Tobler's career had a major impact on the development of quantitative geography, and his research spanned and influenced the study of any discipline investigating geographic phenomena.

His work with analytical cartography included contributions to the mathematical modeling of geographic phenomena, such as human movement in the creation of Tobler's hiking function.

Tobler's work has been described as ahead of its time, and many of his ideas are still unable to be fully implemented due to limitations of technology.

[3][1][4][5] His father's career resulted in moves to Seattle when Waldo Tobler was young, and later to Washington, D.C., when World War II started.

[1] Tobler attended junior high school in Chevy Chase, Maryland, while his father was stationed in Washington, D.C.[1] In May 1945, after the Allied victory in Europe, the family returned to Europe by boat from Boston, Massachusetts to Le Havre France, then by train to Paris, and finally to his parents' native Switzerland.

[1][2] Geographers Pradyumna Prasad Karan and Cotton Mather speculated that this frequent moving in early life may have influenced Tobler's later career choices and passion for geography.

[1][6][2][7] A native speaker of English, Swiss German, and French, the military trained him to speak Russian to serve as an interpreter for the Counterintelligence Corps.

[5][12][13] His master's thesis is titled "An Empirical Evaluation of Some Aspects of Hypsometric Colors", and his dissertation "Map Transformations of Geographic Space".

in geography, Tobler was offered a position as a cartographic assistant at the University of Washington, which enabled him to pursue his master's degree.

In 1972, Tobler translated and published Johann Heinrich Lambert's 1772 "Notes and comments on the Composition of Terrestrial and Celestial Maps.

"[3][6] Tobler served as the third author of a book by Qihe Yang and John P. Snyder titled "Map Projection Transformation: Principles and Applications."

[31] Using his time and experience on the SAGE system, Tobler built upon the concepts and published his work in academic journals.

[34][35] Tobler's research in developing applications for computer cartography is described by Mark Monmonier as "a pivotal place in map history".

[3] Tobler was also concerned with representing flow (due to its involvement with movement as a mechanism of geographic change), and considered them critical to understanding geography.

[3] Combining this interest in movement with his knowledge of cartography, Tobler worked on incorporating flow maps to the problem.

[42] Tobler's approach was more straightforward then other methods of the time, and is more appropriate for samples collected at enumeration units like census tracts.

[42] According to Tobler, a dictionary definition of resolution is "the capability of making distinguishable the individual parts of an object".

[64][65][66][67] The Geographic Information Science and Technology Body of Knowledge "Model Curricula" in particular emphasizes the importance of the first law in the section on "Metrical relationships: distance and direction.

[75][76] In Tobler's 2004 paper, he discussed other potential candidates for laws of geography, including one proposed by Giuseppe Arbia, R. Benedetti, and G. Espa in a 1996 paper that stated "Everything is related to everything else, but things observed at a coarse spatial resolution are more related than things observed at a finer resolution.

[74] The Global Demography Project was conducted by the National Center for Geographic Information and Analysis to map the human population in a series of 5 by 5 minute, or roughly one-kilometer, grids for most of the Earth.

[84] Researchers have suggested this function has applications in various fields, including self-driving cars, route decisions, and wayfinding apps.

[9][86] These ideas serve as the basis for numerous similar computer simulations to model ancient human migration, such as the settlement of Polynesia.

"[89] The Waldo Tobler GIScience Prize is issued to individuals who have "exhibited outstanding and sustained contributions to the discipline worthy of inspiring young scientists in Geoinformatics or Geographic Information Science, and has accomplished significant advances in these fields.

"[89] It has been issued since to David Mark (2016), Thomas Poiker (2017), Helena Mitasova (2018), Michael Batty (2019), Luc Anselin (2022), and Sara Irina Fabrikant (2023).

"[91] It has since been issued to Filip Biljecki (2015), Xingjian Liu (2016), Song Gao (2016), Chen Min (2017), Pablo Cabrera Barona (2017), Auriol Degbelo (2018), Wei Luo (2018), Franz-Benjamin Mocnik (2019), Yingjie Hu (2019), Laura Knoth (2020),Yuhao Kang (2023 ), and Weiming Huang (2022).

[90] The American Association of Geographers Geographic Information Science and Systems Specialty Group (AAG GISS) and the publication Transactions in GIS hosts an annual session at the AAG conference titled "The Waldo Tobler Distinguished Lecture in GIScience.

[27] Mark Monmonier noted that Tobler "is one of a small handful of then-living persons accorded one of the 52 biographical entries in the twentieth-century volume of the History of Cartography.

[24][98] The fund helps "to support open lectures in the fields of demography, mapping and cartography, and geographic information science."

[8] The journal Cartography and Geographic Information Science honored Tobler with both an obituary authored by Keith C. Clarke and a graphic composite on the cover featuring themes of his work.

[6][99] The journal Geographical Analysis dedicated a special issue titled "In honor of Waldo Tobler", edited by Alan T. Murray and Keith C. Clarke, which contained several articles discussing his research, including discussions and overviews of Tobler's contributions to the journal.