.     P(D) = .04               4% of the population has the disease, and therefore P(N)=.96 or 96% of population doesn’t have the disease.

B.       P(Pos|D) = .95       The test gives a positive result 95% of the time when the disease is present

C.       P(Pos|N) = .10       Given no disease, 10% of those tested will falsely test positive

Now, a typical question is: given a positive test result, what is the probability a patient actually has the disease? Using our nomenclature, we are looking for P(D|Pos)  or probability of D, given Pos. We did have P(Pos|D) = .95, but that is different than P(D|Pos). In Bayesian terms, this question is called an inverse probability problem.

Bayes Theorem provides a formula for determining this revised probability, but I think it easier to express our known and unknown probabilities in a table. Our first given facts are pre-filled in the table. 

	Disease Present (D)	No Disease (N)	Total
Positive Test result (Pos)	.95 x .04 = .038 (Fact B)	.10 x .96 = .096 (Fact C)
Negative Test result
Total	.04 (Fact A)	.96

All the remaining entries in the table can be determined by simple addition and subtraction. Adding across the top row, the total proportion of the population with Positive Test results is .038 + .096 = .134; the proportion with Negative Test results when the disease is present is .04 - .038 = .002; the proportion having a Negative Test result with no disease is .96 - .096 = .864; the total proportion having Negative test results is 1.00 - .134 = .866 and with that last item we can complete all the entries in the table.

	Disease Present (D)	No Disease (N)	Total
Positive Test result (Pos)	.95 x .04 = .038	.10 x .96 = .096	.134
Negative Test result	.04 - .038 = .02	.96 - .096 = .864	.866
Total	.04	.96	1.00

For our question of the probability of the Disease being present, given a Positive test result, we just need to focus on the top row of the table representing different ways to have a Positive test result.

.038 will test Positive when they actually have the disease

.096 will test Positive when they don’t have the disease (from false positive results)

In total, the proportion of the population that will have Positive results is .134 and of those .038 actually have the disease. Therefore, P(D|Pos) = .038/.134 = .284 so only 28.4% of those with a Positive test result will actually have the disease. This often strikes people as being too low. This is a common situation of imperfect tests and is known as the Paradox of the False Positive. From the table, we see that many more people had false positives than people who actually have the disease. Even though many medical tests have this False Positive error, the tests are still helpful. In our example, a person testing positive has an increase risk level compared to the general population (28.4% vs 4%) so the positive result would justify further testing and enhanced precautionary measures.

Returning to Bayes' Theorem, the inverse probability is given by:

P(D|Pos) = P(Pos|D) x P(D) / P(Pos)

The table given above provides the same answer as the Bayes' Theorem equation.

Additional Sources on Bayes:

CornellBlog: https://blogs.cornell.edu/info2040/2018/11/28/bayes-theorem-and-the-existence-of-god/

DanKopk article on Bayes and Price: https://qz.com/1315731/the-most-important-formula-in-data-science-was-first-used-to-prove-the-existence-of-god/

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