Feller, William

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William Feller

Mathematician Vilim (William) Feller(July 7, 1906 January 14,

1970) is remembered as the author of the most successful probability

tetboo! e"er #ritten$%t has been claimed that the modern era of

probability be&an #ith 'ellersIntroduction to Probability Theory and

Its Applications (190), #ith all subse*uent introductory tets

measured a&ainst it$ +ian-arlo .ota, 'ellers collea&ue at /rinceton

ni"ersity, described the treatise as one of the &reat masterpieces of

mathematics of all time$

'eller #as born in a&reb, -roatia, the son of a successful businessman$ 2ccordin& to .ota, 'ellers

last name #as 3a la"ic ton&uet#ister,5 #hich he chan&ed #hile still a uni"ersity student and his first

name #as ori&inally illibold$ he name chan&e, at the ur&in& of .ichard -ourant, #as necessary

because of his Je#ish bac!&round and the comin& of po#er of the 8ais$ 'eller #as educated at home

by pri"ate tutors until he entered the ni"ersity of a&reb, #here he studied mathematics and recei"ed

his first de&ree in 19:$ ;e earned his doctorate from the ni"ersity of +


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'eller published 104 papers and fre*uently re"ised and impro"ed his definiti"e t#o"olume tetboo!

by includin& ne# procedures$ 2n interestin& story of the boo!s influence concerns /ersi Biaconis, #ho

dropped out of school at a&e 16 to underta!e a career as a ma&ician$ ;e successfully pursued his craft

for ei&ht years until by fate he came across a copy of 'ellers boo!, but found he could not read it$

Biaconis enrolled at 8e# Cor! -ity -olle&e at ni&ht to learn enou&h mathematics to understand the

material and in 1974 he earned a doctorate$ ;e currently is the Mary unsen professor, Bepartment of

tatistics and professor of mathematics at tanford ni"ersity #here he is a #orldreno#ned

probabilist$

2ccordin& to .ota, 3D'ellersE lectures #ere loud and entertainin&$ ;e #rote "ery lar&e on the

blac!board, in a beautiful %talianate hand#ritin& #ith lots of #hirls$ ometimes only the hu&e formula

appeared on the blac!board durin& the entire periodF the rest #as hand #a"in&$ ;is proofs insofar as

one can spea! of proofs #ere often deficient$ 8onetheless, they #ere con"incin&, and the results #ere

unfor&ettably clear after he had eplained them$ he main idea #as ne"er #ron&$ ;e too! umbra&e

#hen someone interrupted his lecturin& by pointin& out some &larin& mista!e$ ;e became red in the

face and raised his "oice, often to full shoutin& ran&e$ %t #as reported that on occasion he had as!ed the

ob@ector to lea"e the classroom$ he epression Gproof by intimidation #as coined after 'ellers

lectures (by Mar! >ac)$5

'eller belie"ed that the traditional emphasis placed on a"era&es meant that too little attention #as paid

to random fluctuations$ Much of his study of probability theory concentrated on Mar!o" processes,

named after the .ussian probabilist 2ndrei 2ndree"ich Mar!o"$ 2 Mar!o" process is a random series

of actions #hose future probabilities are determined by most recent e"ents and are independent of past

e"ents$ 2 Mar!o" chain is a se*uence of random "alues #hose probabilities at a time inter"al depend


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upon the "alue of the number at a pre"ious time$ 2 simple eample of a Mar!o" chain is a random

#al!, #here the #al!er may not return to the location @ust "acated$ 'eller sho#ed ho# these tools could

be applied in areas #here probability theory had not pre"iously been used$ ;e belie"ed that one should

al#ays ha"e a concrete model to thin! about #hen dealin& #ith abstract mathematical structures$

Many concepts in probability are named for 'eller, includin&H 'eller transition functions, the 'eller test

for eplosions, 'eller semi &roups, 'eller Aro#nian motions, the Iindeber&'eller theorem, and the

'eller property$ ;e #as the first eecuti"e editor of the leadin& mathematical abstractin& @ournal

Mathematical Reviews$ %n 1970 he #as a#arded the hi&hest 2merican honor, the 8ational Medal of

cience$ nfortunately, he died shortly before the a#ard ceremony so the medal #as presented to his

#ido# -lara at the hite ;ouse on 'ebruary 16, 1970$

Quotation of the Day:32ll possible definitions of probability fall short of the actual practice$5

illiam 'eller

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Feller, William