# Mathematician:Mathematicians/Sorted By Nation/Italy

For more comprehensive information on the lives and works of mathematicians through the ages, see the MacTutor History of Mathematics archive, created by John J. O'Connor and Edmund F. Robertson.

*The army of those who have made at least one definite contribution to mathematics as we know it soon becomes a mob as we look back over history; 6,000 or 8,000 names press forward for some word from us to preserve them from oblivion, and once the bolder leaders have been recognised it becomes largely a matter of arbitrary, illogical legislation to judge who of the clamouring multitude shall be permitted to survive and who be condemned to be forgotten.*- -- Eric Temple Bell:
*Men of Mathematics*, 1937, Victor Gollancz, London

- -- Eric Temple Bell:

## Contents

- 1 Italy
- 1.1 Anicius Manlius Severinus Boëthius (c.477 – 524)
- 1.2 Gerard of Cremona (c. 1114 – 1187)
- 1.3 Leonardo Fibonacci (c. 1170 – c. 1250)
- 1.4 Campanus of Novara (c. 1220 – 1296)
- 1.5 Antonio Maria del Fiore (15th century – 16th century)
- 1.6 Piero Della Francesca (1412 – 1492)
- 1.7 Luca Bartolomeo de Pacioli (1447 – 1517)
- 1.8 Leonardo da Vinci (1452 – 1519)
- 1.9 Scipione del Ferro (1465 – 1525)
- 1.10 Francesco Maurolico (1494 – 1575)
- 1.11 Niccolò Fontana Tartaglia (1499/1500 – 1557)
- 1.12 Gerolamo Cardano (1501 – 1576)
- 1.13 Lodovico Ferrari (1522 – 1565)
- 1.14 Rafael Bombelli (1526 – 1572)
- 1.15 Pietro Antonio Cataldi (1548 – 1626)
- 1.16 Galileo Galilei (1564 – 1642)
- 1.17 Bonaventura Francesco Cavalieri (1598 – 1647)
- 1.18 Evangelista Torricelli (1608 – 1647)
- 1.19 Tito Livio Burattini (1617 – 1681)
- 1.20 Vincenzo Viviani (1622 – 1703)
- 1.21 Giovanni Domenico Cassini (1625 – 1712)
- 1.22 Pietro Mengoli (1626 – 1686)
- 1.23 Giovanni Benedetto Ceva (1647 – 1734)
- 1.24 Giovanni Girolamo Saccheri (1667 – 1733)
- 1.25 Luigi Guido Grandi (1671 – 1742)
- 1.26 Jacopo Francesco Riccati (1676 – 1754)
- 1.27 Maria Gaëtana Agnesi (1718 – 1799)
- 1.28 Giovanni Francesco Giuseppe Malfatti (1731 – 1807)
- 1.29 Joseph Louis Lagrange (1736 – 1813)
- 1.30 Lorenzo Mascheroni (1750 – 1800)
- 1.31 Paolo Ruffini (1765 – 1822)
- 1.32 Giuliano Frullani (1795 – 1834)
- 1.33 Barnaba Tortolini (1808 – 1874)
- 1.34 Angelo Genocchi (1817 – 1889)
- 1.35 Baldassarre Boncompagni-Ludovisi (1821 – 1894)
- 1.36 Francesco Faà di Bruno (1825 – 1888)
- 1.37 Giuseppe Battaglini (1826 – 1894)
- 1.38 Antonio Luigi Gaudenzio Giuseppe Cremona (1830 – 1903)
- 1.39 Eugenio Beltrami (1835 – 1900)
- 1.40 Felice Casorati (1835 – 1890)
- 1.41 Ulisse Dini (1845 – 1918)
- 1.42 Vilfredo Federico Damaso Pareto (1848 – 1923)
- 1.43 B. Nicolò I. Paganini (c. 1850 – ?)
- 1.44 Giovanni Frattini (1852 – 1927)
- 1.45 Gregorio Ricci-Curbastro (1853 – 1925)
- 1.46 Alfredo Capelli (1855 – 1910)
- 1.47 Giacinto Morera (1856 – 1909)
- 1.48 Giuseppe Peano (1858 – 1932)
- 1.49 Ernesto Cesàro (1859 – 1906)
- 1.50 Samuel Giuseppe Vito Volterra (1860 – 1940)
- 1.51 Cesare Burali-Forti (1861 – 1931)
- 1.52 Gino Benedetto Loria (1862 – 1954)
- 1.53 Gino Fano (1871 – 1952)
- 1.54 Tullio Levi-Civita (1873 – 1941)
- 1.55 Beppo Levi (1875 – 1961)
- 1.56 Giuseppe Vitali (1875 – 1932)
- 1.57 Francesco Paolo Cantelli (1875 – 1966)
- 1.58 Guido Fubini (1879 – 1943)
- 1.59 Ruggiero Torelli (1884 – 1915)
- 1.60 Leonida Tonelli (1885 – 1946)
- 1.61 Enrico Bombieri (b. 1940 )
- 1.62 Mariano Giaquinta (b. 1947 )

