Editing Claude Shannon (section)

===Logic circuits===
In 1932, Shannon entered the [[University of Michigan]], where he was introduced to the work of [[George Boole]]. He graduated in 1936 with two [[bachelor's degree]]s: one in [[electrical engineering]] and the other in mathematics.

In 1936, Shannon began his graduate studies in [[electrical engineering]] at the [[Massachusetts Institute of Technology]] (MIT), where he worked on [[Vannevar Bush]]'s [[differential analyzer]], which was an early [[analog computer]] that was composed of electromechanical parts and could solve [[differential equation]]s.<ref>{{cite web |url=https://ethw.org/Oral-History:Claude_E._Shannon |title=Claude E. Shannon, an oral history |first=Robert|last=Price |work=IEEE Global History Network |year=1982 |publisher=IEEE |access-date=July 14, 2011}}</ref> While studying the complicated ''ad hoc'' circuits of this analyzer, Shannon designed [[switching circuit]]s based on [[Boolean algebra|Boole's concepts]]. In 1937, he wrote his [[master's degree]] thesis, ''[[A Symbolic Analysis of Relay and Switching Circuits]],''<ref name="SymbolicAnalysis">{{ cite journal
|last = Shannon
|first = C. E.
|title = A Symbolic Analysis of Relay and Switching Circuits
|journal = Trans. AIEE
|year = 1938
|volume = 57 |issue=12
|pages = 713–723
|doi= 10.1109/T-AIEE.1938.5057767
|hdl = 1721.1/11173
|s2cid = 51638483
|hdl-access = free
}}</ref> with a paper from this thesis published in 1938.<ref name="SymbolicAnalysis"/> A revolutionary work for [[switching circuit theory]], Shannon diagramed switching circuits that could implement the essential operators of [[Boolean algebra (logic)|Boolean algebra]]. Then he proved that his switching circuits could be used to simplify the arrangement of the [[electromechanical]] [[relay]]s that were used during that time in [[public switched telephone network|telephone call routing switches]]. Next, he expanded this concept, proving that these circuits could solve all problems that Boolean algebra could solve. In the last chapter, he presented diagrams of several circuits, including a digital 4-bit full adder.<ref name="SymbolicAnalysis" /> His work differed significantly from the work of previous engineers such as [[Akira Nakashima]], who still relied on the existent circuit theory of the time and took a grounded approach.<ref name=":03">{{Cite journal |last=Kawanishi |first=Toma |date=2019 |title=Prehistory of Switching Theory in Japan: Akira Nakashima and His Relay-circuit Theory |url=https://www.jstage.jst.go.jp/article/historiascientiarum/29/1/29_136/_article |journal=Historia Scientiarum |series=Second Series |volume=29 |issue=1 |pages=136–162 |doi=10.34336/historiascientiarum.29.1_136}}</ref> Shannon's idea were more abstract and relied on mathematics, thereby breaking new ground with his work, with his approach dominating modern-day electrical engineering.<ref name=":03" />

Using electrical switches to implement logic is the fundamental concept that underlies all [[Computer|electronic digital computers]]. Shannon's work became the foundation of [[digital circuit]] design, as it became widely known in the electrical engineering community during and after [[World War II]]. The theoretical rigor of Shannon's work superseded the ''ad hoc'' methods that had prevailed previously. [[Howard Gardner]] hailed Shannon's thesis "possibly the most important, and also the most famous, master's thesis of the century."<ref>{{cite book |title=The Mind's New Science: A History of the Cognitive Revolution |first=Howard |last=Gardner |author-link=Howard Gardner |publisher=Basic Books |year=1987 |isbn=978-0-465-04635-5 |page=[https://archive.org/details/mindsnewscience00howa/page/144 144] |url=https://archive.org/details/mindsnewscience00howa/page/144 }}</ref> [[Herman Goldstine]] described it as "surely ... one of the most important master's theses ever written ... It helped to change digital circuit design from an art to a science."<ref>{{Cite book |last=Goldstine |first=Herman H. |author-link=Herman Goldstine |url=https://monoskop.org/images/f/fc/Goldstine_Herman_H_The_Computer_from_Pascal_to_von_Neumann.pdf |title=The Computer from Pascal to von Neumann |publisher=Princeton University Press |year=1972 |isbn=978-0-691-08104-5 |location=Princeton, N.J. |pages=119–120 |language=en}}</ref> One of the reviewers of his work commented that "To the best of my knowledge, this is the first application of the methods of symbolic logic to so practical an engineering problem. From the point of view of originality I rate the paper as outstanding."<ref name=":02">{{Cite thesis |last=Guizzo |first=Erico Marui |date=2003 |title=The Essential Message: Claude Shannon and the Making of Information Theory |url=https://core.ac.uk/download/pdf/4404094.pdf |publisher=Massachusetts Institute of Technology |pages=12 |access-date=29 July 2024 |degree=Master of Science}}</ref> Shannon's master's thesis won the [[Alfred Noble Prize#Recipients|1939 Alfred Noble Prize]].

