mathematics

Jesús Guillera

Jesús Guillera 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 Jesús Guillera rather than just read about it. In short: Jesús Guillera (31 December 1955 – 9 February 2026) was a Spanish mathematician who specialised in number theory, best known for his work on Ramanujan-type series for calculating the mathematical constant π. Largely self-taught in advanced mathematics, he later earned a doctorate from the University of Zaragoza and since then published extensively on hypergeometric identities, WZ-pairs, and related topics in analyti…

Key takeaways

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

Reference excerpt

Jesús Guillera (31 December 1955 – 9 February 2026) was a Spanish mathematician who specialised in number theory, best known for his work on Ramanujan-type series for calculating the mathematical constant π. Largely self-taught in advanced mathematics, he later earned a doctorate from the University of Zaragoza and since then published extensively on hypergeometric identities, WZ-pairs, and related topics in analytic number theory.

Education and career Guillera obtained a Bachelor of Science in Physics from the University of Zaragoza in 1979. For much of his career, he taught physics and mathematics at secondary schools in the province of Zaragoza. In 2002, Guillera took a medical leave from teaching due to stress and began to devote himself to the study of mathematics, focusing on studying the number π. Working independently and without formal academic affiliation, Guillera discovered previously unpublished formulas that drew international attention from the mathematical community. In 2007, he earned his PhD in number theory from the University of Zaragoza under the supervision of Eva Gallardo and Wadim Zudilin. His thesis received the distinction cum laude and was awarded the Extraordinary Prize. Guillera had since served as a researcher in the Department of Mathematics at the University of Zaragoza.

Mathematical work Unlike many mathematicians who spend decades working, often doing their best work when young, Guillera has only been active since the age of 47 when he retired for medical reasons from high-school teaching. Since 2002, he has published over 40 works, and has been cited over 1200 times. His work has been described in some news articles, and some have argued that his talent can be compared to Srinivasa Ramanujan. "“Guillera is our own Ramanujan,” says Javier Cilleruelo, a member of Spain’s Institute of Mathematical Sciences (ICMAT)", while Doron Zeilberger described him as "My great hero Jesús Guillera, a 21st-century incarnation of Ramanujan". Guillera is known for his contributions to the study of Ramanujan-type series for calculating the number π. In 2002, he discovered several new series of this kind. Many of his formulas initially lacked formal proofs; over time, several were proven using the Wilf–Zeilberger pair method. He has also contributed to developing a general methodology for generating new Ramanujan-type series. His research collaborations have included work with mathematicians such as Wadim Zudilin, and he has received support from figures like Doron Zeilberger.

Death Guillera died on 9 February 2026, at the age of 70.

Selected publications Guillera, Jesús (2002). "Some binomial series obtained by the WZ-method". Advances in Applied Mathematics. 29 (4): 599–603. arXiv:math/0503345. doi:10.1016/S0196-8858(02)00034-9. Guillera, Jesús (2010). "On WZ-pairs which prove Ramanujan series". The Ramanujan Journal. 22 (3): 249–259. arXiv:0904.0406. doi:10.1007/s11139-010-9238-1. Guillera, Jesús (2011). "A new Ramanujan-like series for 1/π²". The Ramanujan Journal. 26 (3): 369–374. arXiv:1003.1915. doi:10.1007/s11139-010-9259-9. Guillera, Jesús (2012). "Mosaic Supercongruences of Ramanujan Type". Experimental Mathematics. 21 (1): 65–68. arXiv:1007.2290. doi:10.1080/10586458.2011.579012. Almkvist, Gert; Guillera, Jesús (2012). "Ramanujan-like series for 1/π² and String Theory". Experimental Mathematics. 21 (3): 223–234. arXiv:1009.5202. doi:10.1080/10586458.2012.656059. Guillera, Jesús; Zudilin, Wadim (2013). "Ramanujan-type formulae for 1/π: The art of translation". Max Planck Institute for Mathematics Preprint. arXiv:1302.0548. Guillera, Jesús (2016). "Some challenging formulas for π". doi:10.13140/RG.2.2.33482.77769. Guillera, Jesús (2020). "A method for proving Ramanujan's series for 1/π". The Ramanujan Journal. 52: 421–431. arXiv:1807.07394. doi:10.1007/s11139-018-0113-9.

References

Illustrations

Worked examples

Example 1 — a first encounter with Jesús Guillera

Start with the simplest possible case. Write down what Jesús Guillera 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 Jesús Guillera 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 Jesús Guillera 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 Jesús Guillera

In research: Jesús Guillera 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 Jesús Guillera 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: Jesús Guillera is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1955 births, 2026 deaths, 20th-century Spanish educators, so understanding it makes those chapters shorter.
In everyday life: Look for Jesús Guillera 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 Jesús Guillera in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Jesús Guillera 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 Jesús Guillera out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jesús Guillera in simple terms?

Why does Jesús Guillera 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 Jesús Guillera?

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 Jesús Guillera.