## Italy

##### Anicius Manlius Severinus Boëthius (c.477 – 524)

Roman senator, consul, magister officiorum, and philosopher, who produced editions of some mathematical works which survived to be used throughout Medieval Europe.

Although widely cited as a great scholar, as a mathematician he appears to have been mediocre.
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##### Gerard of Cremona (c. 1114 – 1187)

Italian scholar whose calling was to translate Arabic scientific and mathematical papers into Latin, many of which themselves were translations of works originally written in Greek.

Some sources credit him for the mistranslation that led to the word sine, but this may be more reliably attributed to Robert of Chester, who appears to be earlier.
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##### Leonardo Fibonacci (c. 1170 – c. 1250)

Italian mathematician.

One of the most important figures in the history of the development of mathematics.

Wrote the highly influential and important *Liber Abaci* in which he discussed the Hindu-Arabic number system and its practical applications.

Most famous for the Fibonacci numbers. The number sequence itself was known to Indian mathematicians as early as the $6$th century, but it was Fibonacci's *Liber Abaci* which made them well-known throughout Europe.
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##### Campanus of Novara (c. 1220 – 1296)

Italian mathematician, astronomer, astrologer, and physician who is best known for his work on Euclid's *The Elements*.
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##### Antonio Maria del Fiore (15th century – 16th century)

Italian Renaissance mathematician.

A student of Scipione del Ferro, learned from him the formula for the resolution of the particular cubic equation $x^3 + p x = q$, and boasted that he was the only one who could solve such equations.

Challenged Niccolò Fontana Tartaglia to a contest in $1535$ to solve cubics, but was outclassed.

Some sources suggest that it was **del Fiore** who revealed to Gerolamo Cardano that the solution originated from del Ferro and not Tartaglia.
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##### Piero Della Francesca (1412 – 1492)

Italian painter and mathematician.

Recognized as one of the most important Renaissance painters, but was also a creditable mathematician.

His surviving mathematical works concern such subjects as: the abacus; the five Platonic solids, and perspective in painting.
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##### Luca Bartolomeo de Pacioli (1447 – 1517)

Italian mathematician and Franciscan friar who was a pioneer in the field of accounting.

Sometimes referred to as "The Father of Accounting and Bookkeeping".

The first person to publish a work on the double-entry system of book-keeping.

Published a compilation of the mathematics of his day, the first such work since Leonardo Fibonacci's *Liber Abaci* of $1202$.
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##### Leonardo da Vinci (1452 – 1519)

Italian polymath whose areas of interest included invention, painting, sculpting, architecture, science, music, mathematics, engineering, literature, anatomy, geology, astronomy, botany, writing, history, and cartography.

Variously called the father of palaeontology, ichnology, and architecture.

Widely considered one of the greatest painters of all time.

Sometimes credited with the inventions of the parachute, helicopter and tank.
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##### Scipione del Ferro (1465 – 1525)

Italian mathematician.

First one to come up with a solution to the general cubic equation, which was later published by Cardano and is now known as Cardano's Formula.