Shannon received his PhD in mathematics from MIT in 1940.<ref name="MIT obituary"/> Vannevar Bush had suggested that Shannon should work on his dissertation at the [[Cold Spring Harbor Laboratory]], in order to develop a mathematical formulation for [[Gregor Mendel|Mendelian]] [[genetics]]. This research resulted in Shannon's PhD thesis, called ''An Algebra for Theoretical Genetics''.<ref>{{cite thesis|hdl=1721.1/11174|title=An Algebra for Theoretical Genetics|year=1940|publisher=Massachusetts Institute of Technology|type=Thesis|last1=Shannon|first1=Claude Elwood}} — Contains a biography on pp. 64–65.</ref> However, the thesis went unpublished after Shannon lost interest, but it did contain important results.<ref name=":11" /> Notably, he was one of the first to apply an algebraic framework to study theoretical population genetics.<ref>{{Cite journal |last1=Chalub |first1=Fabio A. C. C. |last2=Souza |first2=Max O. |date=2017-12-01 |title=On the stochastic evolution of finite populations |url=https://doi.org/10.1007/s00285-017-1135-4 |journal=Journal of Mathematical Biology |language=en |volume=75 |issue=6 |pages=1735–1774 |doi=10.1007/s00285-017-1135-4 |pmid=28493042 |issn=1432-1416|arxiv=1602.00478 }}</ref> In addition, Shannon devised a general expression for the distribution of several linked traits in a population after multiple generations under a random mating system, which was original at the time,<ref>{{Cite journal |last1=Hanus |first1=Pavol |last2=Goebel |first2=Bernhard |last3=Dingel |first3=Janis |last4=Weindl |first4=Johanna |last5=Zech |first5=Juergen |last6=Dawy |first6=Zaher |last7=Hagenauer |first7=Joachim |last8=Mueller |first8=Jakob C. |date=2007-11-27 |title=Information and communication theory in molecular biology |url=http://link.springer.com/10.1007/s00202-007-0062-6 |journal=Electrical Engineering |language=en |volume=90 |issue=2 |pages=161–173 |doi=10.1007/s00202-007-0062-6 |issn=0948-7921}}</ref> with the new theorem unworked out by other [[Population genetics|population geneticists]] of the time.<ref>{{Cite web |last=Pachter |first=Lior |author-link=Lior Pachter |date=2013-11-06 |title=Claude Shannon, population geneticist |url=https://liorpachter.wordpress.com/2013/11/05/claude-shannon-population-geneticist/ |access-date=2024-07-29 |website=Bits of DNA |language=en}}</ref>

In 1940, Shannon became a National Research Fellow at the [[Institute for Advanced Study]] in [[Princeton, New Jersey]]. In Princeton, Shannon had the opportunity to discuss his ideas with influential scientists and [[mathematician]]s such as [[Hermann Weyl]] and [[John von Neumann]], and he also had occasional encounters with [[Albert Einstein]] and [[Kurt Gödel]]. Shannon worked freely across disciplines, and this ability may have contributed to his later development of mathematical information theory.<ref>{{cite thesis|hdl=1721.1/39429|title=The Essential Message: Claude Shannon and the Making of Information Theory|year=2003|publisher=Massachusetts Institute of Technology|type=Thesis|last1=Guizzo|first1=Erico Marui}}</ref>