“Today we face a problem that involves two difficult to satisfy conditions. On the one hand we have to find a way for computer assisted verification of mathematical proofs. This is necessary, first of all, because we have to stop the dissolution of the concept of proof in mathematics. On the other hand, we have to preserve the intimate connection between mathematics and the world of human intuition. This connection is what moves mathematics forward and what we often experience as the beauty of mathematics.”

— Vladimir Voevodsky

UniMath by Vladimir Voevodsky, Heidelberg Laureate Forum, Sept. 22, 2016, Heidelberg https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/2016_09_22_HLF_Heidelberg.pdf p. 3

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Today we face a problem that involves two difficult to satisfy conditions. On the one hand we have to find a way for co…" by Vladimir Voevodsky?

Vladimir Voevodsky 4

Russian mathematician 1966–2017

Related quotes

“P. Bernays has pointed out on several occasions that, since the consistency of a system cannot be proved using means of proof weaker than those of the system itself, it is necessary to go beyond the framework of what is, in Hilbert’s sense, finitary mathematics if one wants to prove the consistency of classical mathematics, or even that of classical number theory. Consequently, since finitary mathematics is defined as the mathematics in which evidence rests on what is intuitive, certain abstract notions are required for the proof of the consistency of number theory…. In the absence of a precise notion of what it means to be evident, either in the intuitive or in the abstract realm, we have no strict proof of Bernays’ assertion; practically speaking, however, there can be no doubt that it is correct…”

Paul Bernays (1888–1977) Swiss mathematician

Kurt Gödel (1958, CW II, p. 241) as cited in: Feferman, Solomon. " Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on finitism, constructivity and Hilbert's program* http://math.stanford.edu/~feferman/papers/bernays.pdf." dialectica 62.2 (2008): 179-203.

“A possible explanation of the physicist's use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person. As a result, when he finds a connection between two quantities which resembles a connection well-known from mathematics, he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection.”

Eugene Paul Wigner The Unreasonable Effectiveness of Mathematics in the Natural Sciences

"The Unreasonable Effectiveness of Mathematics in the Natural Sciences," Communications in Pure and Applied Mathematics, February 1960.

“We can… treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“Economists are all too often preoccupied with petty mathematical problems of interest only to themselves. This obsession with mathematics is an easy way of acquiring the appearance of scientificity without having to answer the far more complex questions posed by the world we live in.”

Thomas Piketty book Capital in the Twenty-First Century

Source: Capital in the Twenty-First Century (2013), p. 32.

“Mathematics is an ancient discipline. For as long as we can reliably reach into the past, we find its development intimately connected with the development of the whole of our civilization. For as long as we have a record of man's curiosity and his quest for understanding, we find mathematics cultivated and cherished, practiced and taught. Throughout the ages it has stood as an ultimate in rational thought and as a monument to man's desire to probe the workings of his own mind.”

Mark Kac (1914–1984) Polish-American mathematician

Postscript, p. 150.
Enigmas Of Chance (1985)

“The calculus is to mathematics no more than what experiment is to physics, and all the truths produced solely by the calculus can be treated as truths of experiment. The sciences must proceed to first causes, above all mathematics where one cannot assume, as in physics, principles that are unknown to us. For there is in mathematics, so to speak, only what we have placed there… If, however, mathematics always has some essential obscurity that one cannot dissipate, it will lie, uniquely, I think, in the direction of the infinite; it is in that direction that mathematics touches on physics, on the innermost nature of bodies about which we know little.”

Bernard Le Bovier de Fontenelle (1657–1757) French writer, satirist and philosopher of enlightenment

Elements de la géométrie de l'infini (1727) as quoted by Amir R. Alexander, Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (2002) citing Michael S. Mahoney, "Infinitesimals and Transcendent Relations: The Mathematics of Motion in the Late Seventeenth Century" in Reappraisals of the Scientific Revolution, ed. David C. Lindberg, Robert S. Westman (1990)

“The immediacy of mystic experience simply means that we know God just as we know other objects. God is not a mathematical entity or a system of concepts mutually related to one another and having no reference to experience.”

Muhammad Iqbál (1877–1938) Urdu poet and leader of the Pakistan Movement

Source: The Reconstruction of Religious Thought in Islam https://www.google.com/books/edition/The_Reconstruction_of_Religious_Thought/uCh14nl09jkC?hl=en (1930), p. 14

“Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.”

David Deutsch book The Fabric of Reality

The Fabric of Reality (1997)

“For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.”

Louis Poinsot (1777–1859) French mathematician and physicist

[Louis Poinsot, translated by Charles Thomas Whitley, Outlines of a new theory of rotatory motion, R. Newby (Cambridge), 1834, 4]

“We had principles in mathematics that were granted to be absolute in mathematics for over 800 years, but new science has gotten rid of those absolutism, gotten — forward other different logics of looking at mathematics, and sort of turned the way we look at it as a science altogether after 800 years.”

Mahmoud Ahmadinejad (1956) 6th President of the Islamic Republic of Iran

Columbia University speech, 24 September 2007
[24 September 2007, http://www.azstarnet.com/sn/hourlyupdate/202820.php, "Iran's president at Columbia University - a transcript", azstarnet.com, 2007-09-25]
2007

Help us to complete the source, original and additional information

Vladimir Voevodsky 4

Related quotes

Related topics