Contributed towards the rationalization of fractions.
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##### Francesco Maurolico (1494 – 1575)

Mathematician and astronomer from Sicily, notable for being the first on record to use the Principle of Mathematical Induction.

Contributed to the fields of geometry, optics, conics, mechanics, music, and astronomy.

Edited the works of classical authors including Archimedes, Apollonius, Autolycus, Theodosius and Serenus.

Composed treatises of his own on mathematics and mathematical science.
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##### Niccolò Fontana Tartaglia (1499/1500 – 1557)

Italian mathematician, engineer and surveyor.

- Published first Italian translations of Archimedes and Euclid.
- Devised a solution to the general cubic equation independently of Scipione del Ferro, later published by Gerolamo Cardano and now known as Cardano's Formula.
- Challenged in $1535$ by Antonio Maria del Fiore to a public contest to solve cubics, and won convincingly.

##### Gerolamo Cardano (1501 – 1576)

Italian mathematician, physician, inventor, astrologer and gambler.

- Published systematic methods for solving cubic and quartic equations. Neither were supposedly discovered by him:
- The formula for solving the cubic was passed to him by Tartaglia, but (as he discovered later) was in fact originally discovered by Scipione del Ferro.
- The formula for solving the quartic was discovered by his student Ferrari (and bears Ferrari's name).

- Wrote the first systematic treatment of probability.

##### Lodovico Ferrari (1522 – 1565)

Italian mathematician who was a student of Gerolamo Cardano.

First one to devise a solution to the general quartic equation, which was later published by Cardano and is now known as Ferrari's Method.
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##### Rafael Bombelli (1526 – 1572)

Italian mathematician whose influence may have been greater than is currently recognised.

- Documented the rules for multiplication involving negative numbers.

- Pioneered the work on the understanding of imaginary numbers, using as a springboard Cardano's Formula for the solution of the cubic.

- Developed a method of solving square roots by an approach related to continued fractions.

##### Pietro Antonio Cataldi (1548 – 1626)

Italian mathematician and philanthropist who taught mathematics and astronomy.

Worked on the development of perfect numbers and continued fractions.

Attempted in vain (as so many before and since) to prove Euclid's fifth postulate.

Supposed to have discovered the $6$th and $7$th Mersenne primes $M_{17}$ and $M_{19}$ in $1588$.
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##### Galileo Galilei (1564 – 1642)

Italian mathematician and scientist usually known as just **Galileo**.

At the forefront of a revolution in the understanding of physics. One of the most influential thinkers in history.
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Italian mathematician who worked on optics and motion.

His approach to geometry was a precursor to integral calculus.

Introduced the logarithm to Italy.

A disciple of Galileo.
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##### Evangelista Torricelli (1608 – 1647)

Italian physicist and mathematician, best known for inventing the barometer.

Disciple of Galileo.

Gave his name to Torricelli's Law.
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##### Tito Livio Burattini (1617 – 1681)

Italian inventor, architect, Egyptologist, scientist, instrument-maker, traveller, engineer, and nobleman.

Developed an early system of measurement based on time, similar to today's International System of Units.

Invented the the **metro cattolico** (that is "catholic [i.e. universal] metre"), a unit of length equivalent to the length of a pendulum whose period is $1$ second.

Probably the first to recommend the name **metre** for a unit of length.
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##### Vincenzo Viviani (1622 – 1703)

Italian mathematician and scientist.

Pupil of Evangelista Torricelli and a disciple of Galileo.
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##### Giovanni Domenico Cassini (1625 – 1712)

Italian/French mathematician, astronomer, engineer, and astrologer.

Most of his important discoveries were in the field of astronomy.

Not to be confused with his son, also called **Jean-Dominique Cassini**.
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##### Pietro Mengoli (1626 – 1686)

Italian mathematician who spent most of his working life as a professor at the University of Bologna.

Also ordained into the Priesthood.

Occupies the philosophical transitional ground between the work of Bonaventura Francesco Cavalieri and that of Isaac Newton and Gottfried von Leibniz.
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##### Giovanni Benedetto Ceva (1647 – 1734)

Italian mathematician best known for Ceva's Theorem, a result in geometry.

