Alphonse de Polignac (1826–1863) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

aristocrat The aristocracy (''from Greek'' ''ἀριστοκρατία'' ''aristokratía'', "rule of the best"; ''Latin: aristocratia'') is historically associated with a "hereditary" or a "ruling" social class. In many states, the aristocracy included the ...

. He is known for Polignac's Conjecture.

Biography

His father, Jules de Polignac (1780-1847) was prime minister of

Charles X Charles X may refer to: * Charles X of France (1757–1836) * Charles X Gustav (1622–1660), King of Sweden * Charles, Cardinal de Bourbon (1523–1590), recognized as Charles X of France but renounced the royal title See also * * King Charle ...

until the Bourbon dynasty was overthrown in the

July Revolution of 1830 The French Revolution of 1830, also known as the July Revolution (), Second French Revolution, or ("Three Glorious ays), was a second French Revolution after the first of 1789–99. It led to the overthrow of King Charles X, the French B ...

. Alphonse was born in

London London is the Capital city, capital and List of urban areas in the United Kingdom, largest city of both England and the United Kingdom, with a population of in . London metropolitan area, Its wider metropolitan area is the largest in Wester ...

during his father's time as ambassador to the

United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Northwestern Europe, off the coast of European mainland, the continental mainland. It comprises England, Scotlan ...

. In 1849 he was admitted to Polytechnique and went onto serve in the

Crimean War The Crimean War was fought between the Russian Empire and an alliance of the Ottoman Empire, the Second French Empire, the United Kingdom of Great Britain and Ireland, and the Kingdom of Sardinia (1720–1861), Kingdom of Sardinia-Piedmont fro ...

as an artillery officer, achieving the rank of

Captain Captain is a title, an appellative for the commanding officer of a military unit; the supreme leader or highest rank officer of a navy ship, merchant ship, aeroplane, spacecraft, or other vessel; or the commander of a port, fire or police depa ...

. He was also a historian, a poet, a musician, and authored a translation of the play

Faust Faust ( , ) is the protagonist of a classic German folklore, German legend based on the historical Johann Georg Faust (). The erudite Faust is highly successful yet dissatisfied with his life, which leads him to make a deal with the Devil at a ...

by Goethe. His work in mathematics mainly focused on

Number Theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and he specifically worked with

prime numbers A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

Polignac's Conjecture

In his first year at Polytechnique Polignac formulated his eponymous conjecture, which states that:

For every positive integer ''k'', there are infinitely many
prime gap A prime gap is the difference between two successive prime numbers. The ''n''-th prime gap, denoted ''g'n'' or ''g''(''p'n'') is the difference between the (''n'' + 1)-st and the ''n''-th prime numbers, i.e., :g_n = p_ - p_n. ...
s of size 2''k''.

Other work in Mathematics

Polignac also conjectured Romanov's Theorem, which states that:

Every odd number larger than 3 can be written as the sum of an odd prime and a power of 2

The same year that he formulated his two most famous conjectures, Polignac also formulated a false conjecture which he presented to the Academy of Sciences. It incorrectly asserted that any odd number was equal to the power of 2 plus a prime number.

References

* 1826 births 1863 deaths 19th-century French mathematicians Alphonse Children of prime ministers of France {{France-mathematician-stub