world records in mathematics

world records in mathematics

In the sciences and in sports there are world records for achievements and discoveries. There are

world records in mathematics

, too.

1

Numbers

1.1

Largest numbers

Largest named number

In a standard abridged dictionary of the English

language

, the largest named number is the centillion,

10

600

. Given a googol

10

100

, a

googolplex

10

10

100

is clearly much larger than a centillion; these words may be found in more recent unabridged dictionaries and certainly in mathematics dictionaries. According to the

Guinness Book of World Records 1991

, “the highest number ever used in a mathematical proof is a bounding value published in 1977 and known as Graham’s number. It concerns bichromatic

hypercubes

and is inexpressible without the special ‘arrow’ notation, devised by Knuth in 1976, extended to 64 layers.” (McFarlan, 1990)

Largest number factored

The largest

composite number

factored (for which the

factoring

team did not know the answer beforehand) is RSA-200, 3532461934402770121272604978198464368671197400197625023649303468776121253679423200058547956528088349 times 7925869954478333033347085841480059687737975857364219960734330341455767872818152135381409304740185467, which was factored by a four-man team in 2005 using the

general number field sieve

. This record could be beat by the

factorization

of a

Fermat number

(beyond the known

Fermat primes

, and some partially factored Fermat numbers, the

primality

of most of these numbers remains an open question).

Largest known prime

According to the

Prime Pages

, the largest known prime number is usually a

Mersenne prime

, currently

2

32582657

-

1

, discovered by GIMPS last year. The largest known non-Mersenne prime, seventh overall, is currently

19249

×

2

13018586

+

1

, discovered by Konstantin Agafonov earlier this month using SoBSieve and other programs.

Largest known

perfect number

The largest known perfect number is of course the largest known Mersenne prime times the nearest

power of two

less than the Mersenne prime, in this case,

(

2

32582657

-

1

)

⁢

2

32582656

. No odd perfect numbers are known, and the current

lower bound

for an odd perfect number is significantly smaller.

Newest

constant

As of 1990, the newest mathematical constant was Feigenbaum’s constant, approximately 4.6692016010299, according to

Guinness

.

2

Theorems, proofs, puzzles, etc.

Most-proved

theorem

According to the

Guinness

, Pythagoras’ theorem has been proved the most often. A book of over a thousand proofs of the theorem includes an 1876 proof by then-Congressman James Garfield (

PlanetMath

has a proof with a square (

http://planetmath.org/ProofOfPythagoreasTheorem

), a proof splitting a

triangle

into two smaller triangles (

http://planetmath.org/ProofOfPythagoreanTheorem

), a proof with two triangles inside a square (

http://planetmath.org/ProofOfPythagoreanTheorem2

) and Garfield’s

proof of Pythagorean theorem

). Many people have authored proofs that there are infinitely many primes, however, most of these use either

factorials

or

primorials

and thus don’t count as distinct proofs.

Largest prize

Paul Wolfskehl’s prize for a proof of Fermat’s last theorem was 100000 Deutsche Marks; at the time it was offered, it would’ve been

equivalent

to about two million American dollars today, but because of inflation in Germany, it was only about sixty thousand dollars when

Andrew Wiles

received it. In 1993, Andrew Beal offered US$100000 for a proof of Beal’s conjecture; this remains the largest prize offered by an

individual

. In 2001, the Clay Mathematics Institute offered US$7000000 for solutions of its seven

Millennium Problems

, or US$1000000 for a solution of one of the problems.

3

People

Longest-lived professional mathematician

Austrian topologist Leopold Vietoris was born on June 4, 1891 and died two months short of his

111

th

birthday on April 9, 2002.

Most prolific collaborator

Paul Erdős collaborated with 509 other mathematicians on papers on a wide

variety

of mathematical topics, giving rise to the idea of the Erdős number (

http://planetmath.org/ErdHosNumber

).

Highest documented Erdős number

Michael Hones has Erdős number 8 (Styer, 2005)

References

1

D. McFarlan, editor.

The Guinness Book of World Records 1991

New York: Guinness Publishing Limited (1990): 75 - 76

2

R. Styer

http://www41.homepage.villanova.edu/robert.styer/ErdosNumber.htm

“Erdös numbers at Villanova http://www41.homepage.villanova.edu/robert.styer/ErdosNumber.htm Last updated July 22, 2005, accessed May 25, 2007

Title

world records in mathematics

Canonical name

WorldRecordsInMathematics

Date of creation

2013-03-22 17:09:26

Last modified on

2013-03-22 17:09:26

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

9

Author

PrimeFan (13766)

Entry type

Feature

Classification

msc 01A07

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