Also rediscovered and published Menelaus's Theorem.
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##### Giovanni Girolamo Saccheri (1667 – 1733)

Italian Jesuit priest, scholastic philosopher, and mathematician.

Attempted (but failed) to prove Euclid's fifth postulate by means of Reductio ad Absurdum, and in the process narrowly missed discovering a non-Euclidean geometry.
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##### Luigi Guido Grandi (1671 – 1742)

Italian mathematician, engineer, priest and philosopher, best known for his study of the rhodonea (rose) curve.

Contributed to *Note on the Treatise of Galileo Concerning Natural Motion* in the first Florentine edition of Galileo Galilei's works.

Helped introduce Gottfried Leibniz's ideas on calculus to Italy.

Also known for Grandi's Series.
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##### Jacopo Francesco Riccati (1676 – 1754)

Count **Jacopo Francesco Riccati** was an aristocratic Italian mathematician and jurist from Venice.

Chiefly responsible for introducing Isaac Newton's ideas to Italy.

Best known for having founded the equation which bears his name.

Contributed towards Maria Gaëtana Agnesi's 1748 work *Instituzioni analitiche ad uso della gioventù italiana*.
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##### Maria Gaëtana Agnesi (1718 – 1799)

Italian mathematician, linguist and philosopher famed for writing the first book discussing both integral and differential calculus.

The curve in analytic geometry called the Witch of Agnesi is named for her.
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##### Giovanni Francesco Giuseppe Malfatti (1731 – 1807)

Italian mathematician best known for posing the Malfatti Problem.

Discovered the Gravitational Property of Lemniscate of Bernoulli.
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##### Joseph Louis Lagrange (1736 – 1813)

Italian-born French mathematician who made big advances in the fields of the calculus of variations and analytical mechanics.

Contributed to number theory and algebra.

Extended a lot of the fields established by Euler, and in turn laid down the groundwork for later explorations by Gauss and Abel.
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##### Lorenzo Mascheroni (1750 – 1800)

Professor of mathematics at Pavia.

Wrote *Geometria del Compasso*, published in $1797$, in which he showed that any geometrical construction that can be made with compasses and straightedge can also be achieved by using only compasses.

This had, however, already been demonstrated by Georg Mohr in $1672$.

Published in his $1790$ work *Adnotationes ad Calculum Integrale Euleri* a calculation to $32$ places of the value of what is now known as the Euler-Mascheroni Constant.

However, only the first $19$ places were accurate. The rest were corrected in $1809$ by Johann von Soldner.
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##### Paolo Ruffini (1765 – 1822)

Italian mathematician and philosopher.

Most famous for his incomplete proof of what is now known as the Abel-Ruffini Theorem proving the insolubility of the general quintic with radicals.
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##### Giuliano Frullani (1795 – 1834)

Italian mathematician interested in definite integrals and infinite series.
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##### Barnaba Tortolini (1808 – 1874)

Italian priest and mathematician who founded the first Italian scientific journal with an international presence.
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##### Angelo Genocchi (1817 – 1889)

Italian mathematician who specialized in number theory.

Worked with Giuseppe Peano.
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##### Baldassarre Boncompagni-Ludovisi (1821 – 1894)

Italian historian of mathematics best known for his $1857$ republication of Leonardo Fibonacci's *Liber Abaci*, on whom he wrote extensively.
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##### Francesco Faà di Bruno (1825 – 1888)

Italian mathematician and priest, most famous (in mathematics) for Faà di Bruno's Formula on derivatives of composite functions.

Also notable for his beatification on 25th September 1988 by Pope John Paul II.
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##### Giuseppe Battaglini (1826 – 1894)

Italian mathematician best known for being the founder of *Giornale di Matematiche*, later known as *Giornale di Matematiche di Battaglini*.

Also did considerable work in the field of non-Euclidean geometry.
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##### Antonio Luigi Gaudenzio Giuseppe Cremona (1830 – 1903)

Italian mathematician who studied geometry.

