希爾伯特可能是最後一個全才式的數學家，雖然他的數學一統的夢想被25歲的後生哥德爾打碎了。但是當時他回到柯尼斯堡的「我們必須知道，我們必將知道」的演講仍然讓人感到欽佩和震憾。英文原文引用並後附中文翻譯。
The instrument that mediates between theory and practice, between thought and observation, is mathematics; it builds the connecting bridge and makes it stronger and stronger. Thus it happens that our entire present-day culture, insofar as it rests on intellectual insight into and harnessing of nature, is founded on mathematics. Already, GALILEO said: Only he can understand nature who has learned the language and signs by which it speaks to us; but this language is mathematics and its signs are mathematical figures. KANT declared, 「I maintain that in each particular natural science there is only as much true science as there is mathematics.」 In fact, we do not master a theory in natural science until we have extracted its mathematical kernel and laid it completely bare. Without mathematics today’s astronomy and physics would be impossible; in their theoretical parts, these sciences unfold directly into mathematics. These, like numerous other applications, give mathematics whatever authority it enjoys with the general public.
Nevertheless, all mathematicians have refused to let applications serve as the standard of value for mathematics. GAUSS spoke of the magical attraction that made number theory the favorite science for the first mathematicians, not to mention its inexhaustible richness, in which it so far surpasses all other parts of mathematics. KRONECKER compared number theorists with the Lotus Eaters, who, once they had sampled that delicacy, could never do without it.
With astonishing sharpness, the great mathematician POINCARÉ once attacked TOLSTOY, who had suggested that pursuing 「science for science’s sake」 is foolish. The achievements of industry, for example, would never have seen the light of day had the practical-minded existed alone and had not these advances been pursued by disinterested fools.
The glory of the human spirit, so said the famous Königsberg mathematician JACOBI, is the single purpose of all science.
We must not believe those, who today with philosophical bearing and a tone of superiority prophesy the downfall of culture and accept the ignorabimus. For us there is no ignorabimus, and in my opinion even none whatever in natural science. In place of the foolish ignorabimus let stand our slogan:
We must know,
We will know.
促成理論與實踐、思想與觀察之間調解的工具，是數學；它建起連接雙方的橋梁並將其塑造得越來越堅固。因此，我們整個當今的文化，對理性的洞察與對自然的利用，都是建立在數學基礎之上的。伽利略曾經說過：一個人只有學會了自然界用於和我們溝通的語言和標記時，才能理解自然；而這種語言就是數學，它的標記就是數學符號。康德有句名言：「我斷言，在任何一門自然科學中，只有數學是完全由純粹真理構成的。」事實上，我們直到能夠把一門自然科學的數學內核剝出並完全地揭示出來，才能夠掌握它。沒有數學，就不可能有今天的天文學與物理學；這些學科的理論部分，幾乎完全融入數學之中。這些使得數學在人們心目中享有崇高的地位，就如同很多應用科學被大家讚譽一樣。
儘管如此，所有數學家都拒絕把具體應用作為數學的價值尺度。高斯在談到數論時講，它之所以成為第一流數學家最喜愛研究的科學，是在於它魔幻般的吸引力，這種吸引力是無窮無盡的，超過數學其它的分支。克羅內克把數論研究者比作吃過忘憂果的人——一旦吃過這種果子，就再也離不開它了。
託爾斯泰曾聲稱追求「為科學而科學」是愚蠢的，而偉大的數學家龐加萊則措辭尖銳地反駁這種觀點。如果只有實用主義的頭腦，而缺了那些不為利益所動的「傻瓜」，就永遠不會有今天工業的成就。著名的柯尼斯堡數學家雅可比曾經說過：「人類精神的榮耀，是所有科學的唯一目的。」
今天有的人帶著一副深思熟慮的表情，以自命不凡的語調預言文化衰落，並且陶醉於不可知論。我們對此並不認同。對我們而言沒有什麼是不可知的，並且在我看來，對於自然科學也根本不是如此。相反，代替那愚蠢的不可知論的，是我們的口號
我們必須知道，
我們必將知道！