Reformed advanced mathematical teaching in Italy.
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##### Eugenio Beltrami (1835 – 1900)

Italian mathematician notable for his work concerning differential geometry and mathematical physics.

The first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an $n$-dimensional unit sphere.

Developed singular value decomposition for matrices, which has been subsequently rediscovered several times.

His use of differential calculus for problems of mathematical physics indirectly influenced development of tensor calculus by Gregorio Ricci-Curbastro and Tullio Levi-Civita.
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##### Felice Casorati (1835 – 1890)

Italian mathematician best known for the Casorati-Weierstrass Theorem in complex analysis.
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##### Ulisse Dini (1845 – 1918)

Italian mathematician and politician, best known for his contributions to real analysis.
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##### Vilfredo Federico Damaso Pareto (1848 – 1923)

Italian engineer, sociologist, economist, political scientist, and philosopher.
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##### B. Nicolò I. Paganini (c. 1850 – ?)

Italian amateur mathematician known now only for his discovery of the $2$nd amicable pair $1184$ and $1210$.
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##### Giovanni Frattini (1852 – 1927)

Italian mathematician noted for his contributions to group theory.
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##### Gregorio Ricci-Curbastro (1853 – 1925)

Italian mathematician most famous as the inventor of tensor calculus, which he did in collaboration with Tullio Levi-Civita.
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##### Alfredo Capelli (1855 – 1910)

Italian mathematician best known for Capelli's Identity.

Also pioneered the notation $x^{\overline k}$ and $x^{\underline k}$ for rising factorial and falling factorial respectively.
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##### Giacinto Morera (1856 – 1909)

Italian mathematician and engineer best remembered for his work in complex analysis and the theory of linear elasticity.
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##### Giuseppe Peano (1858 – 1932)

Italian mathematician who contributed significantly to the founding of the fields of mathematical logic and set theory.

Invented many of the symbols used today in these fields.

Worked on the axiomatization of mathematics, and contributed greatly towards the method of mathematical induction.
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##### Ernesto Cesàro (1859 – 1906)

Italian mathematician who worked mainly in the fields of differential geometry and number theory.
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##### Samuel Giuseppe Vito Volterra (1860 – 1940)

Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations.

One of the founders of functional analysis.
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##### Cesare Burali-Forti (1861 – 1931)

Italian mathematician best known for discovering what is now known as the Burali-Forti Paradox.

Disbelieved in the Theory of Relativity, and even went so far as to write a book attempting to refute it.
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##### Gino Benedetto Loria (1862 – 1954)

Italian mathematician and historian of mathematics.
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##### Gino Fano (1871 – 1952)

Italian mathematician best known as the founder of the finite geometry.
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##### Tullio Levi-Civita (1873 – 1941)

Italian mathematician most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity.

His work covered celestial mechanics (notably on the three-body problem), analytic mechanics and hydrodynamics.
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##### Beppo Levi (1875 – 1961)

Italian mathematician best known for his work on algebraic curves and Lebesgue integration.
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##### Giuseppe Vitali (1875 – 1932)

Italian mathematician who worked in several branches of analysis.

Best known for the Vitali set: a subset of the real numbers which is not Lebesgue measurable.
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##### Francesco Paolo Cantelli (1875 – 1966)

Italian mathematician best known for his work in probability theory, and for the Borel-Cantelli Lemma.
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##### Guido Fubini (1879 – 1943)

Italian mathematician best known for Fubini's Theorem and the Fubini-Study metric.
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##### Ruggiero Torelli (1884 – 1915)

Italian mathematician whose work was mainly in algebraic geometry and the non-rational functions of the points of a Riemann surface.
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##### Leonida Tonelli (1885 – 1946)

Italian mathematician, noted for creating Tonelli's Theorem.
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##### Enrico Bombieri (b. 1940 )

Italian mathematician known for his work in analytic number theory, algebraic geometry, univalent functions, theory of several complex variables, partial differential equations of minimal surfaces, and the theory of finite groups
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##### Mariano Giaquinta (b. 1947 )

Italian mathematician mainly known for his contributions to the fields of calculus of variations and regularity theory of partial differential equation.
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